# Engineering Economy Lecture b

July 15, 2019 | Author: Irah Mae Escaro Custodio | Category: Consumer Price Index, Bonds (Finance), U.S. Producer Price Index, Index (Economics), Interest

#### Short Description

ENGINEERING ECONOMY...

#### Description

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Preview Problems 

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What will be the equivalent amount at the end of five years of a uniform 5 yearly deposit of P5,000. if the the nominal annual interest interest rate is 12% compounded monthly? Determine the present value of 10 semi-annual semi-annual payments payments of P10,000 , the first of which to be paid 2 years from now now. Money Money is worth worth 12% pa compounded semiannually. A bond issue of P100,000 redeemable at par in 10-years, 10 -years, in P1,000 units paying10% interest per annum payments, must be retired by the use of sinking fund that earns ear ns 8% pa. What is the total annual expense? An economy economy is experiencing inflation at an annual rate of 7%. If the market interest interest rate is also 5% per annum, what what will be the real value of P500 two years years from now ? A company purchased an equipment for P 110,000. It is estimated that it will have a useful life of 10 years. The scrap value of the equipment is P10,000, a. Compute the book value of the equipment equipment at the start of the 6th year using declining-balance method.  b.  b. Compute the book value at the end of the 5th year using Sinking Fund method, i=10% pa c. Compute the book value at the start of the 6th year using SYDM

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_ study of economic theories and their applications to engin gineerin ring problems with the concept of obtaining maximum benefit at the leas leastt cost ost. Time value of money is central to this study.

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After completing this course, cour se, the student must be able to:

1. Solve problems involving interest and the time value of money; 2. Evaluate Evaluate project alternatives by by applying applying engineering economic principles and methods and select the most economically efficient one; and 3. Deal with risk ri sk and uncertainty uncer tainty in project outcomes by applying the basic economic decision making concepts.

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Course Outline             

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1. Introduction 2. Money-Time Relationship 2.1. Time Value of Money 2.2. Types of Interest 2.3. Inflation/Deflation 2.4. Annuity 3. Depreciation 4. Capital Investments 5. Operational Costs 6. Accounting Fundamentals 7. Basic Methods of Profitability Analysis 8. Methods of Financial Analysis 9. Optimization

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       

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Plant Design and Economics for Chemical Engineers, Max S. Peters and Klaus D. Timmerhaus, 4th Ed 2001 Process Engineering Economics, Schweyer Engineering Economy, de Garmo, Sullivan, Canada, 7 th Ed Engineering Economy, Arreola, 2nd Ed Engineering Economy Sta. Maria, 3 rd Ed Engineering Economy, Sullivan, Bentadilli and Wichs, 12th Ed 2003 Contemporary Engineering Economics, Chan S. Park, 3rd Ed 2002 Engineering Economy by L.T. Blank and A.J. Tarquin, 6th ed., McGraw Hill, 2005. Engineering Economy by W.G. Sullivan, E.M. Wicks, and J.T. Luxhoj, 13th ed., Prentice Hall, 2006. Contemporary Engineering Economics  by Chan S. Park, 4th ed., Prentice Hall, 2007. Excel for Engineering Economics  by R.W. Larsen and Chan S. Park, Prentice Hall, 2003. Engineering Economy and the Decision Making Process by J.C. Hartman, Prentice Hall, 2007. Engineering Economic Analysis by D. G. Newman,T. G. Eschenbach, and J. P. Larelle, 9th ed., Oxford University Press, 2004.

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1. INTRODUCTION

Engineering Economy _ study of economic theories and their applications to engineering problems with the concept of obtaining maximum benefit at the least cost. “Economics _ is the study of scarcity. Resources are limited, and every society wants to figure out how to allocate its resources for maximum benefit. “_   Jodie Beggs, PhD (Harvard U)

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Reasons for Studying Engineering Economy: 

Engineering designs and operations must be equated with costs for practical applications Engineers evolve into managers of their own or other enterprises

Uses of Engineering Economy     

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Application on various fields of engineering Determining of limiting factors Tool in selection of alternates Investment of capital Tool in decision making

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Economists study topics such as: 

  

 

 

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How prices and quantities of items are determined in market economies How much value markets create for society How taxes and regulation affect economic value Why some goods and services are under-supplied in a market economy How firms compete and maximize profit How households decide what to consume, how much to save, and how much to work (or, more generally, how people respond to incentives) Why some economies grow faster than others What effect monetary and fiscal policy has on economic well being How interest rates are determined

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It is NOT an economist’s job to tell people what stocks and bonds they should be investing in.

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SELECTION AND EQUIVALENCE IN PRESENT ECONOMY 

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Present economy involves the analysis of problems for manufacturing a product or rendering a service upon the  basis of present or immediate costs. It is highlighted when the effects of time such as interest and depreciation are negligible. Present economy is employed when the alternatives to be compared will provide the same result and the period involved in the study is relatively short. When alternatives for accomplishing a specific task are being compared over one year or least-and influence of time on money can be ignored, engineering economic analyses are referred to as present economy studies.

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SELECTION AND EQUIVALENCE IN PRESENT ECONOMY

Present economy studies occur in the following situations: 

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a. Selection of material_ In many cases, economic selection among materials cannot be  based solely on the costs of materials. Frequently, a change in materials will affect the design and processing costs, and shipping costs may also be altered.  b. Selection of method to be used_ In mechanical or chemical operations a product may be made by two or more methods giving equivalent results. Some goods may be delivered by various methods such as using different capacity trucks, and the results would still be the same regardless of the truck used. These are but a few of the examples that may be cited to show that certain operations are capable of being done  by two or more methods. c. Selection of design_ In the design of a machine to produce a certain product, the engineer responsible for the work will usually make as many designs as possible and from which, by a process of elimination, he will select the design best fitted for the work to be done with particular care being given to the one which will do the work with most economy. d. Selection location or site for a project_ In the choice of a factory site many factors are often considered such as the cost of the land, the cost of construction in the NTAldon different sites, and the difference in transportation cost, and many other factors.

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e. Comparison of proficiency among workers_ In industrial operations where the efficiency of the workers is a factor affecting costs, it is usually observed that workers have varying efficiencies. In some occupations only those with better average proficiencies are acceptable. In teaching for example, other factors being equal, preference should be given to those teachers who did better than average in their studies. f. Economy of tool and equipment maintenance_ In many activities, tools have to be sharpened from time to time, and equipment have to be kept in good operating condition all the time. In certain cases, experience will show the best time to perform certain operations to maintain equipment at the optimum operating efficiency. g. Economy of number of laborers_ In certain industrial operations it is observed that a certain number of workers cooperating on a certain phase of work will lead to the highest efficiency. An increase beyond this number will usually cause the taking into effect of the law of diminishing returns. In certain cases, the excess of laborers will result in some laborers not working at certain times while waiting for the work of other laborers to be finished.

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A machine part to be machined may be made either from an alloy of  aluminum or steel. There is an order for 8000 units. Steel costs P380/kg, while aluminum costs P870/kg. If steel is used, the steel per unit weighs 110 grams; for aluminum, 30 grams. When steel is used, 50 units can be produced per hour; for aluminum, 80 units per hour with the aid of a tool costing P64,000, which will be useless after 8,000 units are finished. The cost of the machine and the operator is P1080 per hour. If all other costs are identical, determine which material will be more economical. Solution: Steel 0.11kg (P380/kg)= P41.80 P1,080/50 = P 21.60

Material Cost Labor and Machine Tool Cost per piece P63.40 Answer: Aluminum is cheaper!  14

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Aluminum 0.030 kg (P870) = P26.10 P1,080/80 = P13.50 P64,000/8,000 = P8.00 P47.60

A company manufactures 1 million units of a product annually. A new design of the product will reduce material cost by 12%, but will increase processing cost by 2%. If materials cost is P 12/unit and processing will cost P4/unit, how much can the company afford to pay for the preparation of the new design and making changes in equipment? Solution: •

Decrease in materials

1,000,000 (0.12) (P12) = P 1,440,000

Increase in processing costs  Net Savings

1,000,000 (0.02) (P4) = P

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80,000

P 1,360,000

Time affects the cost of money. A peso now is worth more than a peso a year from now because it can earn interest during the year. Interest represents two things:

1.The compensation paid for the use of the borrowed capital  2. The risk taken in making the loan.  The

rate at which interest will be paid is usually fixed at the time the capital is borrowed, and a guarantee is made to return the capital at some set of time in the future or on an agreed-upon pay-off schedule.  Riskier loans require more interest to make them attractive. 16

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 

 

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The concept of interest goes back to earliest recorded history. Babylon 2000 B.C. – money paid for use of grain that was borrowed. Typical rates were 6 to 25% per annum. Usury is prohibited in the Law of Moses, and in Islamic cultures. In the middle ages, interest on loans was prohibited based on these restrictions. In 1536, John Calvin adopted a theory of what constituted usury that allowed interest. Islamic conventions developed to allow those with money to buy a stake in a  business in return for an portion of the profit from that business. Interest and the cost of capital have become an essential part of doing  business.

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INTEREST DEFINED 

Interest

__ the time value of money  __ money paid for the use of money  __ compensation paid for the use of borrowed capital.

Elements of Interest 1. Principal, P = the sum of money lent or borrowed 2. Interest, I  = the price paid or charge made for the use of money 3. Time, n = the period of time during which interest is charged, measured in some specific unit. The unit may be day, week, month, 3 months, 6 months, or a year. 4. Rate, i = the price paid for the use of money for a unit of time. It is given as a percentage of the original amount. 

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CASH FLOW

Cash Flow _ is a systematic presentation of cash receipts and disbursements for a given operating period

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Cashflow Diagram: Investment Transaction

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Cashflow Diagram: Loan Transaction

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A. Simple Interest:The interest is proportional to the original amount of the loan  I   Pin Requires compensation payment at a constant interest rate based only on the orig inal amount The principal P must be repaid eventually; therefore the entire amount F , of principal plus simple interest due after n periods is;

P  F  I

In the payment of  simple interest, it makes no difference whether interest is paid at the end of each time unit or after any number of time units. The same total amount of money is paid during a given length of time, no matter which method is used. Under these conditions, there is no incentive to pay the interest until the end of the total loan period.

1. Ordinary Simple Interest

I   Pin 

( P )(i)(d ) 360

  P i m  12

The time unit used to determine the number of interest period is usually one year, and the interest rate is expressed on a yearly basis.When an interest period of less than one year is involved, the ordinary way to determine the simple interest is to assume the year consists of twelve 30-day months, or 360 days.

2. Exact Simple Interest 23

I   Pin 

( P )(i)(d ) 365

; or 

( P )(i)(d ) 366

The exact method accounts for the fact that there are 365 days in a nor mal year and 366 days in a leap year. NTAldon

Example: Determine the ordinary simple interest on P1000 for 8 months and 15 days if the rate of interest is 15%.

I   Pin

Solution: For ordinary simple interest, it is assumed that 1 year = 12 months; n= 8.5 months P  = 1000 i  = 0.15/12

I   Pin

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8.5     I   10000.15    P 106.25  12  

Example: Determine the exact simple interest on P1000 for the period January 1 to October 15, 2012 if the rate of interest is 15% pa. Solution: 2012 is a leap year = 366 days

Jan 1-31 February March April May June July

I   Pin  25

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31 29 31 30 31 30 31 213

Pid  366

August September October

31 30 15

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10000.15289 366

289 days

 P 118.44

3. Discounted Interest, i d  The interest for the money borrowed (discount) is deducted from the principal in advance.

I d    P id  n  P = amount loaned P’ = actual amount

P '  P  I d  id  

i 1 i

Effective Interest Rate, i  26

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I d   P  i

id  1  id

I d   P '

Example: Man borrowed P10,000 from a bank and agreed to pay the loan at the end of 1 year. The bank discounted the loan and gave him P8,000 1. What was the discounted rate? id  

I d   P

10,000  8,000 10,000

 20%

pa

2. What was the effective rate of interest?

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i

I d

i

id

P '

1  id

10,000  8,000

 25%

pa

 0.25  25%

pa

8,000

0.20 1  0.2

Compound Interest: The interest is proportional to the balance at any point in time Stipulates that interest is due regularly at the end of each interest period. If payment is not made, the amount due is added to the principal, and the interest is charged on this converted principal during the following unit time. Thus an initial loan of P at an annual interest rate i would require payment of Pi as interest at the end of the first year. If this payment were not made, the interest for the second year would be ( P + Pi ) i and the total amount due for interest after 2 years would be :

I T 2  Pi  ( P  Pi)i Therefore, the total amount of principal plus interest after 2 years equals

F 2  P  Pi  ( P  Pi)i  P 1  i 

2

Future Worth

F n  P 1  i  n n  I   F n  P  P 1  i   P  P 1  i   1 n

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1. Nominal Interest Rates, r  Interests are compounded other than on annual basis. It always includes a qualifying statement indicating the compounding period. Example, 12% per annum compounded quarterly. 2. Effective Interest Rates , i  Are always compounded on an annual basis. Conversion of  Nominal Interest rate , r  to Effective Interest Rate, i  : m

r     i  1    1   m  where: r  = nominal interest rate per year m = number of interest periods per year 30

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Compounding Periods 2

Compounded Semi-annually (every six months)

r     i  1    1   2  4

Compounded Quarterly (every three months)

r     i  1    1   4  12

Compounded Monthly 31

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r     i  1    1   12 

Continuous Interest The concept of continuous interest is that the cost or income due to interest flows regularly. If we let the change in the accumulated amount, F  over the change in the unit period, n a function of both the accumulated amount F , and rate, r , then;

dF

 rF

dn  F  dF

P

Ln

Conversion of continuous interest rate to effective interest rate

F   F   P

 r  dn 0

 rn

F n   Pe rn   P  1  i e r   32

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i  e r   1

n

1  i 

n

F  F uture WorthF actor  = 1+i P

n

; (F /P,i%,n)

Example: A person deposits P100,000 in the bank.

a. How much would be his money in the bank after 5 years if interest is 6% per annum compounded annually? n

5

F =P  1+i  =100,000  1.06  =P 133,822.56

b. How much would be his money in the bank after 5 years if interest is 6% per annum compounded monthly?

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 0.06  n F =P  1+i  =100,000  1+  12   NTAldon

 5 12

=P 134,885.02

SAMPLE PROBLEMS:

A person wishes to accumulate P100,000 in the bank after 5 years . a. How much is he going to deposit now assuming that his money earns 6% per annum ?  PresentWorth Factor

P   F

1

1  i 

n

; ( P / F , i%, n)

P 

F

1  i 

n

100,000

1  0.06 

5

 P 74,726

CASHFLOW-Annual

1 year

74,726) x (1.06)

= 79,209.56

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2 years

3 years

79,209.56 x 83,962.13 x (1.06) (1.06)

= 83,962.13 = 88,999.86

4 years

88,999.86 x (1.06)

= 94,339.85

5 years

94,339.85 x (1.06)

= 100,000

SAMPLE PROBLEMS:

A person wishes to accumulate P100,000 in the bank after 5 years .  b. How much is he going to deposit now assuming that his money earns 6% per annum ? compounded monthly  P 

F

1  i 

n

100,000  512

1  0.06    12  

 P 74,137.22

Alternative solution (compute first, i )

 

i  1 

P 

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r  

 m

F

1  i 

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m

n

12

 

i  1 

100,000  5

1  0.061677

0.06  12

  1  0.061677  6.1677% 

 P 74,137.50

Example: Find the nominal interest compounded monthly which is equivalent to 12% pa compounded quarterly? Solution: r  

m

12

4

      0.12  i  1    1  1    1  1   1 4   m      12    r   11 .88 %  pa compounded monthly

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r  

INFLATION or DEFLATION:  f  I nflation is the increase in the price of goods and services from one year to the other, thus decreasing the purchasing power of money.

Deflation involves a decrease in the average price of goods and services resulting to the increase in the purchasing power of money. It is usually associated with a prolonged erosion of economic activity and high unemployment. Some measures of price changes in our economy are the Consumer Price Index (CPI) and Producer Price Index (PPI).

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Consumer Price Index (CPI) Consumer price index (CPI) measures changes in the price level of  consumer goods and services purchased by households. The CPI is a statistical estimate constructed using the prices of a sample of  representative items whose prices are collected periodically. Sub-indexes and subsub-indexes are computed for different categories and sub-categories of goods and services, being combined to produce the overall index with weights reflecting their shares in the total of the consumer expenditures covered by the index. It is one of several price indices calculated by most national statistical agencies. The annual percentage change in a CPI is used as a measure of inflation. A CPI can be used to index (i.e., adjust for the effect of inflation) the real value of  wages, salaries, pensions, for regulating prices and for deflating monetary magnitudes to show changes in real values.  Annual Change  Rate   f   38

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Indexn  Indexn1  Indexn1

100%

Producer Price Index (PPI) Producer Price Index (PPI)_ is a family of indexes that measure the average change over time in the prices received by domestic producers of goods and services. PPIs measure price change from the perspective of the seller. The headline PPI (for finished goods) is a measure of the average price level for a fixed basket of capital and consumer goods for prices received  by producers. The producer price index for finished goods is a major indicator of commodity prices in the manufacturing sector. These prices are more sensitive to supply and demand pressures than the more comprehensive consumer price index. Changes in the producer price index are considered a leading indicator for consumer price changes, although only a small portion of the PPI is directly connected to less than half of the CPI. 39

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Example: An economy is experiencing inflation at an annual rate of 5%. If this continues, what will P500 be worth two years from now in terms of today’s pesos? Solution:  F  500   453.51  P  n 2 1   f  1  0.05

Example: An item presently costs P500. If inflation is at the rate of 5% per year, what will be the cost of the item in 2 years?

Solution:

F   P 1   f 

n

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 F 2  P 1  f   500 1  0.05  551.25 2

2

Sixteenth Rule: The cost of the equipment at a new capacity can be computed if the cost of  the same equipment is known at a given capacity. The cost adjustment is the ratio of the two capacities raised to the power 0.6

 S    C  B  C  A   B   S  A 

0.6

Combination of Price Cost Index and Sixteenth Rule: C  B

  I    S     C  A  n   B    I  K   S  A 

0.6

Example: Six years ago, an 80-kw diesel electric generator costs P400,000. The cost index for this class of equipment six years ago was 187 and is now 194. Determine the cost of a 120 kw unit now?  X

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0 .6   I n   S  B   194 120         400 ,000  C  B  C  A      I  S  187 80           K     A    P 529 ,267

i' The real interest rate, i' would be the REAL value of your money’s actual earnings, i after considering the loss in its purchasing power due to inflation, f .

 1  i 1  i'  1   f 

i' 

1 i 1   f

1

Example IF you P100 deposit in the bank earning 8% pa, what would be the real interest rate if inflation is 5% pa. Solution:

  108

After a year your P100 will become

F   100 1.08

But after a year your P108 is only worth

F ' 

due to inflation.Therefore the real earnings is only  Therefore, the real interest rate is i   f  NTAldon 0.08  0.05 i'    0.0286  2.86% 42  f

108

1.05

102.86

( ACTUAL) ( REAL)

 102.86  100  2.86 2.86  x100 %  2.86% 100

DIFFERENTIAL PRICE ESCALATION OR DEESCALATION RATE:

e j

_ is a real price change in good or service caused by various  factors in the market . It is the increment (%) of price change above or below the general inflation rate  f, during a period (normally a year). The increase or decrease in price is in REAL pesos. 1

e  j  '

1

ej

e  j  '

1    f  

1

ej

1    f  

1

For example, if the unit price of the goods is P100 and after a year its price will be escalated or increased by 10% ( e j ) , then its unit price will becomeP110 (   ACTUAL increase in pesos). But during that time if inflation rate (f) is 5%, therefore the inflated cost should have been P110/1.05=104.76, then the differential price escalation or increase in REAL pesos is 104.76-100= P 4.76; e’ j= 4.76%

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'  j NTAldon

e

1  e j

1   f 

1 

1.10 1 05

 1  0.0476  4.76%

'

e j

_ The price escalation or deTotal PRICE ESCALATION : escalation rate is total rate (%) of price change in the unit price, or cost for a fixed amount during the period (normally) a year for  good or service. It is the sum of the general price inflation rate and the differential inflation rate plus their product.The increase or decrease in price is in ACTUAL pesos.

1  e j

 1  e 1   f  '  j

For example, if the unit price of the goods is P100 and after a year its price will be escalated or increased by 10% ( e j’ ) , then its unit price will becomeP110. But if inflation projected for the  year of 5% is considered, then the actual unit selling price of the goods would be:

FC  PC 1  e j   PC 1  e j' 1   f  44

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 1001  0.101  0.05  P 115.50

45

It is a series of equal PAYMENTS, A occurring at equal time intervals. Interest is paid on all accumulated amounts, and the interest is compounded each payment period. The amount of an ANNUITY F, is the sum of all payments A, plus interest if allowed to accumulate at a definite rate of interest from the initial payment up to the end of the annuity term. An annuity term, n is the time from the beginning of the first payment period to the end of the last payment period. It must be noted that the sum F, is expressed at the end of the last payment period NTAldon

A. Ordinary Annuity  The most common type of annuity. It involves the payment of  amount, A at the end of each interest period.

Future Worth of Ordinary Annuity

P 0

1  A

 1  i n  1  F n   A  i  

2 A

3 A

4 A

n A

F n Present Worth of Ordinary Annuity 46

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P  

A

1  i 

n

 1  i n  1   i  

B. Annuity Due The uniform payments,  A are made at the beginning of   each interest period.

 1  i n   1  i    F n   A  i   1

Future Worth of Annuity Due

P  0  A

1

2 A

3 A

4 A

n A

F n Present Worth of Annuity Due

47

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P  

 1  i n   1  i     i   1

A

1  i 

n

C. Deferred Annuity  It is also an ordinary annuity but the payment of the first amount is deferred a cer tain number of periods after the first. For example, the first annuity payment could be made after 3 annuity terms instead of after the first annuity term.

 1  i n  1  F n   A  i  

Future Worth of Deferred Annuity

m 0

P 0

1

2

1  A

2 A

3 A

4 A

n A

3

F n Present Worth of Deferred Annuity 48

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P  

A

1  i 

nm

 1  i n  1   i  

D. Continuous Cash Flow Continuous Compounding

Continuous flow of funds means a series of cash flows occurring at infinitesimally short intervals of time, corresponding to an annuity having an infinite number of short periods.

 1  i   1   F n   A  i   n

i 

A  49

r  m  A m

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A= cash flow in a period  A = sum of cash flows in a year m = number of periods in a year n = total number of periods

Continuous Cash Flow Continuous Compounding…..

F n

    r     1      A    m     r  m  m  

    r     mn  1  1         m      A r       

  m     rn    r   

  1     

m

As m approaches infinity,

 e rn  1    F n   A    r    50

Where  A NTAldon

   r   r  1   m   e     

 e rn  1    P  rn  e   r     A

is the sum of continuous cash flows in one year

Ordinary Annuity

 1  i n  1  F n   A ; i  

P 

A

1  i 

n

 1  i n  1   i  

Discrete Cash Flow -Continuous Compounding

 e rn  1 ;  F n   A r    e 1 

rn   A e  1  P  rn  r   e  e 1 

Continuous Cash Flow- Continuous Compounding

 e  1  F n   A ;   r   rn

51

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A  e

 1  P  rn   e  r   rn

Interest Factors 1. Single-Payment Future-Worth Factor; F = P (F /P, i%, n)

F   P

 1  i    F/P,i%, n n

2. Single-Payment Present-Worth Factor; F = P (F /P, i%, n)

P

F

1

  P/F,i%, n

1  i 

n

3. Future Worth Annuity Factor; F = A (F /A, i%, n)

F

 1  i 

A

i

n

1

  F/A,i%, n

4. Present Worth Annuity Factor; F = A (P/A, i%, n)

 1  i 1    P/A,i%, n  A 1  i i

P

n

n

52

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Example: 1. A loan of one million pesos is to paid in 10 years at an interest rate of 8.5% pa. a. How much should the 10 annual payments be? Solution: P

0

1 A

2 A

3 A

4 A

5 A

6 A

7 A

8 A

9 A

10 A F

  i 0.085  10   A  P 1  i     1,000,0001.085     152,407.71 n 10  1  i   1  1.085   1 n

b. What would the balance be after the 6th payment ?

Balance  P 1  i

n

 1  i n  1  A  i  

 1,000,000 (1.085)

6

 1  0.085 6  1  152,407.71  499,226.13  0.085  

2. If one million pesos is to be accumulated in 10 years at an interest rate of 8.5% pa, how much should the 10 annual payments be?

53

  0.085  1 , 000 , 000      67,407.70 n 10  1  i   1  1.085   1

A  F 

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i

GRADIENT 1. Uniform Arithmetic Gradient It is also an ordinary annuity but disbursement or payment A increases or decreases by a uniform amount G each period. P 0

1

2

A

A+G

3

n

A+2G A +(n-1)G FAn+FGn

Future Worth of Arithmetic Gradient, G : n   G 1  i   1  n  F G   i  i  n

54

F  NTAldon n  F   A

 F G

F  An

F Gn

 1  i n  1  A  i  

GRADIENT 2. Geometric Gradient It is also an ordinary annuity but disbursement or payment A increases or decreases by a uniform rate  g each period

P 0

1

2

A

A(1+g)

3

n

A(1+g)2  A(1+g)n-1

F n Future Worth of Geometric Gradient, G :

F n

F n

 1  i n  1  g  n    A  i  g   

When g=i 55

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F n

 nA1  i 

n 1

SAMPLE PROBLEM 1.What is the accumulated amount of a series of payments when the initial payment of P1000 increases by P200 each period, until the third period if cost of money is 10% pa. Required: Fn Solution: A= P1000 ,G =P200, and i =10% A 1 P1,000

0

CASH FLOW A+G 2 P1,200

A+2G 3 P1,400 F3

 FAn  F Gn  1  i n  1  G  1  i n 1   Fn  A   n   i i   i    1  0.10 3 1  200  1  0.10 3 1   3  P 3,930  Fn  1000    0.10 0.10 0.10      Fn

Another way of solving this is to project individually the  Future Worth of each payment.  F3 56

2

 1000 1.1  1200 1.1  1400  P 3,930 NTAldon

2. What is the accumulated amount of a series of payments when the initial

payment of P1,000 increases by 15% each period, until the third period if cost of money is 10% pa. Required: Fn Solution: A= P1,000 , g =15%, and i =10% A 1 P1000

0

CASH FLOW A(1+g) 2 P 1000(1.15)=1,150

A(1+g)2 3 2 P1000(1.15) = P1,725 F3

 1  i n  1  g  n    F gn  A    i  g    3  3  1  0.10   1  0.15   F  1, 000    P 3, 798  g 3 0.10  0.15    

Another way of  solving it is to  project individual ly the Future Worth of  each  payment.  F   g 3 57

 1000 1.12  11501.1  1725  P 3,798 NTAldon

BONDS  _is a certificate of  indebtedness of a corporation usually for a period not less than ten years and guaranteed by a mortgage on certain assets of the corporation or its subsidiaries. Bonds are issued when there is a need for more capital such as for expansion of the plant or the services rendered by the corporation. The face or par value of a bond is the amount stated on the bond. When the face value has been repaid, the bond is said to have been retired or redeemed. The bond rate is the interest quoted on the bond. 58

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1. Registered Bonds _ The name of the owner of this bond is recorded on the record books of the corporation and interest payments are sent to the owner periodically without any action on his part. 2. Coupon Bonds _ Have a coupon attached to the bond for each interest payment that will come due during the life of the bond. The owner of the bond can collect the interest due by surrendering the coupon to the offices of the corporation or at specified banks.

59

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BONDS… 

 

  

60

Equipment obligation bonds _ refer primarily to bonds whose guarantee is a lien on equipment. Registered bonds _ the owner's name is recorded in the books of the corporation, and the interest is paid periodically to the owner without their asking for it.  Joint bonds _ bonds which are issued by two or more corporations Par value of the bond or face value_ is the amount stated on the  bond. Bond rate _ is the rate of interest quoted on the bond. Redemption or disposal price — usually equal to par value. Mortgage bonds _ bonds whose security is mortgaged on certain specified assets of the corporation. NTAldon

BONDS… 

61

Debenture bonds _ bonds without security behind them except a promise to pay by the issuing corporation Callable bond _entitles the issuer to pay off the principal prior to the stated maturity date. Similarly, the owner of a putable bond _can force the issuer to pay off the principal before the maturity date. Convertible bond _gives the bondholder the right to exchange the  bond for shares of the issuer's common stock at a specified date. Municipal bonds _are issued by state and local governments and other public entities, such as colleges and universities, hospitals, power authorities, resource recovery projects, toll roads, and gas and water utilities. Municipal bonds are often attractive to investors because the interest is exempt from federal income taxes and some local taxes. There are two types of municipal bonds: general obligation bonds and NTAldon

revenue bonds.

62

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The corporation may issue another set of  bonds equal to the amount of bonds due for redemption. The corporation may set up a sinking fund into which periodic deposits of equal amount are made. The accumulated amount in the sinking fund is equal to the amount needed to retire the bonds at the time they are due.

63

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Bond Periodic Expense  A = periodic deposit to the sinking fund I = interest on the bonds per period  A+I = total periodic expense F = accumulated amount, (par value of the bond) needed to retire the bond i = rate of interest in the sinking fund r = bond rate per period 64

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A

  i  A   F   n  1  i   1

Interests on the Bonds per Period, I

I   Fr

A +I

  i  A  I   F    Fr  n  1  i   1 i = rate of interest in the sinking fund r = bond rate per period n = number of periods 65

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The present worth of all future amounts that are expected to be received through ownership of the bond.

 1  i   1  P   Fr  n n  1  i   i1  i   C

n

P = value of the bond n periods before redemption F = amount needed to retire the bond C = redemption price, usually equal to F (also known as Principal, Face Value, Par Value)

r =  bond rate per period n = number of periods before redemption i = investment rate or yield period 66

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Sample Problems-BONDS 1. A bond issue of P200,000, in 10-years, in P1,000 units paying 16% nominal interest in semi-annual payments, must be retired by the use us e of sinking si nking fund that earns ear ns 12% pa compounded semi-annually. semi-annually. What is the total semi-annual expense? Solution: F = P200,000 

r = 16%/2= 8% per semi-annual

i = 12%/2 = 6% per semi-annual 

67

Total semi-annual expense = A + I

  i Total Semi  annual Expense  F    Fr   n  1  i   1   0.06  200, 000    200, 000  0.08 20  1  0.06   1 NTAldon P 21, 21, 437

Sample Problems-Bonds 2. Find the current price of a 10-year bond paying paying 6% per year that is redeemable at par value, if bought by a purchaser to yield 10% per year. year. The face value of the bond bo nd is P100,000 Solution:

 1  i   1 100  1  0.1  1  100,000 000  Fr   100 P 100,000 0000.06    1  i            i 1 i 1 0 . 1 0 . 10 1 0 . 10     P  38,554 554.33  38,867 867.40  75,421 421.73 n

C

n

68

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10

n

10

10

Sample Problems-Bonds 3. Find the price of a 10-year bond , two years before its redemption, paying 6% per year that is redeemable redeemable at par value if bought by a purchaser purc haser to yield 10% per per year. year. The face face value value of the bond bond is is P100,000 Solution: n 2    1  i   1 100,000 1  0.1  1  C   P    F r   Fr    100,0000.06   n n  2 2 1  i   i1  i   1  0.1  0.10 1  0.10    P   82,644 .83  10,413.22  93,058 .05 69

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Sample Problems-Bonds 4. A 10-year bond with a par value of P1,000 and with bond rate of 10% payable annually is sold now for P1080. If the yield is to be 12%, how much should the redemption price be at the end of 8 years? Solution:

 1  i n  1  1  0.128  1  C   P    Fr   1,0000.10   1080  n n 8 8  1  i           i 1 i 1 0.12 0.12 1 0.12     C   1,444.07  C

70

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DISCOUNT FACTORS and EQUIVALENCE

71

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DEPRECIATION 

72

The decrease in the value of equipment, building or other structures due to the passage of time. The causes of depreciation may be physical or functional. Examples of physical depreciation are, wear and tear, corrosion, accident, deterioration due to age or elements.

The rest are functional depreciation and one good example is obsolescence. This is caused by technological advances or developments which make an existing property obsolete. Even though the property has suffered no physical change, its economic serviceability is reduced  because it is inferior to improved types of similar assets that have been made available through advancements in technology Depletion _ Another kind of depreciation is material loss due to consumption or exploitation particularly applicable to natural resources. NTAldon

73

To provide for the recovery of capital which has been invested in physical property To enable the cost of depreciation to be charged to the cost of producing products or services that results from the use of property. For engineers, depreciation is included as cost of production of any product or the rendering of any service where equipment is used to provide for the replacement either at the end of its physical or economic life or at the time when its operation no longer results in satisfactory profit or to provide for the maintenance of capital to replace the decrease in the value of equipment

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Maintenance _conveys the idea of constantly keeping a property in good condition;

Repairs _connotes replacing or mending broken or worn parts of a property.

Service life of the property _is the period during which the use of property is economically feasible. Both physical and functional depreciation are taken into consideration in determining service life. The term is synonymous with economic or useful life. In estimating the probable service life, it is assumed that a reasonable amount of maintenance and repairs will be carried out at the expense of the property owner. Recovery Period _ The number of years over which the basis of the property is recovered through the accounting process. For the classical methods of depreciation, this is normally the useful life. Under the MACRS, this period is the property class for the General Depreciation System (GDS), and it is the class life for the Alternative Depreciation System (ADS) PresentValue _The value of the asset in its condition at the time of valuation Salvage Value_ is the net amount of money obtainable from the sale of the used property over and above any charges involved in removal and sale. 

74

If a property is capable of further service, its salvage value may be higher. This is not necessarily true, however, because other factors, such as location of the property, existing price levels, market supply and demand, and difficulty in dismantling, may have an effect. The term salvage value implies that the asset can give some type of further service and is worth more than merely its scrap or junk value.

NTAldon

75

Scrap or junk value_ is the amount of money obtained when the property cannot  be disposed as a useful unit but rather dismantled and sold as junk to be used again as a manufacturing raw material. Book value _ also known as depreciated value, is the worth of the property as recorded in the books of account of the enterprise and is equal to the orig inal cost less the amounts which have been charged to depreciation. It is sometimes called the unamortized value. Market value _ The price which could be obtained for an asset if it were placed on sale in the open market. Is the amount which a willing buyer will pay to a willing seller for the property when neither one is under compulsion to buy or sell. Fair Value _ The value is usually determined by a disinterested third party in order to establish a price that is fair to both the seller and the buyer Replacement value _ The cost necessary to replace an existing property at any given time with one at least equally capable of rendering the same service. Adjusted Cost basis _ The original cost of the asset, adjusted by allowable increases or decrease , is used to compute depreciation and depletion deductions. For example, the cost of any improvement to a capital asset with a useful life greater than one year increases the original cost basis, an d a casualty or theft loss decreases it. If the basis is altered , the depreciation deduction may need to be adjusted. Basis, or cost basis _ The initial cost of acquiring an asset (purchase price plus tax) , including transportation expenses and other normal costs of making an asset serviceable for its intended use. This amount is also called the unadjusted cost . basis NTAldon

Methods of Depreciation  A. Uniform Depreciation 1.

Straight Line Method This is the simplest and most widely used method compared to any other method. It is  based on uniform annual charge. It doesn’t take into account the interest or profit earned on accumulated depreciation fund. It is a standard accounting method acceptable by the Bureau of Internal Revenue.

d Tn d    BV n 76

 nd 

FC  SV   L

 FC  nd 

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where:

d = periodic depreciation

dTn= total depreciation after nth period FC = First cost SV = Salvage Value BV n= Book value after nth period L = Service Life n = nth period

2. Sinking Fund Method It is based on uniform annual charge. It is assumed that a sinking fund is created to replace the original cost of equipment. All amounts in the sinking fund (including interest) earn interest. The company uses the amount accumulated in its operations, and therefore assumed to earn interest. It is generally used for economy-study purposes.

  i d    FC  SV   L  1 i 1      

 1  i   1  d   i   n

d Tn

77

BV n  FC  d Tn

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1. Declining-Balance-Method

Also known as Matheson formula. The annual depreciation cost is a constant percentage of the salvage value at the beginning of the year. The annual depreciation cost differs every year, and decreases in absolute value as time progresses. The salvage value of the property can never depreciate to zero.   f  = fractional depreciation

d n

78

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n 1

 FC 1   f   f 

BV n

  FC 1  f 

BV n SV

 1   f 

n

n  L

SV  FC 1   f  1/ L

 SV    f   1      FC  

L

2. Double-Declining Balance Method This method is similar to the declining balance method except that the f is replaced by 2/L.

3. Sum-of-the-Years Digit Method The annual depreciation cost differs each year and decreases as time progresses. It provides for a rapid depreciation during the early years of life of property, hence faster recovery of capital

d n

d Tn 79

 FC  SV  L  1  n  L  1 L / 2

 FC  SV 2 L  1  nn  L  1 L

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BV n  FC  d Tn

4. Service-Output Method This method assumes that the total depreciation that has taken place is directly proportional to the quantity of output of the property up to that time. This method has the advantage of making the unit cost of depreciation constant and giving low depreciation expense during periods of low production. FC = first cost of equipment SV = salvage value of equipment after its service life Q   T  = total units of output up to its service life Q   n = number of units of output during the nth year Q   Tn = total number of units of output on the nth year d n = annual depreciation during the nth year d Tn = total depreciation on the nth year

Depreciation unit output  d n

 d  

 FC  SV  QT

Qn

BV n  FC  d Tn 80

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 FC  SV  QT

d Tn

 FC  SV  QT

QTn

5. Working Hours Method This method assumes that the total depreciation that has taken place is directly proportional to the operating time of the equipment. This method has the advantage of making the unit cost of depreciation constant and giving low depreciation expense during low operating or utilization period. FC  = first cost of equipment SV = salvage value of equipment after its service life H T  = total hours of operation up to its service life H n = hours of operation during the nth year = total hours of operation on the nth year H Tn d n = annual depreciation during the nth year d Tn = total depreciation on the nth year

Depreciation Operating  Period  d n

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d Tn

 FC  SV 

 d  

H T

 FC  SV   H T

 FC  SV   H T

H n

H Tn

C. Depletion This method is usually applicable to natural resources such as petroleum deposits, natural gas, mines, timberlands, etc. A depletion fund is provided for the recovery of the capital invested in the said undertaking. The annual charge set aside for the gradual extraction is called depletion cost. 1. Unit Method This method is similar to service output method of depreciation. The depletion charge depends upon the initial cost of the property and the number of  units in the property.

d n

 Fc  SV  QT

Qn

2. Percentage Method This method allows a fixed percentage of the gross income received during the year to be the depletion charge. Considering that the total depletion charge may exceed the initial cost of the property, it is required that for any year the depletion charge should not exceed 50% of the net taxable income for that year obtained by deducting all expenses excluding depletion from the gross income. 82

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SAMPLE PROBLEMS 1. An asset for drilling was purchased and placed in service by a petroleum production

company. Its cost basis is P6M and has an estimated book value of P1.2 M at the end of an estimated useful life of 14 years. Compute the book value at the end of the fifth year of life by the straight-line method d 3

BV 5

FC  SV   L

6  1 .2

 P 0.3429M 14 0.3429 5  P 4.2855

 6

 

2. The original cost of a certain piece of equipment is P500,000 and is depreciated by a 12% sinking fund method. Determine the annual depreciation charge if the book value of the e quipment after 10 years is the same as if it had been depreciated at P40,000 each year by straight line for mula. 

Using straight line Method: Total depreciation  40,000(10)  400,000 SalvageValue  500,000  400,000  100,000

83

Using sinking fund Method:  i  d  FC  SV   1  i   1 NTAldon

  0.12  400,000   22,793.67 10  1  0.12  1

3. In order to make it worthwhile to purchase a piece of equipment, the annual depreciation costs for the equipment cannot exceed P295,000 at any time. The original cost of the equipment is P3M and a salvage value of P50,000. Determine the length of service life necessary if the equipment is depreciated by a. Sum-of-the-years-digit method d 1

 FC  SV  L  1  n   L  1 L / 2

Maximum depreciation occurs on the 1st year: 295,000 

3,000,000  50,000 L  1  1  L  1 L / 2

L  19 years

b. Straight-line method

d  

FC  SV

L  L  10 years

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 295,000 

3,000,000  50,000  L

4. Solve, using the declining-balance- method, the depreciation cost of an equipment on the 8th year, if its book value on the 7th year is P250,000. The Book value of the equipment is computed to be P460,512 on the 5th year. Soln: 

FC 

BV 7

1   f 

7

BV 5

;

250,000

1   f  1   f  5

1

7

460,512

1   f 

 250,000  2 1   f      0.7368  460,512   f   0.2632 d 8  BV 7 f   250,0000.2632)   65,800 85

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5

250,000 460,512

7 5

 1   f 

5. An asset for drilling was purchased and placed in service by a petroleum production company. Its cost basis is P6M and has an estimated book value of P1.2 M at the end of an estimated useful life of 14 years. Compute the depreciation amount in the third year and the book value at the end of the fifth year of life by SYD method Solution: •

d 3

  FC  SV 

 L  1  n    6  1.2 14  1  3  P 0.5486 M   L  1 L  / 2 14  114  / 2

BV  n  FC  d  Tn  FC 

 FC  SV 2 L  1  nn  6  6 1.2 214  1  5 5  3.257  L  1 L 14  114

or  BV 5  FC  d T 5 86

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 6  6 1.2

14  13  12  11 10 105

 P 3.257 M

6. To develop an oil well containing an estimated 4M barrels of oil required an initial investment of P3B. in a certain year, 400,000  barrels were produced from this well. Determine the depletion charge during that year.

d n

 FC  SV  QT

Qn

 3 x10  400,000  P 300 M  d   9

4 x10

87

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6

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8.

An equipment was purchased at a cost of P1,000,000 with an expected service life of 10 years and a salvage value P100,000. Solve for the annual depreciation cost and book value during the 8th year using a. Straight-line method  b. Sinking fund method, i=10% pa c. Declining balance method d. Sum-of-the-years-digit method

Solution: a. Straight line method

d  

FC  SV

 1,000,000  100,000   P 90,000 / year  d  

L  BV n  FC  d T n

10  FC  d (n)

 1,000,000  90,000 8  P 280,000

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An equipment was purchased at a cost of P1,000,000 with an expected service life of 10 years and a salvage value P100,000. Solve for the annual depreciation cost and  book value during the 8 th year using a. Straight-line method  b. Sinking fund method, i=10% pa c. Declining balance method d. Sum-of-the-years-digit method

8.

Solution:  b. Sinking fund method

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  i d    FC  SV    L   1 i 1       0.1  1,000000  100,000    P 56,471 10  1  0.10  1  1  i n  1  BV 8  FC  d T 8  FC  d   i    1  0.108  1  1,000,000  56,471   P 534,204 0.10  

8.

An equipment was purchased at a cost of P1,000,000 with an expected service life of 10 years and a salvage value P100,000. Solve for the annual depreciation cost and  book value during the 8 th year using a. Straight-line method  b. Sinking fund method, i=10% pa c. Declining balance method d. Sum-of-the-years-digit method

Solution: c. Declining balance method

 FC 1   f n1  f ;  BV n  FC 1   f n  SV 1   f n  L 1 1 SV   L   100,000  10    f   1     0.2057  ;  1    FC    1,000,000  d n

dn

 FC 1 

BVn 91

  f  d  1, 000, 000 1  0.2057  0.2057  P 41, 032  FC 1  f  1, 000, 00 1  0.2057  P 158, 444

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f

n 1

81

8

n

8

8.

An equipment was purchased at a cost of P1,000,000 with an expected service life of 10 years and a salvage value P100,000. Solve for the annual depreciation cost and  book value during the 8 th year using a. Straight-line method  b. Sinking fund method, i=10% pa c. Declining balance method d. Sum-of-the-years-digit method

Solution: d. Sum-of-the-years-digit method (SYDM)

 FC  SV  L  1  n 2 d   1,000,000  100,000 10  1  8 2  P 49,091  L  1 L 10  110  FC  SV 2 L  1  n  n  BV   FC  d  d    L  1 L 1,000,000  100,000 2 10   1  88  P 149,090  BV   1,000,000  10  110 d n

 n

8

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8

Tn

Tn

C. Modified Accelerated Cost Recovery System (MACRS) The principal method for computing depreciation deductions for property in engineering projects in the U.S.. Unlike the conventional method of computing depreciation which requires estimates of useful life (L) and salvage value (SV) at the end of useful life, in MARCS, the SV is defined to be zero, and the useful life estimates are not used directly in calculating depreciation amounts. MACRS consists of two systems for computing depreciation deductions; The main system is called General Depreciation System (GDS) , and the second system is called the Alternative Depreciation System (ADS).

When an asset is depreciated under MACRS, the following information is needed before deductions can be calc:     

The cost basis (B) The date the property was placed in service The property class and recovery period The MACRS depreciation method to be used (GDS or ADS) The time convention that applies (half-year) Note: The depreciation period during the first year is only ½ year. The other ½ is extended after the last year of the recovery period: Example: Recovery period = 3 years 1st year = 0.5 year; 2nd year = 1 year; 3rd year = 1 year; 4th year = 0.5 year

d n

93

2  L

for  3,5,7,10

1.5NTAldon  for  15 20

200% using Declining Balance method with switch-over to Straight-Linemethod (whichever is higher)

150% using Declining Balance method with switch-over to Straight-Line-method

3. Depreciation Methods, Time Convention, Recovery Rates 

94

GDS 3,5,7 and 10-year personal property classes: The 200% DB method, which switches to the SL method when that method provides a greater deduction. GDS 15 and 20-year personal property classes: The 150% DB method, which switches to the SL method when that method provides a greater deduction. GDS nonresidential real and residential rental property classes: SL method over the fixed GDS recovery periods. ADS: The SL method for both personal and real property over the fixed ADS recovery periods. Half-year time convention is used in depreciation calculations for tangible personal property. If asset is disposed of before the full recovery period is used, then only half of the normal depreciation deduction can be taken for that year. If the asset is disposed of in year n+1 the final BV of the asset will be zero. NTAldon

Balance Method to Straight-Line?  

Compare the value of recovery rate: Once the value of SL recovery rate is equal or greater than DB, then you have to switchover to SL. For example for 7-year recovery period The recovery rate=2/L (except the first year, 1/L)

DB

SL

1st year 2/2L= 1/L 1/7 2nd year 2/7=1/3.5 > (7-0.5 )= 1/6.5 1.5 3rd year =1/3.5 > 1/(7-1.5) =1/5.5 2.5 4th year =1/3.5 > 1/(7-2.5) = 1/4.5 3.5 5th year =1/3.5 = 1/(7-3.5) = 1/3.5 6th year =1/3.5 < 1/(7-4.5) = 1/2.5 7th year =1/3.5 < 1/(7-5.5) =1/1.5 8th year =1/3.5 1-(sum of 1 to 6)7.0 95

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period use DB use DB use DB use DB 4.5 5.5 6.5

switch-over to SL

For a 5-year recovery period The DB recovery rate=2/L (except the first year, 1/L) The SL recovery rate=1/LREMAINING

DB 1st year 1/5=0.2 2nd year (1-0.2)(2/5)=0.32 3rd year (1-0.52)(2/5)=0.192 4th year (1-0.712)(2/5)=0.1152 5th year 6th year

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SL 0.2 (1-0.2)/4.5=0.1778 (1-0.52)/3.5=0.1371 (1-0.712)/2.5=0.1152 (1-0.8272)/1.5=0.1152 (1-0.9424) =0.0576

Sample MACRS Problem

1. A firm purchased and placed in service a new piece of semiconductor manufacturing equipment. The cost basis for the equipment is P100,000. Using MACRS Method, determine (a) the depreciation charge permissible in the fourth year, (b) the cumulative depreciation through the third year, and (c) the BV at the end of the fourth year, (d) the BV at the end of the fifth year if the equipment is disposed of at that time. 97

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Solution: From Table N-1, the semi-conductor (electronic manufacturing equipment has a class life of six years and a GDS recovery period of five years (Asset Class 36).

11,520 d 4  0.1152 (100,000)  P

(a) The depreciation deduction, or cost-recovery allowance , that is allowable in year four (d 4) is =0.1152  b) Accumulated depreciation through year three,d3, is the sum of depreciation amounts in years one through three:

dT3=d1+d2+d3

d T 3

 100,000(0.20  0.32  0.192)  P 71,200

c) The BV at the end of year four (BV4) is the cost basis less depreciation charges in years from one through four:

BV 4  100,000  100,000 (0.20  0.32  0.192  0.1152 )  P 17,280

e) The depreciation deduction in year five when the equipment is disposed of prior to year six.

d5=(0.5)(0.1152)(100,00)= P5,760 BV5= BV4-d5 = 17,280-5,760 = P11,520 DB 1/5 =0.2000 (1-0.2)(2/5) =0.3200 (1-0.52)(2/5) =0.1920 (1-0.712)(2/5)=0.1152

1st year 2nd year 3rd year 4th year 5th year NTAldon 98 th 6

SL 0.2000 (1-0.2)/4.5=0.1778 (1-0.52)/3.5=0.1371 (1-0.712)/2.5=0.1152 1-0.8272)/1.5=0.1152 1 0 9424 0.0576

CAPITAL  _

refers to wealth in the form of money or property that can be used to produce more wealth.

Two forms of capital, debt and

equity 99

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CAPITAL INVESTMENT FIXED CAPITAL WORKING CAPITAL 

100

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CAPITAL INVESTMENT 

101

FIXED CAPITAL The capital needed to supply the necessary manufacturing and plant facilities WORKING CAPITAL The capital necessary for the operation of the plant

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TOTAL CAPITAL INVESTMENT 

The sum of the fixed-capital investment and the working capital is known as the total capital investment.

Fixed Capital Investment + Working Capital Total Capital Investment 102

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FIXED CAPITAL INVESTMENT  Before

an industrial plant can be put into operation, a large amount of money must be supplied to purchase and install the necessary machinery and equipment. Land and service facilities must be obtained, and the plant must be erected complete with all piping, controls and services. In addition, it is necessary to have money available for the payment of expenses involved in the plant operation.

The fixed-capital portion may be further subdivided into manufacturing fixed-capital investment and non-manufacturing fixed-capital investment.  

103

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FIXED CAPITAL INVESTMENT 

104

Manufacturing fixed-capital investment represents the capital necessary for the installed process equipment with all auxiliaries that are needed for complete process operation. Expenses for piping, instruments, insulation, foundations, and site preparation are typical examples of costs included in the manufacturing fixed-capital investment. NTAldon

FIXED CAPITAL INVESTMENT  

105

Non-manufacturing fixed capital investments

are fixed capital required for construction overhead and for all plant components that are not directly related to the process operation is designated as the non-manufacturing fixed-capital investment. These plant components include the land, processing buildings, administrative and other offices, warehouse, laboratories, transportation, shipping and receiving facilities, utility and wastedisposal facilities, shops, and other permanent part of the plant. The construction overhead cost consists of field-office and supervision expenses, home-office expenses, engineering expenses, miscellaneous construction costs, contractor’s fees, and contingencies. In some cases, construction overhead is proportioned between manufacturing and non-manufacturing fixed-capital investment. NTAldon

FIXED CAPITAL INVESTMENT 1. Direct Costs Process equipment, Instrumentation/controls, piping, electrical, buildings, yard improvements, service utilities, land 2. Indirect Costs Engineering and supervision, construction expenses of temporary facilities

106

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WORKING CAPITAL 

107

The working capital for an industrial plant consists of the total amount of money invested in 1. raw materials and supplies carried in stocks, 2. finished products in stock and semi-finished products in the process of being manufactured, 3. accounts receivable, 4. cash kept on hand for monthly payment of operating expenses, such as salaries, wages, and raw-materials purchases, 5. accounts payable, and 6. taxes payable.

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ACCOUNTING FUNDAMENTALS 

All accounting is based on the fundamental accounting equation, which is ;

Assets = liabilities + owner’s equity

108

Where: assets _are those things of monetary value that the firm possesses, liabilities  _are those things of monetary value that the firm owes, and owner’s equity  _is the worth of what the firm owes to the stockholders (also referred to as equities, net worth, etc.) Basic Engineering Accounting Terms:  Revenue = total income (or total savings)  Net profits = Gross Profits - income tax  Gross profits = Net sales  – Costs of Sales  Income tax = (Gross Profits) ( tax rate)  Cash flow = Net Profits + Depreciation

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GAAP is a codification of how CPA firms and corporations prepare and present their business income and expense, assets and liabilities on their financial statements. GAAP is not a single accounting rule, but rather the aggregate of many rules on how to account for various transactions. The basic principles underlying GAAP accounting are set forth below. 

1. 2.

3. 4. 5.

109

The Basic Principles Principle of regularity : Regularity can be defined as conformity to enforced rules and laws. Principle of consistency: This principle states that when a business has once fixed a method for the accounting treatment of an item, it will enter all similar items that follow in exactly the same way. Principle of sincerity: According to this principle, the accounting unit should reflect in good faith the reality of the company's financial status. Principle of the permanence of methods: This principle aims at allowing the coherence and comparison of the financial information published by the company. Principle of non-compensation: One should show the full details of the financial information and not seek to compensate a debt with an asset, revenue with an expense, etc. NTAldon

Principle of prudence: This principle aims at showing the reality "as is": one should not try to make things look prettier than they are. Typically, revenue should be recorded only when it is certain and a provision should be entered for an expense which is probable. 7. Principle of continuity: When stating financial information, one should assume that the business will not be interrupted. This principle mitigates the principle of prudence: assets do not have to be accounted at their disposable value, but it is accepted that they are at their historical value. 8. Principle of periodicity : Each accounting entry should be allocated to a given period, and split accordingly if it covers several periods. If a client pre-pays a subscription (or lease, etc.), the given revenue should be split to the entire time-span and not counted for entirely on the date of the transaction. 9. Principle of Full Disclosure/Materiality: All information and values pertaining to the financial position of a business must be disclosed in the records. 10. Principle of Utmost Good Faith : All the information regarding to the firm should  be disclosed to the insurer before the insurance policy is taken 6.

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a method of accounting that counts income or expenses at the time they are earned or incurred, irrespective of when money is received or paid when the business performs a service, makes a sale or incurs an expense, the accountant enters the transaction into the books, whether or not cash has been received or paid. it measures the performance and position of a company by recognizing economic events regardless of when cash transactions occur. The general idea is that economic events are recognized by matching revenues to expenses (the matching principle) at the time in which the transaction occurs rather than when payment is made (or received). This method allows the current cash inflows/outflows to be combined with future expected cash inflows/outflows to give a more accurate picture of a company's current financial condition

111

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FINANCIAL STATEMENTS A.

112

Income Statement

The income statement is a computation of the project’s total revenue and total costs for one period of fiscal year, thereby arriving at the concern’s net income or deficit within the period, together with its performance in terms of profitability and cost control. It differs from the “cash budget” in the sense that it follows the “actual concept” in accounting, by which revenues should be associated with the costs involved in realizing the former within the period of occurrence. A model format for income statement preparation is presented. An analysis of each account in the presentation follows:

Profit (loss) = revenues – expenses

Gross Profit = net Sales – cost of Sales NTAldon

NET SALES Net sales_ in pesos are arrived at by subtracting sales returns, allowances, and discounts from gross sales. 

113

Sales returns_ represent goods sold which could not meet customer requirements and thus have been returned. Allowance_ refer to goods which cannot be sold due to spoilage, wrong specification, and similar cause; Sales discount_ are price reduction occasionally given in favor of customer. The latter items are to be considered as different from sales discount favoring the project, which are entered in the ”other income” account of the statement.

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COST OF SALES Cost of sales_ is a function of  raw materials used,  direct labor expenses, and  factory overhead accounts.

The factory overhead accounts are itemized as follows:  materials and labor expenses indirectly related with production;  heat, light, and power required for manufacturing;  maintenance costs associated with productive fixed assets supplies needed to produce fixed assets;  taxes associated with the manufacturing fixed assets;  and insurance expenses related to the productive operation. 114

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Operational costs A. Variable Costs

Raw materials, direct labor, utilities, direct supervision, laboratory charges, royalty, packaging, spoilage, losses A. Fixed costs Depreciation, taxes, insurance, interest, overhead, management expenses (GAE)

115

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Pro- f orma Inco Incom me Statements Y ears ear s ending: 31 Decem ec ember

P roduction (in Units) Units)

1s t y ear

2nd y ear

308,000

300,000

A dd: Invento ry, beginning Units Units av ailable ailable fo r sale Less: Invento Invento ry investm ents Sales, gros s Sales, gros s (in P) Less: sales returns and allowances sales disco disco unts Sales, net

(8,000)

308,000

308,000

(8,000)

(8,000)

3r d y ear   300,000 (8,000) 308,000 (8,000)

300,000

300,000

300,000

750,000

789,000

828,000

(60,000)

(63,120)

(66,240)

(15,000)   675,000

(15,780)   710,100

(16,560) 745,200

Cos t of sales: sales: Raw materials: P urchases urchases

57,500 420

A dd: freight in

57,920

Co st of raw materials materials availabl available e fo r use

57,920

Less : Invento ry, ending

To tal purchases purchases  A dd:invento dd:invento ry beginning  beginning

Co st o f raw materia materials ls  A dd:

Direc t labor

(5,000)

56,160

58,890

441

463

56,601

59,353

5,000

6,000

61,601

65,353

(6,000)

(7,000)

52,920

55,601

58,353

17,280

18,144

19,051 124,632

113,009

118,659

Indirect Indirect labo r

13,200

13,860

14,553

Heat, light and po wer  wer

50,640

25,162

26,764

M aintenan aintenance ce

7,126

7,126

7,126

Supplies

10,499

11,010

11,471

Depreciation Depreciation

43,010

43,010

43,010

Taxes

2,600

2,600

2,600

Insurance, etc.

4,751

3,819

2,887

298,991

310,447

M anufacturin anufacturing g co sts

315,035

A dd: Go o ds-in pro ces s invent o ry, begnng Less:Goo ds- inpro inpro cess invento ry, ending Co sts o f goo ds availab available le fo r sale sale

(9,000)

306,035

Less: finished-goo ds invento ry, ry, ending ending

116

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Cos ts of sales

9,000 (10,000)

297,991

10,000 (11,000) 309,447

20,000

21,000

306,035

317,991

330,447

(20,000)   286,035

(21,000)   296,991

(22,000) 308,447

A dd: finis hed-go o ds invent o ry, beginning Co sts o f goo ds availab available le fo r sale sale

388,965 1 s t ye a r

Gross Gross profit profit Operating expenses:

413,109 2 n d ye a r

436,753 3 rd ye a r

General and and administrativ e salaries: General and and administrativ e sa Fringe benefits Research and develo pment Engineering Engineering co sts Depreciation Depreciation

36,480   6,511 180 36,387   3,600

38,304 6,794 189

40,220 7,051 198

3,600

3,600

6,012 120 806

6,550 126 846

Taxes Insurance Office supplies Heat, light and po wer Telephone Telephone

5,520 114 768

Water supply

700   90,260

700 56,525

700 59,291

7,439   16,620

7,794 17,451

8,168 18,324

43,188   13,500   80,747

45,435 14,202 84,882

47,681 14,904 89,077

Operating expenses

171,007

141,407

148,368

Operating prof it

217,958

271,702

288,385

28,506

27,714

24,546

Total

28,506

27,714

24,546

Profit before before income tax

189,452

243,988

263,839

Provision fo r income income tax

(56,308)

(75,396)

Net income (net (net lost )

133,144

168,592

181,495

105,660

M iscellaneous: iscellaneous: Am ortization Total Selling expenses: Salaries Storage Storage of go ods Billing Transportation Public relations  Adv ertisment , sales taxes M iscellaneous: iscellaneous: bad debts Total

Financial Financial expenses expenses (net of ot her income): Interest Bo rrowing rrowing costs

117 11 7

NTAldonLess: Cash div idends, declared

(98,038)   35,106

35,106

(98,038)   105,660

(82,344)

(98,038) 189,117

CASH FLOW 

118

The cash-flow statement or the” cash budget” is a systematic presentation of cash receipts and disbursements for a given operating period or fiscal year, year, taking for granted the” accrual concept “ in account illustrates a cash budget model , showing the inflow and presenting a large-scale schedule sc hedule for the determination deter mination of ending cash balance sheet. The budget is used to estimate future loans or financing needs, optimize the timing of project financing, and maximize profitability by efficient cash utilization. a. Cash receipts are subdivided into those which flow from financing the project and those coming from sales revenues. Cash flow from financing may take the form of stocks stoc ks issued including stock premium or discount being closed, the net of the latter two accounts being closed to the “paid -in surplus” account; bond issues: and long-terms loans. In computing for cash in- flows from sales revenues; the “profit –  before before-income tax” account is entered in the budget, and this is increased to the period such suc h as depreciation and amortization. Other account which increase the entries entr ies are increases in account payable, payable, accrued expenses, and deferred income.  b.  b. Under cash disbursement, out-of-pocket expenses on intangible assets acquisition are entered. Other account included here are decreases in account payable, payable, notes payable, payable, bankdrafts payable, accrued accrued expenses, mortgage bonds payable and long-terms long- terms notes receivable, inventories, and investment. Cash dividends issued and income tax payments also comprise cash disbursements. The beginning cash balance for the period is then added to the net cash flow to arr ive at ending cash balance in the balance sheet. It should be noted that all accounts entered in the cash budget should tally with the same account in the income statement and balance sheet. NTAldon

Pro-fo Pro-formal rmal cas h-flow h-flow s tatements Years ending 31 December (in pesos ) CASH RECEIP TS:

1 s t ye a r

Com mon s t oc ks i s s u e d

4 0 0 ,0 0 0

P re ffe re d s t oc ks i s s u e d

9 0,19 2

2 n d ye a r

3 r d ye a r

Paid-in surplus Mort ga ge b onds p a ya b l e -i nc re a s e s

1 1,15 1

L on g-t e rm not e s p a ya bl e -i n c re a s e s

2 0 0 ,0 0 0

Tot a l re c e i p ts from fi n a nc i ng

7 0 1 ,3 4 3

P rofi t be fore i nc ome t a x

1 8 9 ,4 5 2

243,988

263,839

4 6,61 0

46,610

46,610

700

700 70 0

De pre c i a t i on of fi xe d a s s e s t Amortizati Amortizati on of pre-pai d expens expens es Amortizati Amortizati on of deferred cha rges Amort i za t i on of i nt a ngi b l e a s s e t s

7 00

Other non-out-of-pocket non-out-of-pocket expense s Ac c oun ts p a ya b l e

6,39 4

Not e s p a ya bl e -i n c re a s e s

2 0,00 0

Bank drafts payable-increase s Accrued Accrued expense expense s-increas es Deferred income-increase income-increase s Total inflow from production, ope ra ti ons a nd fi na n c i a l a c c oun t s TOTAL ASSUMED CASH RECEIP TS

119

NTAldon

2 6 3 ,1 5 6

291,298

311,149

9 6 4 ,4 9 9

291,298

311,149

TOTAL ASSUMED CASH RECEIPTS

964,499

CASH DISBURSEMENTS:

1st year

291,298

2nd year

311,149 3rd year

Expense s on intangibl e as sets (Out of Pocket) Good will Patents

500

500

Franchises

500

Or ga ni za ti on a nd p re -o pe ra ti ng e xp en se

2 ,0 00

Acquisitions of fixed ass ets (out-of-pocket): Land

200,000

Buildings

60,000

Equipment

77,545

Machinery

100,000

Accounts payable-decreases Notes payable-decrease s Bank drafts payable-decreases Accrued expenses-decreases Treasury stocks-increases Mortgage bonds payable-decreases

1,394

1,394

Long-term notes payable-decreases Cash dividends issued

25,000

25,000

98,038

98,038

Marketable securities-increases

85,507

78,196

89,297

Accounts receivable-increases

317,520

16,511

16,511

Notes receivable-increases Inventories-increases: Raw materials

5,000

1,000

1,000

Supplies

2,000

1,000

1,000

Goods in process

9,000

1,000

1,000

Finished goods

20,000

1,000

1,000

56,308

75,396

Income tax payments Investment-increases (pre-paid and deferred charges)

2,000

2,000

2,000

TOTAL CASH DISBURSEMENTS

882,072

281,447

311,636

NET CASH FLOW (Ne t ca sh de fi ci t) = re ce ipts - di sburs eme nts

82,427

9,851

82,427

92,278

92,278

91,791

120

NTAldon

balance, beginning

82,427

(487)

BALANCE SHEET The balance sheet shows the assets derived by the project from corresponding liabilities and equities (net worth).It is an overall picture of a film’s financial condition as of a certain time. Furthermore, it shows the major changes brought about by the project’s operation within the fiscal period. The assets are entered under the debit portion of the balance sheet while the liability and equity claims on these assets are found under the credit portion. Exhibit F-3 present a model balance sheet. 

121

Comprising the asset portion of the statement are current asset , fixed asset, and intangible assets. Current assets  _ to those type with are either cash account or other account expected to be converted into cash with one year. The item listed in this division are of course cash, marketable securities, receivables, inventories, prepaid expense, and deferred change. The latter two accounts signify cash expenditures for the services of a creditor not yet received in full by the project in question, such as prepaid insurance.

Fixed assets  _ are the tangible assets of an enterprise of an enterprise, the service life of which usually extends to over one year. Land, building, machinery, and equipment are typical example of fixed assets. The balance sheets or book value of these assets are derived by subtracting their accumulated depreciation from their cost of acquisition, depreciation being the portion of cost allocated to one fiscal period. Intangible assets _ service life, like fixed will, patents, copyrights, leases, licenses, franchises, and organization and pre-operation expenses fall under other assets. When an intangible asset is amortized, the accumulated amortization account is not entered in the balance sheet, which contains only the net  book value of assets in this category. Assets = liabilities + (beginning owner’s equity + revenue – expenses) NTAldon

122

Intangible assets _ have not physical substance. Examples are, goodwill, leaseholds, copyrights, patents, franchises, licenses, and trademarks. Accounting for an intangible asset is rendered somewhat difficult  because the lack of physical substance makes evidence of its existence more elusive, may make its value debatable and its useful life may be questionable.

NTAldon

LIABILITIES  _ are debts or claims anyone other than the owners

of the property upon the assets of the company. 

Other liabilities: Mortgage bonds payable ,Long-term notes payable NTAldon 

123

Current liabilities: Accounts payable ,Notes payable, Bank-drafts payable , Estimated tax liability, Accrued expenses (Dividends payable):

OWNER’S EQUITY  COMMON STOCK  _ represents the ownership of stockholders who have residual claim on the assets of the corporation after all other claims have been settled. No return is guaranteed on the investment of common stockholders. They have the right to call meetings, to vote, to elect members of the board of directors, amend charter and constitution and by-laws, inspect books of the corporation, receive dividends, share remaining assets if corporation is dissolved. PREFERRED STOCK_   _ also represent ownership. And it possesses the same rights as common stock, but in addition, it enjoys certain preferences, not possessed by common stock. It has priority over common stock in receipt of dividends, and it is usually guaranteed a fixed annual dividend, regardless of the amount of the earnings of the corporation. In case the corporation is dissolved, the owner of the preferred stock, has priority over the common stockholders. They NTAldon may have right to vote in meetings. 

124

(in pesos )

ASSETS:

1st year

2nd year

3rd year

Current assets Cash

82,427

92,278

91,791

M arketable securities

85,507

163,703

253,000

A cco unt receivable, net

317,520

334,031

350,542

Raw materials

5,000

6,000

7,000

Supplies

2,000

3,000

4,000

Go ods-in-pro cess

9,000

10,000

11,000

Finished goo ds

20,000

21,000

22,000

P re- paid expenses

1,000

2,000

3,000

Deferred charges

1,000

2,000

3,000

523,454

634,012

745,333

Land

200,000

200,000

200,000

B uilding

60,000

60,000

60,000

Equipment

77,545

77,545

77,545

M achinery

100,000

100,000

100,000

To tal fixed assets,

437,545

437,545

437,545

Les s:ac cum ulat ed deprec iat io

(93,220)

(139,830)

To tal fixed assets net

344,325

297,715

Notes receivable Inventories

To ta current assets

Fixed assets :

125

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(46,610) 390 935

1st year

2nd year

3rd year

Other assets: Investments Intangible ass ets, net of amortization: Goodwill Patents Copyrights Lease Licenses Franchises Orga ni za ti on a nd pre -ope ra ti ng expe ns es Total other assets

400

300

200

400 400 1,600 2,800

300 300 1,200 2,100

200 200 800 1,400

917,189

980,437

1,044,448

6,394 20,000

6,394 20,000

6,394 20,000

56,308

75,396

82,344

98,038

98,038

98,038

180,740

199,828

206,776

Mortgage bonds payable

11,151

9,757

8,363

Long-term notes payable

200,000

175,000

150,000

211,151

184,757

158,363

391,891

384,585

365,139

Common stocks

400,000

400,000

400,000

Preferred stocks

90,192

90,192

90,192

TOTAL ASSETS (current, fixed, other) LIABILITIES AND EQUITY: Current liabilities Accounts payable Notes payable Bank-drafts pa yable Estimated tax liability Accrued expenses : Dividends payable Deferred income Total current liabilities Other liabilities:

Total other liabilities

TOTAL LIABILITIES

OWNER'S EQUITY:

Less :

treasury stocks

Paid-in surplus Retained earnings

126

NTAldon

35,106

105,660

189,117

TOTAL EQUITIES

525,298

595,852

679,309

TOTAL LIABILITIES AND EQUITY

917,189

980,437

1,044,448

WHOLE-LIFE COSTS Total Cost of Ownership(TCO) 

Refers to the total cost of ownership over the life of an asset. Also commonly referred to as “cradle to grave” or “womb to tomb” costs.

Areas of expenditure:        

 127

Planning Design Construction/acquisition Operations Maintenance Rehabilitation Financial Replacement/disposal These costs are converted into present value together with benefits in order to compute the benefit-cost ratio. NTAldon

128

EBITDA_ an initialism for earnings before interest, taxes, depreciation, and amortization. It is a non-GAAP (generally accepted accounting principles) metric that is measured exactly as stated. All interest, tax, depreciation and amortization entries in the income statement are reversed out from the bottom-line net income. It purports to measure cash earnings without accrual accounting, canceling tax-jurisdiction effects, and canceling the effects of different capital structures. EBITDA differs from the operating cash flow in a cash flow statement primarily by excluding payments for taxes or interest as well as changes in working capital. EBITDA also differs from free cash flow because it excludes cash requirements for replacing capital assets (capex). EBITDA margin refers to EBITDA divided by total revenue. EBITDA margin measures the extent to which cash operating expenses use up revenue. Use by debtholders_ EBITDA is widely used in loan covenants. The theory is that it measures the cash earnings that can be used to pay interest and repay the principal. Since interest is paid before income tax is calculated, the debtholder can ignore taxes. They are not interested in whether the business can replace its assets when they wear out, therefore can ignore capital amortization and depreciation. NTAldon

1. Return on Investment , ROI 

Profit or savings (before income tax) divided by investment required.

ROI  

ROI  

129

NTAldon

Profit  x 100%  Investment

Incremental  Profit  x 100%  Incremental  Investment

Minimum Acceptable Rate o Return 

Also known as Minimum Attractive Rate of Return or known as hurdle rate, the interest rate used in the valuation of profitability of a project in Present Worth, Future Worth and Annual Worth Methods . It is usually a policy issue by the top management of an organization in view of the following considerations: The amount of money available for investment,  Number of good projects available for investment,  The amount of perceived risk associated with investment opportunities available and  Type of organization involved. 

130

In business and engineering, the minimum acceptable rate of return , often abbreviated MARR, or hurdle rate is the minimum rate of return on a project a manager or company is willing to accept before starting a project, given its risk and the opportunity cost of forgoing other projects. NTAldon

Minimum Acceptable Rate of Return; Hurdle Rate 

The hurdle rate is usually determined by evaluating existing opportunities in operations expansion, rate of return for investments, and other factors deemed relevant by management. A risk premium can also be attached to the hurdle rate if management feels that specific opportunities inherently contain more risk than others that could  be pursued with the same resources. A common method for evaluating a hurdle rate is to apply the discounted cash flow method to the project, which is used in net present value models. The hurdle rate determines how rapidly the value of the dollar decreases out in time, which, parenthetically, is a significant factor in determining the payback period for the capital project when discounting forecast savings and spending  back to present-day terms. Most companies use a 12% hurdle rate, which is based on the fact that the S&P 500 typically yields returns somewhere between 8% and 11% (annualized). Companies operating in industries with more volatile markets might use a slightly higher rate in order to offset risk and attract investors. The hurdle rate is frequently used as synonym of cutoff rate, benchmark and cost ofNTAldon capital.

131

SAMPLE PROBLEMS; ROI Given: Investment

Total Investment Net profit

1

P 100,000

P 23,000

2

P 150,000

P 28,000

3

P 180,000

P 37,000

Required: Select the best alternative if minimum acceptable return on investment required is 10% Solution: ROI  based on initial total investment:

132

ROI1

ROI 2

ROI3

NTAldon

 23,000 100,000 28,000 150,000 37,000

100  23%  10%, ok

100  18.67%  10%, ok

180,000

100  19.05%

 10%, ok

All three investments passed the MARR therefore evaluate the investments using ROI  based on incremental investment:

Comparing 1 and 2 Additional investment of P50,000 will yield additional net profit of P5,000)  ROI12

150, 000  100,000

100  10%, ok

investment 2 is better than 1

Comparing 2 and 3; Additional investment of P30,000 will yield additional net profit of P9,000)

ROI 23

133

 28, 000  23, 000

NTAldon

 37, 000  28, 000 

180, 000  150, 000 

100  30%  10%, ok

Therefore, select # 3

The annual cost of the alternatives including the minimum return on investment is determined. The alternative with the least annual cost is chosen. This method, like the rate of return on investment method, applies only to alternatives which have a uniform cost data for each year and a single investment of capital at the beginning of the project life. Typical cost factors a. Depreciation Costs(usually as sinking fund)  b. Annual Operating Costs

c. Annual Labor Costs d. Insurance and Taxes e. Other Costs f. Return on Investment or Cost of Money 134

NTAldon

Total Annual Costs

S ample P roblem  A company is considering two types of equipment for its new plant. The following data are given. If the minimum return on investment is 15%, which equipment should be selected using  A nnual C os t Method.

Given: Equipment A P 2.0 M P 350,000 P 500,000 3.5% of First Cost 8% of first Cost P200,000 10 years

First Cost Annual Operating Cost/yr Annual Labor Cost/yr Insurance and Taxes/yr Other Cost/yr Salvage Value Estimated life

Equipment B P 3.0 M P 250,000 P 350,000 3.5% of First Cost 8% of First Cost P300,000 10 years

Solution: Annual Cost Method Annual Costs a. Depreciation Cost (Sinking fund)  b. Annual Operating Cost c. Annual Labor Cost d. Insurance and Taxes,3.5% FC e. Other Cost, 8% FC f. Return on Investment,15% FC Total Annual Costs  FC 1  i 

Equipment A, Pesos 88,654 35,0000 50,0000 70,000 160,000 300,000 1,468,654

 SV  1  i   1

Equipment B, Pesos 132,981 250,000 350,000 105,000 240,000 450,000 1,527,981

L

a   f   capital  re cov ery

135

NTAldon

 CR 

L

i

S ince total annual cos t of equipment A is les s than equipment B , therefore chose A

3. Discounted Cash Flow, Internal Rate of Return (IRR) 

The method of approach for discounted cash flow takes into account the time value of money and is based on the amount of the investment that is unreturned at the end of each year during the estimated life of the equipment. A trial-and-error method is used to establish a rate of return which can be applied to yearly cash flow so that the original investment is reduced to zero (or to salvage and land value plus working capital investment) during the project life. Thus, the rate of return by this method is equivalent to the maximum interest rate (normally after taxes) at which money could be borrowed to finance the project over its life that would just  be sufficient to pay all principal and interest accumulated on the outstanding principal. The discount rate reflects two things: 1. The time value of money - investors would rather have cash immediately than having to wait and must therefore be compensated by paying for the delay. 2. A risk premium - reflects the extra return investors demand because they want to be compensated for the risk that the cash flow might not materialize after all.NTAldon

136

3. Discounted Cash Flow, Internal Rate of Return (IRR) 

Internal Rate of Return is the most widely used rate of return method for performing engineering economic analyses. It is sometimes called by several names, such as the investor’s method , the discounted cash flow method, and the profitability index. Also means that the value of this measure depends only on the cash flows  from an investment and not on any assumptions about reinvestment rates.

The internal rate of return (IRR) is a rate of return used in capital budgeting to measure and compare the profitability of investments. It is also called the discounted cash flow rate of return (DCFROR) or simply the rate of return (ROR). In the context of savings and loans the IRR is also called the effective interest rate. The term internal refers to the fact that its calculation does not incorporate environmental factors (e.g. the interest rate). The internal rate of return is the rate of return promised by an investment project over its useful life. It is some time referred to simply as yield on project. The internal rate of return is computed by finding the discount rate that equates the present value of a project's cash out flow with the present value of its cash inflow In other words, the internal rate of return is that discount rate that will cause the net present value of a project to be equal to zero.

Total Capital  Investment  137

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CF 1

1  i 

1

CF 2

1  i 

2

 ... 

CF n

1  i 

n

Sample Problem: Discounted Cash Flow Compute for the IRR given by the sequence of cash flows i=29%

1 2

A

B

year, n Cash Flow, Cn

3

0

-100

4

1

40

5

2

59

6

3

55

7

4

20

8

IRR

29%

138 9

solving by trial and error

NTAldon

Solving using Excel program =IRR(B3:B7)

SAMPLE PROBLEM : Discounted Cash-flow IRR Given:

Initial Fixed-Capital Investment = P100,000 Working capital Investment = P10,000 Service life = 5 years Salvage value @ the end of service life = P10,000

Required: Internal Rate of Return (IRR) Solution: By Trial-and-Error: i = 0.207 (20.72%)

110,000 

30,000

1  i 1

Solving using Excel program

139

YEAR

Cash-flow, P

0

-110,000

1

30,000

2 3

31,000 36,000

4 5 IRRNTAldon

40,000 63,000 20 72%

31,000

1  i 2

36,000

1  i 3

40,000

1  i 4

43,000

1  i 5

YEAR

Cash-flow, P

1

30,000

2

31,000

3

36,000

4

40,000

5

43,000

10,000  10,000

1  i 5

This method determines the number of years within which the invested capital can be recovered out of the expected cash flow. It does not consider the possible earnings of the reinvested capital during the pay-put period.  A.Without Interest

N  

N  

B.With Interest

N  

Depreciabl e Fixed Capital  Investment   AverageCashFlow / yr   Fixed Capital  Investment  SalvageValue

AverageNet Pr ofit  /  yr   AverageDepreciation /  yr

Depreciabl e Fixed Capital  Investment  Interest On Total  Investment

N  

Average CashFlow /  yr

DFCI   TCI  1  i

n

1

 AverageNet Pr ofit / yr   AverageDepreciation / yr 

as annuity

Note: 140

Depreciable Fixed Capital Investment= Fixed Capital Investment- Salvage Value TCI=Total capital Investment=Fixed Capital Investment +Working Capital

NTAldon

SAMPLE PROBLEM:

PAY-OUT PERIOD

Given: Total fixed capital P 100,000

Working capital P 11,000

Salvage Value

Service Life,  Net Profit years

P 10,000

6

Required: Pay-out Period, N, without interest  Solution:

Depreciable Fixed Capital Investment   N=   Net Profit+ Depreciation ave  year   Annual  Dep 

N  

141

NTAldon

100,000  10,000 6

100,000  10,000  2  .5 years 21,000 15,000

 15,000

P21,000

SAMPLE PROBLEM: •

PAY-OUT PERIOD

Given: Total fixed capital P 100,000

Working capital P 11,000

Salvage Value

Service Life,  Net Profit years

P 10,000

6

P21,000

Required: Pay-out Period, N, with interest ; i = 10% pa Solution:

N  

Depreciabl e Fixed Capital  Investment  Interest On Total  Investment   Average CashFlow / yr

   L  1  i   1  0.10   100,000  10,000   11,664.66 6    1.10  1 d    FC  SV 

i

100,000  10,000   100,000  11,000  1.10  1  5.4 years  N  6

21, 000  11, 664.66

142

NTAldon

SAMPLE PROBLEM: •

PAY-OUT PERIOD

Given: Total Fixed Capital

Working capital

Salvage Value

Service life, years

Annual Cash flow

P 100,000

P 11,000

P10,000

6

P 36,000

Required: Pay-out Period, N, with interest ; i = 10% pa Solution:  N  

Depreciabl e Fixed Capital  Investment  Interest On Total  Investment

N  

143

NTAldon

Average CashFlow /  yr

100,000  10,000   100,000  11,000  1.106  1 36,000

 4.88  years

Present Worth (Net Present Worth) The difference between the present value of the annual cash flows (CF) and the total initial investment (TCI). If the present worth of the net cash flow is equal to or greater than zero, the project is justified economically.

NPW  

CF 1

CF 2

1  i  1  i 

2

 .. 

CF n

1  i 

n

 TCI

SAMPLE PROBLEM

GIVEN:

Total Fixed Capital P 100,000

Required: Net Present Value Solution:

Working capital P 11,000

Net Pr esent Worth 

144

NTAldon

CF1

Salvage Value P10,000

CF2

 .. 

CF n

Service Annual life, years Cash flow 6 P 36,000

 FC  n 1  i  1  i 2  1 i    1  0.12 6  1  11, 000  10, 000   36, 000   100, 000  11, 000   47, 650  6 6   0.12 1 0.12 1 0.12       

Future Worth Method This method is comparable to the present worth method except that all cash inflows and outflows are compounded forward to a reference point in time called the future. If the future worth of the net cash flow is equal or greater  than zero, the project is justified economically.

n 1

F   CF 1 1  i 

145

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n2

 CF 2 1  i 

 ..  CF n  TCI 1  i 

n

Capitalized Cost, K  The total amount of money that must be available initially to purchase the equipment and simultaneously provide funds for interest accumulation to permit perpetual replacement of the equipment. In perpetuity, the amount required for replacement must be earned as compounded interest over a given length of time. Let P be the amount of present principal or present worth which can accumulate to an amount F during the interest periods at periodic F = P (1+i )n interest i . Then, If perpetuation is to occur, the amount F  accumulated after  n periods minus cost for  the replacement must equal the present worth P . If we let C R represent the replacement cost, n

I  CR  F  P  P 1  i C   R  P  n 1 i 1

 P

K   FC  P   K   FC 

C   R

1  i 

n

1

where: FC  C R  K

P

146

= First Cost of the equipment = Replacement/Maintenance Cost of the equipment after certain period ,n = Capitalized Costs = additional investment which interest will take care of the perpetual replacement of the equipment NTAldon

Sample Problem

Working in millions  K

 FC 

K   25 

147

NTAldon

C  R

1 i

n

1

2

1 0.12

1

1

 41.67

Sample Problem: Given: The initial cost of the equipment is P100,000, a salvage vale of   P20,000 after 5 years and a maintenance cost of P10,000 per year, and cost of money of 10% pa. Required: Capitalized Cost Solution:

100, 000  20, 000    10,000    P 331, 038  K  100, 000  1  0.10  1 1  0.10   1 5

148

NTAldon

1

Capital Recovery, CR The minimum income that must be earned by the investor in order to recover the cost of depreciation of the equipment plus the interest earned by the initial investment made.  1  i  L  1  L  F    SV   L  FC 1  i   CR  i    FC 1  i 

 SV   FC  A/P, i%, n   SV  A/F, i%, n   L 1  i   1  L

CR 

i where: FC = First cost of the equipment SV = salvage value at the end of service life L = service life, i = periodic interest 149

NTAldon

Sample Problem: Capital Recovery Given:

Installed cost of Equipment = P400,000 Service life = 5 years Salvage value = P40.000 Cost of money = 10% p.a.

Required: Capital Recovery, CR Solution:  L

CR 

FC 1  i 

5

 SV  400, 000 1.1  40, 000   P 98,969  L 5 1  i   1 1.1  1 i

0.1

Explanation:

    i 0.10  annual dep  d   FC  SV       400, 000  40, 00     58,967.09  L 5  1  i   1  1  0.10   1   Interest

 150

year

 I   400, 000  0.10   40, 000

Minimum NTAldon annual earnings=Capital Recovery  58, 967.09  40, 000  98,967.09

SAMPLE PROBLEM:  A company requires an initial fixed capital investment of P100,000 and a working capital of P10,000. The fixed capital investment has a salvage value of P10,000 after 5 years, The projected annual cash flow is P36,000 and annual expenses is P44,000.  Assume a minimum yield on investment of 15% pa. Determine the ff. a. ROI b. Minimum pay-out period, w/o and w/ interest c. Present worth d. Capitalized costs

SOLUTION: a. ROI Profit = Cash flow  Annual depreciation Total Investment = FCI + working capital  Annual depreciation = (100,000 10,000)/ 5 = P18,000 Total investment = 100,000 + 10,000 = P110,000 Profit = 36,000 18,000 = 18,000  –

–

–

ROI   151

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Profit

18,000

Investment  110,000

100%  16.36%

a.

Minimum pay-out period, without interest

Depreciable Fixed Capital Investment

N  

Cash Flow 100, 000  10, 000 36,000

 2.5  years

b. Minimum pay-out period, with interest

N  

 152

Depreciable Fixed Capital Investment  Interest on Total Investment  Cash Flow 100,000  10,000  110,000 1  0.15

NTAldon

36,000

5

 1

 5.6 years

c.

Net Present Worth

NPW

CF1

CF2

1  i  1  i 

2

 .. 

CF n

1  i 

n

 FC

 1  0.155  1  10, 000  10, 000   36, 000   110, 000  P 20, 622  5 5  1  0.15  0.15   1  0.15 

d. Capitalized Costs

K  FC 

CR

1  i n  1

 110, 000  153

NTAldon

44,000 0.15

100, 000  10, 000  P 492,322 5 1  0.15  1

Break Even Analysis Break-even point _ level of production where the total income is equal to the total expenses

Basic Production Assumptions: 1. That the variable costs are substantially directly proportional to production rate over the range from 0 to 100% capacity. 2. That the fixed charges are constant regardless of the annual production. 3. That there are no financial costs. 4. That there is no income other than from operations. 5. That all units produced are sold at a constant price per unit. Gross Profit = net Sales  – cost of Sales = net Sales  – (Variable costs + Fixed Costs)

Z  nS  nV  F  0  n S  V   F   F  n S  V

154

NTAldon

Where:

Z =

gross profit in pesos n = number of units sold per year  S  = nets sales, pesos/unit V = variable cost, pesos/unit F = annual fixed cost, pesos

Note: If  S and V  are in terms of total sales pesos and total variable cost pesos, respectively, at 100% capacity, then n is terms of fractional capacity.

SAMPLE PROBLEM  A company has the capacity to produce one million units of product per year. At present it can only produce and sell 800 thousand units annually at a total sales of P800 million. Variable costs per unit is P500 with an annual fixed costs of P50 million. a. Calculate the company's annual profit or loss for this present production. b. What is its break-even point? Use analytical and graphical method Solution:

a. Profit  Sales  Costof Sales  Z   S-(FC  VC)

  800 ,000 ,000  50 ,000 ,000  800 ,000 units   selling  price/unit   s 

variable cost/unit b. BEP 

155

NTAldon

FC   s-vc

n

P 800 ,000 ,000

 vc 

800 ,000

P 1 ,000 unit

;

P 500 unit

50 ,000 ,000

1 ,000  500 

 100  ,000 units

 500   P 350 M    unit     

SAMPLE PROBLEM: The annual fixed costs of a plant are P100,000, and the variable costs are P140,000 at 70% capacity with net sales of P280,000. What is the break-even point in units of production if the selling price per unit is P40? Solution: The variable costs and net sales are based on 70% capacity, therefore we express them based on 100% capacity:

V = P 140,000/0.7 = P200,000 ; S = P 280,000/0.7 = P400,000 FC = P 100,000

n

156

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F  S  V

100,000 400, 000  200, 000

P  400,000  P 40 / unit

100%  50%

 0.50   5,000 units

Graphical Solution 500 450 400   s   o   s   e    P    d   n   a   s   u   o    h    T

Sales

350

BEP Sales=Cost of Sales

300 250

Costs of Sales FC+VC

200 150

VariableCosts

100

Fixed Costs

50 0

10

20

30

40

50

60

-50 -100 157

NTAldon

% Capacity

70

80

90

100

OPTIMIZATION Sample Problem: The cost of operating a large ship (Co) varies as the square of  its velocity (v); specifically, Co=kLv2, where L is the trip length in kilometers and k is a constant of proportionality. It is known that at 12 kilometers per hour the average cost of operation is P10,000 per kilometer. The owner of the ship wants to minimize the cost of operation, but it must be balanced against the cost of perishable cargo (Cc), which the customer has set at P150,000 per hour. At what velocity should the trip be planned to minimize the total cost (CT), which is the sum of the cost of operating the ship and the cost of perishable cargo? 158

NTAldon

SOLUTION:

Co

k 

L

2

 kv  k 12   10,000; 2

k  69.444

L    CT  kLv   150,000;  v  150,000 L 2 CT  69.444  Lv   ; 2

d CT dv

CT CT

159

 138.888 Lv 

v 150,000 L

2

 69.444  Lv  

2

v 150,000 L 2

 69.444  L10.26  

NTAldon

 0;

v  10.26km / h

v 150,000 L 10 26

 21,930

A company produces circuit boards used to update outdated computer equipment The fixed cost is P2.0 M per month, and the variable cost is P2,700 per circuit board. The selling price is S=7500-2n. Where n is the number of units produced. Maximum plant capacity is 4,000 units a month.

a. Determine the optimum demand for this product.  b. What is the maximum profit per month c. At what volume does breakeven occurs 160

NTAldon

a. Daily Profit  Z   7500  2n   2,700 n   2.1 x10 6 dZ   4,800  4n  0; n  1,200 dn

 4,800n  2n 2  2.0 x10 6

b. Maximum Profit per month 2  Z   4,8001200  21,2000   2.0 x10 6  P 0.880 M  c. BEP :  Z   0  4,800n  2n 2

 2.0 x10 6  2n 2  4,800 n  2.0 x10 6 4,800  4,800 2  422 x10 6  n  1863; 537 22

161

NTAldon

A plant produces a type of product at a rate of P units per day. The variable costs per unit have been determined to be P4,773 + 10P1.2. The total daily fixed charges are P 175,000, and all other expenses are constant at P732,000 per day. If the selling price per unit of product is P17,300. a. Determine the daily profit at a production schedule giving the minimum cost per unit of product

b. Determine the daily profit at a production schedule giving the maximum daily profit c. Determine the production schedule at the break-even 162

NTAldon

Economic Order Quantity, EOQ The order quantity which minimizes the inventory cost unit time.

EO  EOQ 

2aK

h

where:

163

NTAldon

a= cons consta tant nt depl deplet etio ion n rate rate (ite (items ms/u /uni nitt time time)) K= the fixed cost per order (peso) h= the inv invento entory ry stora torage ge cost cost (pes (peso/ o/un unit it ite item)

Sample Problem Given: a= constant constant depletion depletion rate rate (items/u (items/unit nit time) time) = 1000 kg/month kg/month K= the fixed cost per order (peso) = P 2,000 h= the inventory storage cost (peso/unit item) = P100/kg/month

EOQ 

164

NTAldon

2aK

h

21000 2000  100

 200 kg

FINANCIAL FINANCIA L ANAL ANALYSIS YSIS 1. Test of Liquid Liquidity ity These measures are used to determine a firm’s ability to meet short -term obligations, and to remain solvent in the event of adversities.    

Liquidity ratios are used to measure your enterprise's enterpr ise's ability to pay its bills on time. They can be overall measures of liquidity or measures of specific assets. Liquidity is the availability of liquid assets to an enterprise. Liquid assets are those assets held in or easily converted into cash.

1. A.  A. Curre Curren nt Ratio 

Current As sets  sets Current Current Li L iabilities

The ratio is mainly used to give an idea of the company's ability to pay back its shortterm liabilities (debt and paya p ayables bles) with its short-term assets (cash, cas h, inventory, receivables rece ivables). The higher the current ratio, the more capable the company is of paying its obligations. A ratio under 1 suggests that the company would be unable to pay off its obligations if they came due at that point. While this shows the company is not in good financial health, it does not necessarily mean that it will go bankrupt - as there are many ways ways to access financing financing - but it is definitely not a good sign. 165

NTAldon

1 B. . Quick Quick or Acid Te st Ratio  

166

Current As sets  sets

  Invent  Invento ories

Current Liabilities

A stringent indicator that determines whether a firm has enough shortterm assets to cover its immediate liabilities without selling inventory . The acid-test ratio is far more strenuous than the working capital ratio, primarily because the working capital ratio allows for the inclusion of inventory assets. Companies with ratios of less than 1 cannot pay their current liabilities and should be looked at with extreme caution. Furthermore, if the acidtest ratio is much lower than the working capital ratio, it means current assets are highly dependent on inventory. Retail stores are examples of this type of business. The term comes from the way gold miners would test whether their findings were real gold nuggets. Unlike other metals, gold does not corrode in acid; if the nugget didn't dissolve when submerged in acid, it was said to have have passed the acid test. If a company's financial statements pass the figurative acid test, this indicates its financial integrity.

NTAldon

1.C. Invent ory Turn-Over Ratio  

Cost of Goods  Average Inventory

The liquidity of a firm's inventories is reflected in the number of time the fir m's average inventory is turned over during the year. The inventory ratio requires confirmation by other measures and a more thorough examination of contents because rapid turnover on a few items or a slow turnover on others could skew the results. Example: Cost of Goods Sold = P 1,520,891 Inventory Beginning = P 139,725 Inventory Ending = P 141,410  Inventory Turn-Over Ratio 

Cost of  G ods Sold   Average Inventory

1,520,891 139,725  141,410

 10.82

2 

167

The company turns its inventory almost eleven times a year (almost every month). It's a good strategy to mention in your plan the false assumptions associated with this conclusion. Average inventory is the average of the beginning and ending inventories. Sales are sometimes used in the numerator of the inventory ratio rather than the cost of goods sold. This would include markup, a variable which fluctuates across different situations. NTAldon

1.D. Cash Ratio 

168

Cash

 Short Term or  Marketabl e Securities Current Liabilities

The cash ratio is the most conservative liquidity ratio of all. It only measures the ability of a firm's cash, along with investments that are easily converted into cash, to pay its shortterm obligations. Along with the quick ratio, a higher cash ratio generally means the company is in better financial shape.

NTAldon

These tests are employed to present the project’s ability to meet long -term obligations. 2. A. Debt  to  Net Worth Ratio 

169

Total Liabilities Total Equities

Measure used in the analysis of financial statements to show the amount of protection available to creditors. The ratio equals total liabilities divided by total stockholders' equity; also called debt to net worth ratio. A high ratio usually indicates that the business has a lot of  risk because it must meet principal and interest on its obligations. Potential creditors are reluctant to give financing to a company with a high debt position. However, the magnitude of debt depends on the type of business. For example, a bank has a high debt ratio but its assets are generally liquid. A utility can afford a higher ratio than a manufacturer because its earnings can be controlled by rate adjustments. Usually, book value is used to measure a firm's debt and equity securities in calculating the ratio. Market value may be a more realistic measure, however, because it takes into account current NTAldon conditions. market

2.B. Total Capitalization  Ratio  

170

Long term Liabilites  Long term  Liabilities   Equities

The capitalization ratio measures the debt component of a company's capital structure, or capitalization (i.e., the sum of long-term debt liabilities and shareholders' equity) to support a company's operations and growth. Long-term debt is divided by the sum of long-term debt and shareholders' equity. This ratio is considered to be one of the more meaningful of the "debt" ratios - it delivers the key insight into a company's use of leverage. There is no right amount of debt. Leverage varies according to industries, a company's line of business and its stage of development. Nevertheless, common sense tells us that low debt and high equity levels in the capitalization ratio indicate investment quality.

NTAldon

2.C. Debt Service  Ratio 

171

Earnings before Interest and T axes  Interest

The ratio measures debts servicing capacity of a business so far as interest on long-term loans is concerned. This ratio shows how many times the interest charges are covered by the earnings. Debt service ratios is also known as interest coverage ratio. The interest coverage ratio is used to determine how easily a company can pay interest expenses on outstanding debt. The ratio is calculated by dividing a company's earnings before interest and taxes (EBIT) by the company's interest expenses for the same period. The lower the ratio, the more the company is burdened by debt expense. When a company's interest coverage ratio is only 1.5 or lower, its ability to meet interest expenses may be questionable. The ability to stay current with interest payment obligations is absolutely critical for a company as a going concern. While the non-payment of debt principal is a seriously negative condition, a company finding itself in financial/operational difficulties can stay alive for quite some time as long as it is able to service its interest expenses. NTAldon

2.D. Fixed  Ch arg e Coverage Ratio  Earnings before Interest & Taxes

172

  Lease Payments

Lease Payments  Interest C h arg es

Equation that indicates whether the company is able to meet its fixed commitments (i.e., interest) from its profits. A high ratio reflects favorably upon the firm's ability to refinance obligations as they mature. The ratio equals earnings available to meet fixed charges divided by fixed charges. Fixed charges include rent and interest. The fixed charge coverage ratio includes lease payments as well as interest payments. Lease payments, like interest payments, must be met on an annual basis. The fixed charge coverage ratio is especially important for firms that extensively lease equipment, for example. Here is the calculation for the fixed charge coverage ratio : EBIT, Taxes, and Interest Expense are taken from the company's income statement. Lease Payments are taken from the balance sheet and are usually shown as a footnote on the balance sheet. The result of the fixed charge coverage ratio is the number of times the company can cover its fixed charges per year. The higher the number, the better the debt position of the firm, similar to the times interest earned ratio. Like all ratios, you can only make a determination if the result of this ratio is good or bad if you use either historical data from the company or if you use comparable data from the industry. NTAldon

The above formula can be explained with the help of an example: For example, a company has P13,000 as EBIT and P2,000 as lease payments and P1,000 as interest payments the fixed charge coverage ratio is measured as: Fixed charge coverage ratio

13,000  2,000 1,000  3,000

5

This means that the company has earned five times its fixed charges, the company is able to pay the fixed charges of the company. Therefore this means that by calculating the fixed charge coverage ratio, it helps in ascertaining the company’s ability to pay the various fixed costs of the company in case the business tends to fall. Every business would have its own share of risks involved and every company must be well prepared to handle all the expenses and losses that can occur to the company. This is why it is important to calculate the fixed charge coverage ratio and it enables a business to understand the loss or expense taking capacity of the business in case some misfortune strikes the company. This ratio like all other ratios can provide a basic idea of the standing of the company’s finances based on the historical data provided to you. Therefore it is important that you determine fixed charge coverage ratio to ascertain the standing of the company. 173

NTAldon

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Amortization _ method of repaying a debt, the principal and interest included, usually by a series of equal payments at periodic interval of time. Assets _ anything of value possessed by a enterprise, classified as current, fixed and other assets (goodwill, copyrights, franchises, etc. ) Authorized capital_ The authorized capital of a company (sometimes referred to as the authorized share capital , registered capital or nominal capital, is the maximum amount of share capital that the company is authorized by its constitutional documents to issue (allocate) to shareholders. Part of the authorized capital can (and frequently does) remain unissued. This number can be changed by shareholders' approval Average cost method _ all materials in the store room are mixed and no attempt is made to determine which materials came in first or last, and therefore all materials issued are to be priced at the average price of the all the materials in the store room at that time. NTAldon

Bond _ is a certificate of indebtedness of a corporation usually for a period not less than 10 years, and guaranteed by a mortgage on certain assets of  the corporation or its subsidiaries. Coupon bonds _ bonds which are attached coupons indicating the interest due and the date which such interest is to be paid. The owner of the bond can collect the interest due by surrendering the same to the officers of the corporation or the same may be cashed at specified banks. Collateral bonds _ the corporation pledges securities which it owns, such as stocks or bonds of one of its subsidiaries Equipment obligation bonds _ refer primarily to bonds whose guarantee is a lien on equipment. Registered bonds _ the owner's name is recorded in the books of the corporation, and the interest is paid periodically to the owner without their  asking for it. Joint bonds _ bonds which are issued by two or more corporations Mortgage bonds _ bonds whose security is mortgaged on certain specified assets of the corporation. •

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Debenture bonds _ bonds without security behind them except

a promise to pay by the issuing corporation Callable bond _entitles the issuer to pay off the principal prior to the stated maturity date. Similarly, the owner of a putable bond _can force the issuer to pay off the principal before the maturity date. Convertible bond _gives the bondholder the right to exchange the bond for shares of the issuer's common stock at a specified date. Municipal bonds _are issued by state and local governments and other public entities, such as colleges and universities, hospitals, power authorities, resource recovery projects, toll roads, and gas and water utilities. Municipal bonds are often attractive to investors because the interest is exempt from •

Par value of the bond or face value_ is the amount stated on the bond. Bond rate _ is the rate of interest quoted on the bond. NTAldon 176 Redemption or disposal price usually equal to par value •

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Leveraged _ company that raises funds by issuing bonds. Book costs_ are those that do not involve cash payments, but rather represent the recovery of past expenditures over a fixed period of time. The most common of which is the depreciation charge for the use of assets such as plant and equipment. Book value _ also known as depreciated value, is the worth of the property as recorded in the  books of account of the enterprise and is equal to the original cost less the amounts which have  been charged to depreciation. Bookkeeping _ is the systematic recording of all business transactions in financial terms. Borrowed capital_ are those supplied by others on which a fixed rate of interest must be paid and the debt must be repaid at a specified time. Break-even point _ level of production where the total income is equal to the total expenses Break-even analysis_ a means of identifying the value of a particular project variable that causes the project to exactly break even. Capacity or plant factor _ the ratio between the average load and the total available capacity.

Capitalized cost _ is the sum of the first cost and the additional investment necessary in order to take care of the replacement and operating costs of the equipment etc. to perpetually operate it. Only the interest of the additional investment will take care all the replacement and operating expenses. NTAldon 177

1. Equity capital_ capital owned by individuals who have invested their money or property in a business project or venture in the hope of receiving profit. 2. Debt capital _ also known as borrowed capital. Capital obtained from lenders (e.g. obtained from sale of bonds) for investment. In return, the lenders receive interest from the  borrowers. Capital_ collective term for a body of goods and monies from which future income can be derived. Land, buildings, equipment, inventory, and raw materials, as well as stocks, bonds, and bank balances available are considered as capital. Generally, consumer goods and monies spent for present needs and personal enjoyment are not included in the definition or economic theory of capital. Homes, furnishings, cars, and other goods that are consumed for personal enjoyment (or the money set aside for purchasing such goods) are not considered capital in the traditional sense. Paid-in-capital_ amount of money received from the sale of stock more than the par value of the stock. Outstanding stock is the number of shares issued that is actually held by the public. If the corporation buys back part of its own issued stock, it is listed as Treasury Stock on  balance sheet. Subscribed capital_ also known as issued share capital_ the total of a company’s shares that are held by shareholders. A company can, at any time, issue new shares up to the full amount of authorized share capital. 178

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Capital gains tax_ tax on sale of assets; a tax on profit above a fixed level made from the sale of financial assets Capital Recovery_ The minimum income that must be earned by the investor in order to recover the cost of depreciation of the equipment plus the interest earned by the initial investment made. Cartel_ a group of businesses controlling market: an alliance of companies formed to control production, competition and prices. A formal organization of producers within industry forming perfect collusion purposely formed to increase profit and block new comers from the industry. Cash Costs_ are those that involves payment of cash (and results in cash flow). It is distinguished from non-cash costs or book costs like depreciation. Cash Flow _ is a systematic presentation of cash receipts and disbursements for a given operating period or fiscal year, taking for granted the accrual concept in accounting. It details how the company  generated the cash and how the company used the cash during the reported  period. NTAldon

Common stock _ represents the ownership of stockholders who have residual claim on the assets of the corporation after all other claims have been settled. No return is guaranteed on the investment of common stockholders. They have the right to call meetings, to vote, to elect members of the board of directors, amend charter and constitution and by-laws, inspect books of the corporation, receive dividends, share remaining assets if corporation is dissolved. Consumer goods and services_ are those products or services that are directly used by people to satisfy their wants. Food, clothing, homes, cars, television sets, haircuts, cinema, and medical services are examples. Consumer price index (CPI) _measures changes in the price level of consumer goods and services purchased by households. The CPI is a statistical estimate constructed using the prices of a sample of representative items whose prices are collected periodically. Sub-indexes and sub-sub-indexes are computed for different categories and sub-categories of goods and services, being combined to produce the overall index with weights reflecting their shares in the total of the consumer expenditures covered by the index. It is one of several price indices calculated by most national statistical agencies. The annual percentage change in a CPI is used as a measure of inflation. A CPI can be used to index (i.e., adjust for the effect of inflation) the real value of wages, salaries, pensions, for regulating prices and for deflating monetary magnitudes to show NTAldon 180 changes in real values.

Copyright _ is an exclusive right granted by the government to protect the production and sale of literary or artistic works for a period of 50years. Corporation _ is a distinct legal entity, separate from the individuals who own it, and which can engage in practically any business transaction which a real person could do. It may sue, or be sued in its own name. It is separate from its owners and managers. This separation gives the corporation four major advantages: 1) It can raise capital from large investors by issuing stocks and bonds; 2) it permits easy transfer of ownership interest by trading shares of stock; 3) it allows limited liability-personal liability is limited to the amount of the individual’s investment in the business; 4) it is taxed differently than the proprietorships and partnerships, and under certain conditions, the tax laws favor corporations. On the negative side, it is expensive to establish a corporation. Furthermore, a corporation is subject to numerous governmental requirements and regulations. Cost accounting _ is the process of determining the actual cost of manufacturing a product or of rendering a service. Methods used are, postmortem cost accounting, method of predicted cost, and method of standard cost. Elements of cost are materials, direct labor and overhead. 

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Current liabilities _ these are liabilities which mature within a short time, usually a year. Current or liquid assets - include cash, accounts receivables within a short period of time or at least within the present accounting period and inventories (Examples are, raw materials, goods in the process of production, and finished goods ready for sale). Types of current assets 1. Cash_ represents actual money. Cash equivalent like marketable securities and short term investments. 2. Accounts receivable_ money which is owed to the firm but has yet to be received. 3. Inventories_ money invested in raw materials, work-in-process, finished goods available. Demand _ is the quantity of a certain commodity bought at a certain price at a given place and time. Demand factor _ the ratio between the maximum power demand and NTAldon

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Depression _ in economics, a period in an industrial nation characterized by low production and sales and a high rate of  business failures and unemployment. Depreciation and devaluation are sometimes incorrectly used interchangeably, but they always refer to values in terms of other currencies. Inflation, on the other hand, refers to the value of the currency in goods and services (related to its purchasing power). Altering the face value of a currency without reducing its exchange rate is a redenomination, not a devaluation or revaluation.

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Direct Costs_ are costs that can be reasonably measured and allocated to a specific output or work activity. The labor and material costs directly associated with a product, service, or construction activity are direct costs. Direct materials _ are materials which are used in the finished product itself. Discount _ the difference between the value of a negotiable paper between now and the future. Discounted interest_ The interest for the money borrowed (discount) is deducted from the principal in advance Disposal costs_ includes those nonrecurring costs of shutting down the operation and the retirement and disposal of assets at the end of the life cycle. NTAldon

Discounting_ is a financial mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a charge or fee. Essentially, the party that owes money in the present purchases the right to delay the payment until some future date. The discount, or charge, is simply the difference between the original amount owed in the present and the amount that has to be paid in the future to settle the debt Duopoly_ concentration of power in two forces: an economic situation in which two powerful groups or organizations dominate commerce in one business market or commodity. Duopsony _ two rival buyers’ control over sellers: a situation in which two competing buyers exert controlling influence over many sellers. Economic life _ is the length of time during which an equipment or property will operate at a satisfactory profit. Effective interest _ is the actual rate of interest on the principal for one year. NTAldon 185 Efficiency output divided by input

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Elastic demand _ occurs when a decrease in selling price will cause greater than proportionate increase in sales. Usually applicable to luxury goods. Equipment obligation bonds _ refer primarily to bonds whose guarantee is a lien on equipment. Equities _ are the claims of anyone against the asset of the enterprise. It includes the liabilities to the creditors as well as the claims of the owners. Equity capital_ or ownership funds_ are those supplied and used  by the owners of an enterprise in the expectation that a profit will be earned. Expense _ the cost of producing income or revenue, or the value of commodities and services needed in the operation of the  business. Also classified as operating and non-operating expenses. NTAldon

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Fair value _ is the value which a disinterested third party, different from the buyer or the seller, will determine in order to establish a price that is fair and acceptable to both the buyer and the seller. FIFO _ first-in, first out method. The principle behind this method is that the materials issued at any time are taken from the oldest stock and should be priced at the cost when they are purchased. Ex food manufacturing. First cost of property _ includes original purchase price, freight and transportation, installation, taxes, permits and all other expenses to put it into operation. Fixed liabilities _ liabilities which are not due for payment until sometime in the future, usually after a period exceeding one year. NTAldon

Franchise_ the right and privilege granted to an individual or corporation to do business in a certain region. Franchise value _ is an intangible item of value arising from the exclusive right of a company to provide a specific product or service in a stated region of the country. Going concern value _ The value of a company as an ongoing entity. This value differs from the value of a liquidated company's assets, because an ongoing operation has the ability to continue to earn profit, while a liquidated company does not. Goodwill _ an intangible value_ is that element of value which a business has earned through the favorable consideration and patronage of its customers arising from its well-known and well conducted policies and operation. Gratuitous_ an obligation with no condition attached.

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Gross Domestic Product (GDP) _ measures the value of all goods and services produced within a nation’s border’s regardless of the nationality of the producer. GDP measures a country’s economic activity regardless of who owns the productive assets in that country. For example, the output United Statesowned companies based in the Philippines is considered part of Philippine’s GDP rather than part of the U.S.. GDP may be calculated in three ways: (1) by adding up all the value of all goods and services produced (2) by adding up the expenditures on goods and services at the time of sale, or (3) by adding up producers’ incomes from the sale of goods or services . GDP is usually divided by its population to arrive at GDP per head. The figure is then converted to dollars to allow for its comparison between countries. If GDP grows at a higher rate than the population, standards of living are said to be rising. If the population is growing higher than GDP, living of standards are said to be falling. GDP per head does not take the cost of living into account. Gross National Product (GNP)_ used to describe in monetary value the total annual flow of goods and services in the economy of a nation. It is measured by totaling all personal spending, all government spending, and all investment spending by a nation’s industry both domestically and all over the world. In other words, the income earned by a U.S.-owned business based in the Philippines would be considered part of the U.S. Gross Margin_ net sales less the cost of goods sold. NTAldon

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Hedge funds_ risk-taking investment company: an investment company that is organized as a limited partnership and uses highrisk techniques in the hope of making large profits Income _ the value of personal and professional services rendered or of goods sold in the operation of the business. Usually classified as operating and non-operating income. Income statement _ or a profit and loss statement, is a summary of the incomes and expenses of an individual or enterprise for a given period. The next in importance to the balance sheet. Incremental Costs _ are additional costs that result from increasing the output of a system by one (or more) units. Indirect Costs_ are costs that are difficult to attribute or allocate to a specific output or work activity. For example, the costs of common tools, general supplies, and equipment maintenance in plant are treated as indirect costs. Indirect materials _ are materials not directly part of the product  being produced Inelastic demand _ occurs when a decrease in the selling price NTAldon will cause a little a less than prop in sales.

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Inflation_ is the increase in the prices of goods and services from one year to another, thus decreasing the purchasing power of money. Intangible assets _ have not physical substance. Examples are, goodwill, leaseholds, copyrights, patents, franchises, licenses, and trademarks. Accounting for an intangible asset is rendered somewhat difficult because the lack of physical substance makes evidence of its existence more elusive, may make its value debatable and its useful life may be questionable. Inventory_ stock of goods; the merchandise or stock a store or company has on hand Investment Cost_ is the capital required for most of the activities in the acquisition phase. This cost is often called a capital investment.  Joint bonds _ bonds which are issued by two or more corporations.  Journal _ is an accounting book where the original record of all transaction is ordinarily recorded. It is the book of original entry NTAldon

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Kelvin's Law _ the most economical cross sectional area for a conductor is that one for which the investment cost just equals the annual cost of lost energy. Law of Diminishing returns _ when one of the factors of production is fixed in quantity or is difficult to increase, increasing the other factors of production will result in a less than proportionate increase in output. Law of diminishing utility _ an increase in the quantity of any good consumed or acquired by an individual will decrease the amount of satisfaction derived from that good. Ledger _ serves as a secondary record of business transactions. The ledger sheets are used as intermediates, between journal records, balance sheets, income statements, and general records. Examples are, cash, equipment, accounts receivables, inventory, accounts payable and manufacturing expense. Liabilities _ are debts or claims anyone other than the owners of theNTAldon property upon the assets of the company.

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Life-cycle cost_ refers to a summation of all costs, both recurring and non-recurring, related to a product, structure, system, or service during its life plan. Life cycle_ refers to the notion that a fair, holistic assessment requires the assessment of raw material production, manufacture, distribution, use and disposal including all intervening transportation steps necessary or caused by the product's existence. The sum of all those steps - or phases - is the life cycle of the product. The concept also can  be used to optimize the environmental performance of a single product (ecodesign) or to optimize the environmental performance of a company. LIFO _ last-in. last out method. The materials last to obtained are the first to be issued. Ex sand and gravel industry Load factor _ the ratio between the average demand and the maximum demand. Luxuries_ are those products or services that are desired by humans and will be purchased if money is available after the required necessities have been obtained. NTAldon

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Marginal cost _ is the additional cost of producing one more unit.

Marginal revenue _ is the amount received from the sale of an additional unit of a product. Marginal utility _ is the utility of the last unit of the same commodity which is consumed or acquired. If a man has three shirts of the same kind of brand, the marginal utility of the 2nd unit is greater than the marginal utility of the fourth unit. Market - is a place where sellers and buyers come together Market value _ is the amount which a willing buyer will pay to a willing seller for the property when neither one is under compulsion to buy or sell.

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Monopoly _ a unique product or service is available only from a single supplier and entry of all other possible suppliers are prevented. Monopsony_ single-customer market: a situation in which a product or service is only bought and used by one customer Mortgage bonds _ bonds whose security is mortgaged on certain specified assets of the corporation. Mutual Fund_ form of management-investment company that combines the money of its shareholders and invests those funds in a wide variety of stocks, bonds, and so-called money market instruments. The latter include short-term investments such as United States Treasury bills and other federal securities, commercial paper, and bank certificates of deposit. Mutual funds provide the investor with professional management of funds and diversification of investment among the securities offered by leading corporations, federal and state governments, and other entities. NTAldon

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Necessities _ are those products or services that are required to support human life activities that will be purchased in somewhat the same quantity even though the price varies considerably.

Non-recurring costs_ are those which arte non-repetitive, even though the total expenditure may be cumulative over a relatively short period of time.. For example, the purchase of a real estate upon which the plant will be constructed is a non-recurring cost, as the cost of constructing the plant itself. Obsolescence - refers to the changes external to the equipment such as, decrease or disappearance of demand, invention of more efficient equipment or style of products may have changed considerably. Organization cost_ an intangible value_ is the amount of money spent in organizing a business and arranging for its financing and building. Oligopoly _ occurs when there are few suppliers and any action taken  by one of them will definitely affect the course of action of the others. NTAldon

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Operation and maintenance cost_ includes many of the recurring annual expenses associated with the operation phase of life cycle. The direct and indirect costs of operation associated with the five primary resource areas- people, machines, materials, energy, and information- are a major part of the costs in this category. Opportunity Cost_ is incurred because of the use of limited resources, such as the opportunity to use those resources to monetary advantage in an alternative use is foregone. Overhead expenses _ consist of those expenses which cannot be readily included under direct materials and direct labor. Also known as indirect costs or burden. Ownership or proprietorship _ it represents the investment of a person or several persons in the enterprise. NTAldon

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Partnership _ is an association of two or more persons for the purpose of engaging in a business profit. Usually formed by the voluntary agreement of the partners either verbally or in writing. The agreement among the partners usually states the relations  between partners on matters relating to the proportion in which profits or losses are to be shared, their investments , rights and duties of each partner, and provisions for the withdrawal of any partner or the dissolution of the partnership. A partnership has many advantages, among which are its low cost and ease of formation. Because more than one person makes contributions, a partnership typically has larger amount of capital available for business use. Since the personal assets of all partners stand behind the business, a partnership can borrow money more easily from a bank. Each partner pays only personal income tax on his or her share of a partnership’s taxable income. Patent _ is an exclusive right granted by the government for the manufacture, use, and sale of a specific product. When a company acquires a patent or copyright by purchase of from the owner, the purchase price is classified as an intangible asset. NTAldon

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Payout period _ the minimum period needed to recover an investment. Depreciable fixed capital/ net cash flow Perfect competition_ a situation where a commodity or service is supplied by a number of vendors and there is nothing to prevent additional vendors entering the market. Perpetual Inventory _ consists of the preparation of inventory cards, and their being kept up-to-date for each type of equipment or materials used or issued, and for the products completed or in the process of manufacture. Perpetuity _ is an annuity where the payments periods extend or in which the periodic payments continue indefinitely.

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Physical Life of an equipment _ is the length of time during which it is capable of performing the function for which was designed and manufactured. Power factor _ ratio of the power output in watts and the product of volts and amperes Preferred stock _ also represent ownership. And it possesses the same rights as common stock, but in addition, it enjoys certain preferences, not possessed by common stock. It has priority over common stock in receipt of dividends, and it is usually guaranteed a fixed annual dividend, regardless of the amount of the earnings of the corporation. In case the corporation is dissolved, the owner of the preferred stock, has priority over the common stockholders. They may have right to vote in meetings.

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Prepaid expense _ assets in the form of money paid for certain materials not yet delivered or services not yet rendered to the company. Prepaid income _ these are liabilities representing income which have been paid to the enterprise but for which the goods have not been delivered or any service rendered to the payer. Present economy _ involves the analysis of problems for manufacturing a product or rendering a service upon basis of present or immediate costs. Present value _ is the amount which if invested now will give a value of F after n interest periods. It is also defined as projected cash inflows and outflows expressed or discounted to the present time. Price _ is defined as the amount of money or its equivalent which is given in exchange of the goods being sold. NTAldon

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Producer goods and services_ are used to produce consumer goods and services or other producer goods. Machine tools, factory buildings, buses, and farm machinery are examples. Project Risk_ the possibility that an investment project will not meet the minimum requirements for acceptability and success. Producer Price Index (PPI)_ is a family of indexes that measure the average change over time in the prices received by domestic producers of goods and services. PPIs measure price change from the perspective of the seller. The headline PPI (for finished goods) is a measure of the average price level for a fixed basket of capital and consumer goods for prices received by producers. The producer price index for finished goods is a major indicator of commodity prices in the manufacturing sector. These prices are more sensitive to supply and demand pressures than the more comprehensive consumer price index. Changes in the producer price index are considered a leading indicator for consumer price changes, although only a small portion of the PPI is directly connected to less than half of the CPI. Proprietorship_ the simplest form of business organization wherein the business is owned entirely by one person. Pyramid scheme_ a fraudulent scheme in which the perpetrators recruit people to pay money to those above them in a hierarchy on the expectation that they will get payments from those below. When the number of newly recruited people eventually dwindles, the payment structure collapses. Also known as Ponzi scheme.

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Recurring Costs _are those that are repetitive repetitive and occur when an organization produces similar goods or services ser vices on a continuing basis. Variable costs are also recurring costs because they repeat with each unit un it of output. A fixed cost that is paid on a repeatable basis is also a recurring cost. REER (Real effective effective exchange rate)_ measures the competitiveness of a currency in terms of making exports expor ts more or less expensive. It takes into account the movement of one currency against several several others, and the inflation rates in other countries. Inflation is taken into account to measure currency competitiveness competitiveness in real real terms because affordability of export goods is determined not just by the mov m ovement ement of an exchange excha nge rate, but also by movement movement of prices of raw materials. materials. Replacement value _ The cost necessary to replace an existing property at any given time with one at least equally equally capable capable of rendering the same service. Retained earnings_ the cumulative net income of the firm since its beginning, less the total dividends that have been paid to stockholders. stockh olders. It indicate the amount of assets that have have been financed by plowing profits back into the  business. Therefore, Therefore, these retained retained earnings belong to the stockholders. stoc kholders. Revenue_ the price of goods sold and services rendered during a given accounting period. NTAldon

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Scenario analysis_ a means of comparing a “base -case” or expected project measurement (such as NPW) to one or more additional scenarios, such as best and worst case, to identify the extreme and most likely project outcomes. Sole proprietorship _ or individual ownership, is the simplest of  business organization, wherein the business is owned owned entirely by by one person who w ho is responsible for the operation, firm’s firm’s policies, and is personally liable for its debts. The proprietorship proprietor ship has two two major advantages. First, it can be formed easily and inexpensively. No legal

and organizational requirements are associated with setting up a proprietorship, proprietors hip, and organizational costs are therefore, virtually nil. ni l. Second, the earnings of a proprietorship proprietorshi p are taxed at the owner’s owner’s personal tax rate, which may be lower than the rate at which corporate cor porate income is taxed. Apart from personal liability considerations, the disadvantage of a proprietorship is that it cannot issue stocks and  bonds, making it difficult to raise capital for any business business expansion. Standard Costs _ are representative costs per unit of output that are established in advance of actual production or ser s ervice vice delivery. delivery. The are developed from anticipated direct labor hours, materials, and overhead overhead categories (with their established cost per unit). uni t). NTAldon

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Stock _ in business business and finance finance,, a share share of of ownershi ownershipp in a corporati corporation. on. Shares Shares in a corporation can be bought and sold, usually on a public stock exchange. Consequently, the owner of shares can realize a profit or capital gain if the stock is sold at a price above above what the owner originally paid for it. Stock Exchange_ Exchange_ organized organized market market for buying buying and selling selling financia financiall instrument instrumentss known as securities, which include stocks, bonds, options, and futures. Most stock exchanges have specific locations where the trades are completed. For For the stock s tock of a company to be traded at these exchanges, it must be listed, and to be listed, the company must satisfy certain requirements. But not all stocks are bought and sold at a specific site. Such stocks are referred to as unlisted. Many Many of these stocks are traded over the counter  — that that is, by telephone or by computer. Stock Holder_ share holder, owner of company stock, Stockholder’s Stockholder’s Equity_ the amount available available to the owners after all other debts have have  been paid

Sunk cost _ money which has been spent or capital which has been invested and which cannot be recovered due to certain reasons. They are non-refundable cash outlay, such as earnest money on a house, capital that has been invested and cannot  be retrieved or money spent on on passport. Supply _ is the quantity of of a certain commodity that is offered for for sale at a certain NTAldon

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Income taxes_ expressed as a function of gross g ross revenues minus allowable allowable deductions. Property taxes_ are assessed as a function of the value of property owned, such as land,  buildings, equipment, and so on, and the the applicable tax rates. rates. They are independent independent of the income or profit of the company. Sales taxes_ are assessed on the basis of purchases of goods or services and are thus independent of gross income or profits. Excise Taxes_ assessed as a function of the sale of certain goods or services often considered non-necessities (alcohol, tobacco), and are hence independent of the income or profit of a  business. The Law of Demand _ the demand for a commodity varies inversely as the price price of commodity, though not proportionately. commodity varies directly directly as the price of the The Law of Supply _ the supply of commodity commodity, though not proportionately. The Law of Supply and Demand _ when free competition exists, the price of a product will be that value where supply is equal to the demand. Time value of money_ is the value of money figuring in a given amount of interest earned over a given amount of time.The time value of money is the central concept in finance theory. For example, P100 of today's money invested for one year and earning 5% interest will be worth \$105 after one year. Therefore, P100 paid now or P105 paid exactly one year from now  both have have the same value to the the recipient who who assumes 5% interest; using time value of money terminology, P100 invested invested for one year at 5% interest has a  future value of P105.

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Tort_ a wrongful act that causes injury to a person or property and for which the law allows a claim by the injured party to recover damages. Unitary elasticity of demand _ occurs when the mathematical product of price and volume of sales remain constant regardless of any change in price. PV=C Utility _ is the capacity of a commodity to satisfy human wants and needs. Utility or use value _ is what it is worth to the owner of a property when in actual operation. Value_ the price that must be paid in order to obtain a particular item Valuation_ or appraisal_ is the process of determining the value of certain property for specific reasons. Variable Costs_ are those associated with an operation that vary in total with the quantity of output or other measures of activity level. Working capital_ refers to the funds required for current assets (other than fixed assets) that are needed for the start-up and support of operational activities. Also known as the circulating capital, includes all funds which are required to make the enterprise a going concern. NTAldon