Engineering Economy Reviewer

Beatrice Amistoso Abesamis

Simple Interest F=P+ I I =Pin

F=P(1+¿)

Remember: - Default interest is per year. - Value of m if: Semi - Annually - 2 Quarterly - 4 Monthly - 12 Daily - 360 Ordinary Simple Interest - 1 year = 360 days Exact Simple Interest One year is: - 365 days if ordinary year. - 366 days if leap year. It is leap year if: - Divisible by 4 - If it is century year, it must be divisible by 400.

Compound Interest F=P(1+i)n F=P(1+

r mt ) m

F=P ern

Effective Rate ER=(1+ i)n−1 ER=er −1

Cash Flow Diagram 1. Draw the cash flow diagram. Lender's Side - F up, P down Borrower's Side - P up, F down 2. Set the focal point. 3. Equate up = down.

Annuity

[ [

(1+i)n −1 F=A i P= A

]

−n

1−(1+i) i

]

DeferredAnnuity P= A

[

−n

1−(1+i) i

]

(1+i)−k

Perpetuity P=

A i

VARIABLES F = Future Amount P = Present Amount I = Interest i = Interest Rate n = Number of Years m = No. of Compounding Years t = Number of Years ER = Effective Rate A = Annuity k =Number of Years Before

Beatrice Amistoso Abesamis

Depreciation Straight Line Method - Simplest Method d=

C o−C n n

C (¿¿ n−dismantle) C o− n d=¿ D m=d (m)

d x 100 Co

C o−C n

[

n

(1+i ) −1 i

D m=d

[

k=

2 n

m−1

2 n

( )

d m=C o 1−

2 n

m

Sinking Fund Method - Annuity-like - Fixed cost for every year - Sinking Fund Deposit Factor (Just multiply with Co d=

Double Declining Balance Method - Exactly similar as DBM but k is 2/n.

2 Cm =C o (1− ) n

Cm =C o−Dm k=

Dm=C o−Cm

(1+i ) −1 i

Dm=C o−Cm

Sum of the Year's Digit Method ReverseYear=n−m+1

∑ Years=

]

m

√

2 n C =1− n n Co

]

Cm =C o−Dm

d m=C o −Cn

d m=C o (1−k )m−1 k

(

ReverseYear ∑ Years

)

Dm=d 1+ d2 … D m=

Declining Balance Method/Matheson Formula - Fixed percentage

n(n+1) 2

(RY 1 + RY 2 …) (C o−C n ) ∑ Years

Cm =C o−Dm

Service-Output Method

m

Cm =C o (1−k )

√ √

k =1−

m

k =1−

n

Cm Co Cn Co

a. Working Hours Method d n=

(

Co −Cn H year Ht

)

b. Output Method

Beatrice Amistoso Abesamis

d n=

(

Co −Cn Q year Qt

)

VARIABLES Co = First Cost Cn = Cost After n Years / Trade-in Value n = Life of the Property Dm = Total Depreciation After m Years i = Interest Rate k = Rate of Depreciation Ht = Total No. of Hours Hyear = No. of Hours for a Certain Year Qt = Total No. of Output Qyear = No. of Output for a Certain Year

Beatrice Amistoso Abesamis

Bonds Total Periodic Expense A=

F

(

( 1+i )n−1 i

)

I =Fr A+I

Bond Value

[

−n

1−(1+i) V n=Fr i

]

−n

+C(1+i )

I =Fr A = Periodic Deposit to the Sinking Fund Vn = Value of the Bond in n Periods Before Redemption F = Face Value C = Redemption Price/Selling Price r = Bond rate I = Interest on the Bond per Period F = Accumulated Amount, Amount Needed to Retire the Bond

Gradient P= A

[

] [

1−( 1+i )−n G 1−( 1+i )−n ± −n(1+i)−n i i i

P = Present Worth of All Cash Disbursement

]

Economic Studies Rate of Return Method Net Annual Profit Capital Invested *Total Annual Cost > Expenses + Owner's Salary (If given) + Depreciation Value (Depreciation is not always an outcome. It can also be an income.): Use Sinking Fund and Revenue or Sales. > When given is in %, multiply by the investment > If two are given like the other one is the cost after n years, use depreciation. If ever that the cost becomes higher after n years, it will be an income. * Investment is also called first cost and project cost. * Net Annual Profit = Revenue or Sales - Total Annual Profit (also means earnings before income taxes)

Beatrice Amistoso Abesamis

Annual Worth Method * * * *

Given Percent x Investment Product +Total Annual Cost Given Revenue - Sum If Negative (Not Justifiable)

Present Worth Method * Inflow: Revenue (P/A,%,n) + Salvage Value(P/A,%,n) ^ Do this if the given has salvage value. * Outflow: Investment + Expenses (Total Annual Cost without Depreciation) (P/A,%,n) * Inflow - Outflow

Future Worth Method

* Payroll taxes are deducted from labor cost. * Annual Savings = Annual Cost A - Annual Cost B * Additional Investment = First Cost A - First Cost B * ROR less than interest rate: NO

Annual Cost Method * Given Percent x Investment * Product +Total Annual Cost * Pick the lesser one.

Present Worth Method

* Refer to the Present Worth's Cash Flow Diagram

* Two different years: Get the multiple. * Depreciation, Final Year, and First Cost must be aligned.

Payback (Payout) Method

EUAC

Investment −Salvage Value Net Annual Cash Flow * Net Annual Cash Flow = Revenue - Total Annual Cost without Depreciation

Comparing Alternatives Rate of Return on Additional Investment Annual Net Savings Additional Investment

Annual Cost ( Without Depreciation )+ ¿ n

1−( 1+ i ) −¿ i ¿ ¿ ¿ P ¿

Capitalized Cost ¿ Co +

C o−C n n

( 1+i) −1

+

A i