GEN HW2

College of engineering Engineering Economy

Homework #2

3.4 Standby power for water utility pumps and other electrical devices is provided by diesel-powered generators. As an alternative, the utility can use natural gas to power the generators, but it will be a few years before the gas is available at remote sites. The utility estimates that by switching to gas, it will save $22,000 per year, starting 3 years from now. At an interest rate of 8% per year, determine the present worth in year 0 of the projected savings that will occur in years 3 through 10. P=22000( P / A ,8 , 8)( P /F , 8 , 2)

¿ 22000(5.7466)(0.8573) ¿ $ 108384

3.11 Two engineering graduates who recently got married are planning for their early retirement 20 years from now. They believe that they will need $2,000,000 in year 20. Their plan is to live on one of their salaries and invest the other. They already have $25,000 in their investment account. ( a ) How much will they have to invest each year if the account grows at a rate of 10% per year? ( b ) If the maximum they have available to invest each year is $40,000, will they reach their goal of $2 million by year 20? (a)2000000=25000( F / P ,10 ,20)+ A( F / A , 10 , 20)

2000000=25000(6.7275)+ A (57.2750) A=$ 31983 per year

( b ) They will exceed their goal by $ 459,188

3.24

New actuator element technology enables engineers to simulate complex computer-controlled movements in any

direction. If the technology results in cost savings in the design of amusement park rides, what is the future worth in year 5 of savings of $70,000 now and $20,000 per year in years 1 through 3 at an interest rate of 10% per year? F=70000(F /P , 10 , 5)+ 20000( P/ A , 10 , 3)( F / P ,10 ,5) ¿ 70000(1.6105)+ 20000(2.4869)(1.6105)

¿ $ 192838

3.44 A private equity fi rm purchased a cable company and

assumed the company’s debt as part of the transaction. The deal was structured such that the private equity fi rm received $3 million immediately after the deal was closed (in year 0) through the sale of some assets. This year (year 1) income was $3.36 million, and it is projected to increase by 12% each year through expansion of the customer base. What was the present worth in the year of purchase of the income stream over a 10-year period? The firm’s expected rate of return for any purchase is 15% per year. (First method is finding Pg in year 1 and the move it to year 0 Second method is handling initial $3 million separately and start gradient in year 1) Pg ,−1=3 {1 – [(1+0.12)/(1+0.15)]11}/(0.15 – 0.12) ¿ 3 {1 – 0.74769 }/0.03 ¿ $ 25.2309 P 0=25.2309(F / P ,15 ,1)

¿ 25.2309(1.15) ¿ $ 29.0156($ 29015600)

4.5

Identify the compounding period for the following interest statements: ( a ) 3% per quarter; ( b ) 10% per year, compounded semiannually; ( c ) nominal 7.2% per year,

compounded monthly; ( d ) effective 3.4% per quarter, compounded weekly; and ( e ) 2% per month, compounded continuously. a- Quarter, b- Semiannual, c- Month, d-Week, e-Continuous

4.28 Irvin Aerospace of Santa Ana, California, was awarded a 5-year contract to develop an advanced space capsule airbag landing attenuation system for NASA’s Langley Research Center. The company’s computer system uses f uid structure interaction modeling to test and analyze each airbag design concept. What is the present worth of the contract at 16% per year, compounded quarterly, if the quarterly cost in years 1 through 5 is $2 million per quarter? P=2000000(P / A , 4 , 20)

¿ 2000000(13.5903) ¿ $ 27180600

4.33 In October 2009, Wal-Mart started selling caskets on its website that undercut many funeral homes. Prices ranged from $999 for steel models such as Dad Remembered to $3199 for the Sienna Bronze casket. Part of the business model is to get people to plan ahead, so the company is allowing people to pay for the caskets over a 12-month period with no interest. An individual purchased a Sienna Bronze casket and made 12 equal monthly payments (in months 1 through 12) at no interest. How much did this person save each month compared to another person who paid an interest rate of 6% per year, compounded monthly? A 0 =3199/12

¿ $ 266.58 per month A 0.5 =3199( A/ P , 0.5 , 12)

¿ 3199(0.08607)

¿ $ 275.34 per month Savings=275.34 – 266.58

¿ $ 8.76 per month

4.52

U.S. Steel is planning a plant expansion that is expected to cost $13 million. How much money must the company set aside now in a lump-sum investment to have the money in 2 years? Capital funds earn interest at a rate of 12% per year, compounded continuously. i=e 0.12 – 1 ¿ 0.1275∨12.75 per year P=13000000( P /F ,12.75 ,2)

Find factor value by interpolation , formula,∨spreadsheet . P=13000000(0.7866) = $10226105