M I M E 3 1 0 E N G I N E E R I N G E C O N O M Y Class Test #2 Thursday, 23 March, 2006 90 minutes PRINT your family name / initial and record your student ID number in the spaces provided below. FAMILY NAME / INITIAL S O L U T I O N S STUDENT ID # This test consists of 22 multiple-choice questions, and three problems with sub- questions requiring full solutions. There are no penalties for incorrect answers. The problems are worth a total of 30 points. MULTIPLE-CHOICE QUESTIONS Circle the correct answer on this test paper and record it on the computer answer sheet. PART 1. True or False Statements Circle the correct answer on this paper and record it on the computer answer sheet. (1.5 points each for a total of 12) Note: There are no penalties for incorrect answers. 1. If a firm has to choose among a number of projects, some of which are mutually exclusive and some of which are independent, it must first determine the best of each group of mutually exclusive alternatives. Then, the best of the acceptable independent projects can be selected. 2. To increase its production capacity, a firm is considering three options: 1) to expand its plant; 2) to acquire another company; 3) to contract with another company for production. These three options are examples of independent projects. 3. The specific cost of each source of financing is the after-tax cost of obtaining the financing using the historically based cost reflected by the existing financing on the firm's books. 1
4. An internal rate of return greater than the cost of capital guarantees that the firm earns at least its required return. Such an outcome should enhance the market value of the firm and therefore, the wealth of its shareholders. 5. Preferred stock represents a special type of ownership interest in the firm and thus, the preferred stockholders must receive their stated dividends prior to the distribution of any earnings to common stockholders and bondholders. 6. The acceptance of projects beginning with those having the greatest positive difference between their IRR and the weighted-average cost of capital (WACC), down to the point at which IRR just equals the WACC, should result in the maximum total NPV for all independent projects accepted. 7. One weakness of the payback period is its failure to recognize cash flows that occur beyond the payback period. 8. The internal rate of return (IRR) is defined as the discount rate that equates the net present value of a project with its discounted capital investment. PART 2. Multiple-choice Statements Circle the correct answer on this paper and record it on the computer answer sheet. (2 points each for a total of 8) Note: There are no penalties for incorrect answers. 9. A project has a return on investment equal to the firm s cost of capital of 15 % and a five year production life. Which of the following statements is inconsistent with the other four? A) The discounted payback period is five years. B) Profitability Index = 0 C) NPV = $0. D) IRR = 15 %. E) The present value of the production period cash flows equals the absolute present value of the investment period cash flows. 10. When using the internal rate of return criterion to select projects, it is assumed that cash flows can be reinvested at the: A) cost of raising funds through equity sources (i.e. issuing shares). B) cost of capital. C) internal rate of return. D) prevailing interest rate. E) all of the above. 2
11. Which one of the following statements is correct concerning the accounting rate of return (ARR)? A) The average book value used in the ARR formula will always equal one-half of the initial investment as long as the investment is depreciated by the straight-line method down to a salvage value of zero over the life of the project. B) The average net income is the same as the total cash flow from the project less the initial cash outflows representing the capital investment. C) The ARR is similar to the profitability index in that both are based on accounting values rather than on financial cash flows. D) Under the ARR rule, a project should be accepted if the targeted ARR is greater than the project's ARR. E) The ARR is a true financial rate of return, which is relatively easy to compute. 12. Which of the following statements correctly ranks the accounting rate of return (ARR), discounted payback period (DPP) and net present value (NPV) from the most useful to the least useful in project ranking? A) ARR, DPP, NPV B) ARR, NPV, DPP C) DPP, ARR, NPV D) NPV, ARR, DPP E) NPV, DPP, ARR PART 3. Multiple-choice Problems Circle the correct answer on this paper and record it on the computer answer sheet. (5 points each for a total of 50) Note: There are no penalties for incorrect answers. 13. Ginny is considering two independent projects. Each project requires an initial investment of $10 000. Project A produces cash inflows of $3000 per year for four years and Project B produces no cash flows over the first two years and $6000 per year for the following two years. Ginny wants to recover her investment within 3 years. What should Ginny do? A) She should accept both projects. B) She should accept Project A and reject Project B. C) She should reject Project A and accept Project B. D) She should reject both projects. E) Ginny cannot make a decision based on the information provided. 14. A firm is evaluating two independent projects utilizing the internal rate of return criterion. Project X has an initial investment of $80 000 and cash inflows of $25 000 over each of the next five years. Project Z has an initial investment of $120 000 and cash inflows of $40 000 over each of the next four years. The firm should: A) accept both projects if its cost of capital is 15 %. B) accept only project Z if its cost of capital is 15 %. C) reject both projects if its cost of capital is 12 %. D) accept only project X if its cost of capital is 15 %. Payback A: 10 000 / 3000 = 3.33 yrs Payback B: 2+ 10 000 / 6000 = 3.67 yrs Both projects have a PP > 3. Using the TVM functions, find I/Y (i.e. IRR) using N, PV and PMT. IRR X : 17.0 % IRR Z : 12.6 % Only project X has an IRR > 15 % 3
Use the information below to answer questions 15 to 17. A fibreglass boat producer sells his boats for $700 apiece. At a production rate of 100 boats per month, the selling price of $700 consists of an average fixed cost of $210, an average variable cost of $400 and a profit margin of $90. Assume a linear production cost function. 15. The contribution margin is: A) $300 B) $490 C) $90 D) $100 For a linear cost function, vc is constant Contribution margin: (p vc) = 700 400 = $300 16. The monthly break-even production rate (units) is: A) 700 B) 70 C) 43 D) 53 17. By how much must the fixed monthly cost be reduced if the break-even rate is to be 60 units per month? A) $7000 B) $1800 C) $3000 D) $8400 FC: fc (100) = 210 (100) = 21 000 B/E: FC / (p vc) = 21 000 / (700 400) = 70 For B/E=60 FC: 60 (p vc) = 60 (700 400) = $18 000 \FC must be reduced by $3000. Use the information below to answer questions 18 and 19. A firm is evaluating two mutually exclusive projects with cash flows as given below. Year Project A Project B Time 0-200 -275 1 100 125 2 100 125 3 100 125 18. Based on the profitability index (PI) and a discount rate of 14 %, which of the following statement is true? PI A) The PI of project A is less than 1.0. A : 100 (P/A,14%,3) / 200 = 1.16 PI B : 125 (P/A,14%,3) / 275 = 1.05 B) The PI of project B is less than 1.0. C) Based on the PI, project A is preferable in a situation in which funds are limited. D) Both projects would be rejected based on the PI criterion. E) Judging from the PIs, it is obvious that the IRR of both projects is less than 14 %. 4
19. The crossover rate for the projects, i.e. the discount rate at which their NPVs are equal, is: A) The NPV profiles of the projects do not cross over B) 0.0 % C) 2.2 % D) 3.5 % E) 8.7 % 20. Suppose a firm invests $600 in a project. The initial cost is depreciated by the straight-line method down to zero over 3 years. The net income from the project is $100, $125, and $140 in each of the three years of it's life. The accounting rate of return is: A) 20.3 % B) 35.5 % C) 40.6 % D) 60.8 % 21. Based on market values, a firm s debt ratio is 2 : 5 and its debt to equity ratio is 3 : 5. The weights to use for debt and equity in the calculation of the firm s weighted-average cost of capital are, respectively: A) 0.2857 and 0.7143 B) 0.3750 and 0.6250 C) 0.40 and 0.60 D) 0.60 and 0.40 22. A project is characterised by the following distribution of operating profits (i.e. revenues less operating expenses): Year Operating Profits ($) 1 to 2 40 000 3 to 8 80 000 9 to 12 60 000 13 to 15 40 000 At the end of its 15-year life, the project will require dismantling expenses of $30 000. Given a minimum acceptable return on investment of 14 percent, the maximum capital investment that can be incurred at time 0 is: (round your answer to the nearest $100) A) $376 048 B) $385 803 C) $381 600 D) $380 200 If NPV A = NPV B, then NPV A-B = 0: CF at time 0 1 2 3-75 25 25 25 Find i for NPV=0 IRR=0 % Average net income: (100 + 125 + 140) / 3 = 121.67 Average investment: 600 /2 = 300 ARR: 121.67 / 300 = 0.4056 The debt ratio is irrelevant. A debt to equity ratio of 3 : 5 indicates that for every $3 of debt, there are $5 of equity. Thus, the weights are for debt, 3/8 and for equity, 5/8. The PV of operating profits @ 14% is the maximum capital investment that can be incurred at t=0. Note that CF 15 is (40 000-30 000 ) or $10 000. Using the cash flow worksheet in the BA II Plus, PV=381 600. 5
FULL-SOLUTION PROBLEMS For full marks, show the complete solutions on the lines provided and record the answers in the boxes. 23. Two machines are being considered to perform a particular job. Machine A has an initial cost of $65 000, annual operating costs of $22 000 and a salvage value of $15 000 at the end of its useful life of 5 years. Machine B has an initial cost of $95 000, annual operating costs of $18 000 and a salvage value of $30 000 at the end of its useful life of 8 years. Using a cost of capital of 12 percent, which machine is economically preferred? Show your mathematical approach and justify your answer. (8 points) Determine the EAC of each machine over its life. For A, N=5, I/Y=12%, PV=65 000 and FV= -15 000. CPT PMT 15 670 \ EAC A : 15 670 + 22 000 = $37 670 For B, N=8, I/Y=12%, PV=95 000 and FV= -30 000. CPT PMT 16 685 \ EAC B : 16 685 + 18 000 = $34 685 \ Machine B with the lowest EAC is preferred. Determine the EAC of each machine over its life. For A, N=5, I/Y=12%, PV=65 000 and FV= -15 000. CPT PMT 15 670 \ EAC A : 15 670 + 20 000 = $35 670 For B, N=8, I/Y=12%, PV=95 000 and FV= -30 000. CPT PMT 16 685 \ EAC B : 16 685 + 20 000 = $36 685 \ Machine A with the lowest EAC is preferred. Machine B is economically preferred because it has the lowest equivalent annual cost. ($34 685 for B versus $37 670 for A) 6
24. Based on market values, a firm s capital structure consists of 60 percent long-term debt and 40 percent common equity. The firm is subject to an income tax rate of 40 percent. LONG-TERM DEBT The firm s existing long-term debt consists of bonds with a face value of $1000, a coupon rate of 5 percent payable semi-annually, 8 years to maturity and a market price of $975. EQUITY The firm's common stock has a current market price of $75 per share. The dividend expected at the end of the coming year is $5. Dividend payments have been growing at a constant rate. Five years ago, the dividend payment was $3.10. 24.1 Determine the after-tax cost of funds associated with the firm s existing common equity. (5 points) (Growth rate of 8.29% over 6 years) 14.96 % Dividend growth rate over past 6 years: 3.10 (1 + g) 6 = 5.00 g=8.29% K e : 5 / 75 + 0.0829 = 0.1496 or 14.96% Dividend growth rate over past 7 years: 3.10 (1 + g) 7 = 5.00 g=7.07% K e : 5 / 75 + 0.0707 = 0.1374 or 13.74% 14.96 % 24.2 Determine the after-tax cost of funds associated with the firm s existing debt. (5 points) Semi-annual A-T coupon: 1000 (0.025) (1 t) = 25 (1 0.4) = 15 With N=16, PV= -975, PMT=15 and FV=1000, CPT I/Y 1.68% K d : (1 + 0.0168) 2 1 = 0.0339 or 3.39% Semi-annual A-T coupon: 1000 (0.03) (1 t) = 30 (1 0.4) = 18 With N=16, PV= -975, PMT=18 and FV=1000, CPT I/Y 1.98% K d : (1 + 0.0198) 2 1 = 0.0400 or 4.00% 3.39 % 7
24.3 Determine the firm s existing weighted-average cost of capital. (5 points) WACC: 3.39 (0.6) + 14.96 (0.4) = 8.02% WACC: 4.00 (0.6) + 13.74 (0.4) = 7.90% 8.02 % 25. A firm is to finance a project requiring an investment of $60 million. Using external financing, the firm will incur after-tax issuing expenses of 10 % of the market price for equity sources and 6.5 % of the face value for debt sources. The target capital structure is 60 percent debt and 40 percent equity. How many common shares at a market price of $100 must the firm issue? (7 points) $60 mil. are required after issuing expenses. Thus, $Debt (1 0.065) + $Equity (1 0.1) = 60 mil. Debt/Equity: 60 / 40 = 1.5 Debt = 1.5 Equity 1.5 $Equity (1 0.065) + $Equity (1 0.1) = 60 $Equity = $26.059 mil. \ # shares: 26.059 / 100 = 260 590 $60 mil. are required after issuing expenses. Thus, $Debt (1 0.065) + $Equity (1 0.1) = 60 mil. Debt/Equity: 60 / 40 = 1.5 Equity = Debt / 1.5 $Debt (1 0.065) + ($Debt / 1.5) (1 0.1) = 60 $Debt = $39.088 mil. \ # bonds: 39.088 / 1000 = 39 088 260 590 common shares THIS IS THE LAST PAGE OF THE TEST PAPER 8
Answer Key for Version #2 1. A 2. A 3. B 4. A 5. B 6. A 7. B 8. B 9. D 10. A 11. B 12. E 13. A 14. B 15. C 16. C 17. B 18. D 19. E 20. B 21. D 22. B 9