#18: /10 #19: /9 Total: /19 VERSION 1 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 Wednesday, 12 November, 2008 90 minutes PRINT your family name / initial and record your student ID number in the spaces provided below. FAMILY NAME / INITIAL STUDENT ID # S O L U T I O N S This test consists of 17 multiple-choice questions, and two problems requiring a full solution. The multiple-choice question are worth a total of 81 points. There are no penalties for incorrect answers. The problems are worth a total of 19 points. MULTIPLE-CHOICE QUESTIONS Circle the correct answers on this test paper and record them on the computer answer sheet. Multiple-choice Statements Circle the correct answer on this test paper and record it on the computer answer sheet. (2.5 points each for a total of 15) Note: There are no penalties for incorrect answers. 1. When investment alternatives are mutually exclusive, A) they can only be accepted if capital funds are limited. B) the selection of one alternative excludes the selection of all other alternatives. C) the selection of one alternative is not affected by either the selection or rejection of another alternative. D) the present value ratio should be used to rank the projects. E) the firm can decide to proceed with as many projects as possible. 2. In which one of the following situations will a firm in a perfectly competitive market earn profits? A) Marginal revenue > average variable costs B) Marginal revenue > average cost C) Average cost > marginal cost D) Average cost > average revenue E) Average revenue > average variable cost 1
3. Which one of the statements listed below is correct? A) Preferred shares allow the expansion of a company s equity base without diluting the voting power of the bondholders. B) The objective of business firms that attempt to maintain a pre-determined capital structure in the long run is to maximise their weighted-average cost of capital. C) The maturity date on a bond specifies the time at which the interest becomes payable. D) Leverage refers to the ability of a business to increase its return on equity by including long-term debt in its capital structure. E) The periodical interest payment paid by a bond is called its yield-to-maturity. 4. Which capital investment evaluation criterion is described by the following characteristics? (1) Is a measure of investment efficiency; (2) May result in multiple answers; (3) May lead to incorrect decisions when applied to mutually exclusive investment projects. A) Net present value B) Internal rate of return C) Accounting rate of return D) Payback period E) Discounted payback period 5. The figure below represents the curves necessary for a perfectly competitive firm to make its production decision (ATC: average cost, MC: marginal cost). In the short run, if the market price of the product is $8 (horizontal line), the firm should produce of output, thus incurring a. A) 10 units; loss of $40 B) 10 units; loss of $80 C) less than 10 units; loss of $120 D) 10 units; profit of $40 E) less than 10 units; loss of less than $40, but greater than $0 In the short run, produce as long as the selling price is above the MC. In the figure, the MC curve crosses the selling price a little below a quantity of 10 units. 6. The payback period rule can be best stated as: A) A project is acceptable if its payback period is less than some pre-specified number of years. B) A project should be accepted if its payback period is positive and rejected if it is negative. C) A project should be rejected if its payback period is positive and accepted if it is negative. D) A project is acceptable if its payback period is greater than some pre-specified number of years. are acceptable. 2
Problems with Multiple-choice Answers Circle the correct answer on this paper and record it on the computer answer sheet. (6 points each for a total of 66) Note: There are no penalties for incorrect answers. 7. Suppose that the Canadian Space Agency has two mutually exclusive projects: landing a woman on Mars or landing a man on Venus. Project Mars has an IRR of 12 percent and project Venus has an IRR of 15 percent. The WACC is 8 percent and the crossover rate (i.e. the rate at which both projects have equal NPVs) is 9 percent. Which project(s) should be accepted? A) Mars B) Venus C) Both Mars and Venus D) Neither Mars nor Venus E) Insufficient information to determine From the IRR results, it is concluded that project Venus has a greater NPV than project Mars above a discount rate of 9%. Therefore, Mars has the greater NPV at a discount rate below 9%. 8. Suppose you have an opportunity to invest in a project expected to generate $6800 in year 1, $7200 in year 2 and $7500 in year 3. The appropriate discount rate is 10.5 percent. What is the project s initial investment (i.e. at t=0) if its NPV is $2609? A) $15 000 B) $17 609 C) $20 218 D) $21 500 E) $18 891 Using CF worksheet with I/Y=10.5%, Discounted +CFs: CPT NPV 17 609 CF 0 = 17 609 2609 = -15 000 9. Suppose that you have an opportunity to invest in a project that requires a cash outlay of $25 000 today. The project is expected to generate its first cash flow of $8000 in year 2, which will remain constant over a period of ten years. Given a WACC of 14 percent, what is the project s NPV? A) $7109 B) $9236 C) $11 604 NPV @ 14%: -25 000 + 8000 (P/A,14%,10) / 1.14 = 11 604 D) $16 729 10. What is the IRR of a project that requires an investment of $9900 today and generates cash flows of $1500 per year over a ten-year period as well as an additional $10 000 at the end of the tenth year? A) 8.4 % B) 11.8 % C) 14.4 % D) 15.2 % Using TVM keys with N=10, PV= -9900, PMT= 1500 and FV=10 000, CPT I/Y 15.20 % 3
11. What is the payback period of a project that requires a cash outlay of $16 000 today and generates cash flows of $4500 in year 1, $5500 in year 2, $6500 in year 3, and $7500 in year 4? Assume a cost of capital of 10 percent. A) 2.1 years B) 2.4 years C) 2.7 years D) 2.9 years E) 3.5 years Cumulative CF: (0) -16 000, (1) -11 500, (2) -6000, (3) 500, (4) 8000 PP: 2 + 6000 / 6500 = 2.92 12. A firm has determined the cost of each of its sources of capital along with its optimal capital structure expressed as target market value proportions: Source of capital Target Market Proportion (%) After-tax Cost (%) Long-term debt 40 6 Preferred equity 10 11 Common equity 50 15 The firm s weighted-average cost of capital is: A) 11.0 % B) 15.0 % C) 10.7 % WACC: 6 (0.4) + 11 (0.1) + 15 (0.5) = 11.0 % D) 6.0 % 13. Five years ago, a firm s issued 12-year bonds with a face value of $1000 and a coupon rate of 8 percent paid semi-annually. Issuing expenses amounted to $50 per bond on an after-tax basis. The bonds now have a market value of $1106. Using a corporate tax rate of 36 percent, the cost of existing debt to the firm is: A) 5.2 % B) 8.9 % C) 3.4 % D) 6.1 % Semi-annual after-tax interest payment: 1000 (0.08) / 2 (1-0.36) = 25.60 With N=14, PV= -1106, PMT=25.60 and FV=1000, CPT I/Y 1.70 % Convert to an effective annual rate: (1 + 0.017) 2-1 = 3.43 % 14. A firm is evaluating two independent projects using the internal rate of return. Project X has an initial investment (t=0) of $80 000 and cash inflows of $25 000 over a life of five years. Project Z has an initial investment (t=0) of $120 000 and cash inflows of $40 000 over a life of four years. The firm should: A) reject both projects if its cost of capital is 11 %. B) accept both projects if its cost of capital is 15 %. C) accept only X if its cost of capital is 15 %. D) accept only Z if its cost of capital is 15 %. E) accept both projects if its cost of capital is 18 %. Internal rates of return X: With N=5, PV= -80 and PMT=25, CPT I/Y 17.0 % Z: With N=4, PV= -120 and PMT=40, CPT I/Y 12.6% 4
15. Stephenson & Sons maintains a capital structure consisting of 20 percent common equity and 80 percent debt. The company expects to report $3 million in net income this year, and 60 percent of this amount will be paid out in dividends. How large can the firm s capital budget (i.e. the amount it can invest) be this year without having to issue any new common shares? A) $1.20 million B) $13.00 million C) $1.50 million D) $0.24 million E) $6.00 million Earnings retained: 3 (1 0.6) = 1.2 This amount represents the equity component of the budget, i.e. 20% of the total, according to the capital structure. ignoring issuing expenses on debt, total budget: 1.2 / 0.2 = $6.0 Use the following information to answer questions 16 and 17. Ozark Industries total monthly production costs (TC) function are: TC = 6 + 22 R + 2 R 2 in which TC is expressed in thousands of dollars and R, the monthly production rate, is expressed in thousands of units. 16. Given a constant selling price of $30 per unit, the break-even production rate is: A) 3000 At break-even, TR = TC B) 2000 30 R = 6 + 22 R + 2 R 2 C) 1000 2 R 2 8 R + 6 = 0 D) 5500 (2 R 2) (R 3) = 0 R 1 =1 and R 2 =3 (lower root is B/E rate) 17. Given a constant selling price of $30 per unit, the production rate that maximises the monthly before-tax profit is: A) 1000 B) 2000 C) 3000 D) 5500 Annual BT profit maximised at rate at which MC=MR. 22 + 4 R = 30 R=2 5
FULL-SOLUTION PROBLEMS For full marks, give complete solutions on the lines provided and record your answers in the boxes. 18. A company must choose between two mutually exclusive projects, Alpha and Bravo, to enhance its current operations. The projects have the following cash flows: Time 0 Year 1 Year 2 Year 3 Year 4 Alpha CFs ($) -12 000 6000 6500 7000 Bravo CFs ($) -20 000 7000 8000 9000 7800 The cost of capital is 10 percent. Assuming that both projects can be replicated, which one should the firm choose? Justify your answer. (10 points) (V2: COC=8%) VERSION 1 NPV Alpha : Using CF worksheet with I/Y=10%, CPT NPV 4086; CPT PMT -1643 NPV Bravo : Using CF worksheet with I/Y=10%, CPT NPV 5065; CPT PMT -1598 Since the projects have different lives, their NPVs over a common period must be compared. Alpha over 12 years: Using CF worksheet with CFs of 4086 at t=0, 3, 6 and 9 and I/Y=10%, CPT NPV $11 195 Bravo over 12 years: Using CF worksheet with CFs of 5065 at t=0, 4 and 8 and I/Y=10%, CPT NPV $10 887 Choose Alpha with the higher overall NPV or EAR VERSION 2 NPV Alpha : Using CF worksheet with I/Y=8%, CPT NPV 4685; CPT PMT -1818 NPV Bravo : Using CF worksheet with I/Y=8%, CPT NPV 6218; CPT PMT -1877 Since the projects have different lives, their NPVs over a common period must be compared. Alpha over 12 years: Using CF worksheet with CFs of 4685 at t=0, 3, 6 and 9, and I/Y=8%, CPT NPV $13 700 Bravo over 12 years: Using CF worksheet with CFs of 6218 at t=0, 4 and 8, and I/Y=8%, CPT NPV $14 148 Choose Bravo with the higher overall NPV or EAR ANSWER Alpha with higher overall NPV or EAR 6
19. Due to expanding business activities, a construction company is planning to add a truck to its existing fleet. The company s is considering the purchase of a truck that costs $95 000, has a useful life of three years, and operating and maintenance costs of $20 000, $25 000 and $30 000 in years 1, 2 and 3, respectively. The truck has a salvage value of $35 000. If the company s cost of capital is 12 percent, what minimum annual benefit must the truck generate to justify its purchase? (9 points) (V2: COC=10%) VERSION 1 PV of overall costs: 95 000-35 000 (P/F,12%,3) + 20 000 (P/F,12%,1) + 25 000 (P/F,12%,2) + 30 000 (P/F,12%,3) = 129 228 EA costs: 129 228 (A/P,12%,3) = 53 804 The minimum annual benefit must equal the equivalent annual costs, i.e. $53 804. VERSION 2 PV of overall costs: 95 000-35 000 (P/F,10%,3) + 20 000 (P/F,10%,1) + 25 000 (P/F,10%,2) + 30 000 (P/F,10%,3) = 130 086 EA costs: 130 669 (A/P,10%,3) = 52 310 The minimum annual benefit must equal the equivalent annual costs, i.e. $52 310. ANSWER $53 804 This is the last page of the test paper. 7
Answer Key for Version 2 1. C 2. D 3. A 4. D 5. B 6. C 7. C 8. E 9. A 10. A 11. B 12. D 13. A 14. B 15. C 16. A 17. D 8