ME 353 ENGINEERING ECONOMICS

Transcription

1 ME 353 ENGINEERING ECONOMICS Final Exam Sample Scoring gives priority to the correct formulas. Numerical answers without the correct formulas for justification receive no credit. Decisions without numerical justification receive no credit. Interest tables and factor formulas are at the end of the exam. 1. (10 Points) A luxury apartment building project requires an investment of $1,250,000. The building has 50 units. We expect the maintenance cost for the apartment building to be $150,000 in the first year, $200,000 in the second year, and will continue to increase by $50,000 per year in subsequent years. The cost to hire a manager for the building is estimated to be $50,000 per year. After five years of operation the apartment building can be sold for $750,000. What is the annual rent per apartment unit that will provide a return on investment of 15%? Assume the building will remain fully occupied during the five years. 2. (10 Points) We use the cost of data of problem 1, but now we assume that each apartment unit rents for $1000 per month. In this problem you are to include the effect of taxes. The tax rate on net income per year is 30%. The building is depreciated with the straight-line method using a tax life of 25 years and a tax salvage of zero. Tax on capital gains is 30%. The after tax minimum acceptable rate of return is 12%. We repeat the other data from problem 1. The building project requires an investment of $1,250,000. The building has 50 units. We expect the maintenance cost for the apartment building to be $150,000 in the first year, $200,000 in the second year, and will continue to increase by $50,000 per year in subsequent years. The cost to hire a manager for the building is estimated to be $50,000 per year. After five years of operation the apartment building can be sold for $750,000. Show the after-tax cash flows in the table below. Also, write the formula for the after-tax net present worth of this project. Use as few terms as possible and show time value of money factors with the appropriate interest rates. You do not have to evaluate the formula. Year 0 After Tax Cash Flow

2 3. (10 Points) We use the cost of data of problem 1, but now we consider inflation. Do not consider taxes. We first repeat the other data from problem 1. These estimates of future values are estimated with today s prices, however actual cash flows escalate in the manner described in the next paragraph. The building project requires an investment of $1,250,000. The building has 50 units. We expect the maintenance cost for the apartment building to be $150,000 in the first year, $200,000 in the second year, and will continue to increase by $50,000 per year in subsequent years. The cost to hire a manager for the building is estimated to be $50,000 per year. After five years of operation the apartment building can be sold for $750,000. We assume that each apartment unit rents for $1000 per month. This rent amount is guaranteed to the renters and is not affected by inflation during the five-year period. The maintenance and management costs are expected to escalate in the future at the same rate as general inflation. The resale value of the building will escalate at a 20% rate. The general inflation rate is expected to be 6% per year. The after minimum acceptable rate of return is 18%. This is the market rate of return. Show the cash flows to be used for an analysis in the table below. Indicate whether the cash flows are in real or actual dollars. Also, write the formula for the net present worth of this project. Use as few terms as possible and show time value of money factors with the appropriate interest rates. You do not have to evaluate the formula. Kind of dollars in the cash flow: Year 0 Cash Flow

3 4. (12 Points) You are considering purchasing a bond with a face value of $1000. The company issuing the bond will pay you an annual interest payment of 10% of the face value. The next interest payment will occur one year from now. The bond matures in 9 years at which time you will receive the face value of the bond. a. What is the most that you should pay for the bond if your minimum acceptable rate of return (MARR) is 15%? b. Will the purchase price change up or down if the MARR decreases? Explain your answer. c. In addition to the information above, you expect an inflation rate of 7%. The payments from the bond are fixed and are not affected by inflation. You require a real rate of return of 15%. Write a formula with which he can compute the purchase price of the bond in this case. Show numerical interest rates in your formula. 5. (12 Points) A company is considering producing a new product. The manufacturing process can either be based on manual operations or robotic machines. The manual option costs nothing to install, has operating cost of $300,000 per year and will last indefinitely. The robotic option costs $1,000,000 to install, has no annual operating cost, but will last only 3 years. The manual option has no salvage value, but the robotic option has a salvage value of $500,000 when you sell it after 3 years. Both methods produce the product equally well. Neglect inflation for this problem. Do an after tax analysis to help the company make the right choice. The robotic option is depreciated with the ACRS method using the 3-year class. Depreciation percentages are shown below. The tax rate is 40%. The company s after tax MARR is 15% per year. Year Percent % % % % 6. (10 Points) You have three options to perform some function. The required investment and annual costs are shown below. Use a rate of return analysis to select the best. All three options have 0 salvage. Your MARR is 20%. Compute rates to nearest interest rates given in the tables at the end of the test. Option A B C Investment Annual Cost Life

4 7. (12 Points) A chemical plant stores raw materials, finished goods and intermediate products in tanks. The materials are pumped to and from the various processing operations through pipes. There are several pumps in the system. The original investment in the pumps was $500,000 when they were purchased 3 years ago. Unfortunately, there must be a design problem because the pumps are leaking. Last year $180,000 was spent to replace seals and to clean up leaked materials at the pumps. The plant management is tired of the expense of pump repair and is considering two alternatives. The first alternative is to extensively rebuild the pumps. Management likes this idea because the original cost of the pumps will not have been entirely wasted. The renovation cost for the pumps will be $200,000. If this is done the maintenance cost will be reduced to $60,000 next year. If the renovated pumps are kept for a second year, the maintenance cost will increase to $120,000. For the third year, the maintenance cost will be back to $180,000. The renovated pumps will last no more than 3 years. The scrap value of the pumps is $100,000 if they are removed now or at any time in the future. The second alternative is to replace the pumps with an advanced design with gas seals. The cost to purchase and install the gas seal pumps and the gas distribution system that they require is $600,000. The annual cost of maintaining the gas system is $40,000. Its salvage value is zero. The economic life of the new pump system is five years. Using a 15% MARR make the most economic decision for the plant. Should the pumps be renovated or replaced? Justify your conclusion. 8. (12 Points) You own a site at which there is the possibility of discovering oil. Your options are: a 1 : drill for oil yourself, a 2 : lease the site to someone else to drill, a 3 : lease the site, but maintain an interest in the results. There are four possible outcomes regarding the success of the well. q 1 : 600,000 barrel well, q 2 : 400,000 barrel well, q 3 : 100,000 barrel well, q 4 : dry hole. Your net present worth of the profit depends on which development option you choose and the results of the drilling. NPW Profit Well success q 1 q 2 q 3 q 4 a Option a a Based on information about the site we make estimates of probabilities of the four results P(q 1 ) = 0.1, P(q 2 ) = 0.15, P(q 3 ) = 0.25, P(q 4 ) = 0.5. a. Compute the expected value of the three drilling options. In order to maximize your expected value, which option should you choose? 4

5 b. Compute the standard deviations of the option that you chose in part a and the option with the second highest expected value? Comment on what role the standard deviation might play in your decision process. 9. (12 Points) The questions in this problem use the cash flow shown at the right. When formulas are requested in the question, use as few factors as possible a. What is the NAW of the cash flow for a 4-year study period when the MARR is 0%? b. Write the formula for the NAW. Use i as the interest rate in the formula. c. We compute the NAW of the cash flow using i = 30% to be $ Now we want to analyze the cash flow with inflation. Say the general inflation rate is 10% and the cash flow above is expressed in real dollars. The value of i r = 30%. Write the formula for the NPW expressed in actual dollars. Use a numerical interest rate in your formula. d. The $1200 value at time 0 is an investment. We depreciate the investment using the SYD method with a tax life of 4 years and a tax salvage of 0. Write the formula for the NAW of the after tax cash flows. The tax rate is 50%. Use i as the after-tax MARR. 5

6 Compound Interest Factors (F/P, i, n) = (1 + i) n Single Payment Compound Amount Factor Single Payment Present Worth Factor (P/F, i, n) = 1 (1 + i) n = 1 (F/P, i, n) Uniform Series Compound Amount Factor (F/A, i, n) = (1 + i)n 1 i Uniform Series Sinking Fund Factor (A/F, i, n) = i (1 + i) n 1 = 1 (F/A, i, n) Uniform Series Present Worth Factor (P/A, i, n) = (1 + i)n 1 i(1 + i) n Uniform Series Capital Recovery Factor (A/P, i, n) = i(1 + i) n (1 + i) n 1 = 1 (P/A, i, n) Arithmetic Gradient Present Worth Factor (P/G, i, n) = (1 + i)n in 1 i 2 (1 + i) n Arithmetic Gradient Uniform Series Factor (A/G, i, n) = (1 + i)n in 1 i(1 + i) n i Factor Table for 5 periods at various interest rates Periods Interest F/P P/F A/F A/P F/A P/A A/G P/G Interest 0.00% % 0.25% % 0.50% % 0.75% % 1% % 2% % 3% % 4% % 5% % 6% % 7% % 8% % 9% % 10% % 12% % 15% % 18% % 20% % 25% % 30% % 35% % 40% % 45% % 6

7 50% % Periods 5 5 Interest F/P P/F A/F A/P F/A P/A A/G P/G Interest 0.00% % 0.25% % 0.50% % 0.75% % 1% % 2% % 3% % 4% % 5% % 6% % 7% % 8% % 9% % 10% % 12% % 15% % 18% % 20% % 25% % 30% % 35% % 40% % 45% % 50% % 7

8 Factor Table for an interest rate of 15%. Interest Rate 1 5 % 15% n F/P P/F A/F A/P F/A P/A A/G P/G n inf. inf inf inf. 8