SEEM 2440A/B - ENGINEERING ECONOMICS First term (2011 – 2012)

Assignment 3 Due: 5:00 p.m., 3-Nov-2011

Important notes: 1. You must submit your assignment on time. No late assignment will be accepted. 2. You must drop your assignment into the assignment collection box A18. Don’t

hand in your assignment to instructor and TAs. 3. Unless otherwise stated, each question carries 4 points. The number in the parentheses is the problem number in the textbook (Engineering Economy, by William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling, 15th edition, Pearson Education, Inc.). 1. (4-15) Mr. Smith has saved $1,200 each year for 20 years. A year after the saving

period ended, Mr. Smith withdrew $7,500 each year for a period of five years. In the sixth and seventh years, he only withdrew $4,500 per year. In the eighth year, he decided to withdraw the remaining money in his account. If the interest rate was 8% per year throughout the whole period, what was the amount he withdrew at the end of the eighth year?

2. (4-30) Luis wants to have $2,000,000 in net worth when he retires. To achieve this

goal, he plans to invest $10,000 each year (starting one year from now) into an account that earns 10% interest compounded annually. The amount of time before Luis achieves his goal is how many years? Round your answer to an integer.

3. What are A(F/A, 0%, N) and A(P/A, 0%, N) equal to?

Hint: You cannot compute them directly from the formulas given in the lecture notes.

4. (4-61) It is estimated that you will pay about $80,000 into the social security

system (FICA) over your 40-year work span. For simplicity, assume this is an annuity of $2,000 per year, starting with your 26th birthday and continuing through your 65th birthday. a. What is the future equivalent worth of your social security savings when you

retire at age 65 if the government’s interest rate is 6% per year? b. Assume the first retirement withdrawal is at age 66, what annual withdrawal can

you make per year if you expect to live 20 years in retirement? Let i = 6% per year.

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5. (4-73) Determine the value of P0, as a function of H, for these two investment alternatives to be equivalent at an interest rate of i = 15% per year:

6. (4-78) You owe your best friend $2,000. Because you are short on cash, you offer

to repay the loan over 12 months under the following condition. The first payment will be $100 at the end of month one. The second payment will be $100 + G at the end of month two. At the end of month three, you will repay $100 + 2G. This pattern of increasing G amounts will continue for all remaining months. a. What is the value of G if the interest rate is 0.5% per month? b. What is the equivalent uniform monthly payment? c. Repeat Part (a) when the first payment is $150 (i.e., determine G).

7. (4-88) A small company heats its building and spends $8,000 per year on natural

gas for this purpose. Cost increases of natural gas are expected to be 10% per year starting one year from now (i.e., the first cash flow is $8,800 at EOY one). Their maintenance on the gas furnace is $345 per year, and this expense is expected to increase by 15% per year starting one year from now. If the planning horizon is 15 years, what is the total annual equivalent expense for operating and maintaining the furnace? The interest rate is 18% per year.

8. An environmental soil cleaning company got a 3-year contract to remove BTEX

contamination from an oil company tank farm site. Under the contract, the oil contract can receive $140,000 per quarter starting one quarter from now. What is the present equivalent worth of the contract through the 3-year treatment period at an interest rate of 1% per month?

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9. Rob is an engineer of Alcoa Aluminum. He has brought new equipment from a contractor. Rob developed the following cash flow diagram from Alcoa’s point of view. Included are payments to the contractor (negative cash flow) and the revenues (positive cash flow) generated from this equipment. What is the future equivalent worth at the end of the year of his cash flow if the interest rate is 12% per year compounded quarterly and the interperiod cash flows earn no interest?

Cash flow diagram (in the unit of $1,000)

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