M I M E E N G I N E E R I N G E C O N O M Y SAMPLE CLASS TESTS. Department of Mining and Materials Engineering McGill University

Transcription

1 M I M E E N G I N E E R I N G E C O N O M Y SAMPLE CLASS TESTS Department of Mining and Materials Engineering McGill University

2 F O R E W O R D The following are recent Engineering Economy class tests. Their purpose is to give you examples of typical problems that you should be able to solve in the course of such tests. These are supplied without solutions (answers are given for numerical problems), to maximize the benefits that you will derive from solving them on your own. If you have questions concerning any particular problem, please consult the TAs or course instructor(s) during the appropriate hours. Prof. Bilodeau Note: Prior to the Fall 2003 term, the second class test covered material from chapters 1 to 6. ii

3 TEST # 2 FALL '04 PART 1. Multiple-choice Problems and Statements Use the following information to answer questions 1 to 3. A fiberglass boat producer has the following production variables: Fixed cost (FC), $ per month; constant average variable cost (vc), $320; selling price (p), $ Determine the contribution margin if the fixed cost is reduced to $5000, the average variable cost is increased to $520, and the selling price is increased to $720. [$200] 2. By how much must the fixed cost be reduced if the break-even rate is to be 40 units per month? [ $7800] 3. Which statement(s) is/are correct when the situation in question 1 above is compared to the original situation described in the problem statement? [I, II & III] I) More flexible operation II) Less risk III) Higher profit growth 4. RJ purchased at par a bond with a 10% annual coupon, 5 years to maturity and a face value of $1000. On the day he received the second coupon payment, RJ sold the bond for $1200 and immediately reinvested this amount in other bonds with a 7% annual coupon, 3 years to maturity and selling at their par value of $1000 (assume that RJ can purchase a fraction of a bond, so that the full $1200 can be reinvested). If RJ kept these second bonds to maturity, what was his yield-to-maturity over the five-year period? [12.28 %] 5. A project with an initial investment of $ will generate cash flows of $3000 per year over a 5-year period. The discount rate is %. The project s net present value (NPV) and internal rate of return (IRR) are, respectively: [$0.764 and 15.2 %] 6. A project that costs $1.5 million today will generate annual cash flows of $1 million for the next 3 years. At the end of 3 years, the project s salvage value will be zero, but there will be a disposal expenditure of $ The internal rate of return (IRR) of this project is: [34.6 %] 7. Consider a 10-year period characterised by payments of $ at the beginning of years 8, 9 and 10. Determine the equivalent ordinary annuity over the first seven-year period using an interest rate of 12% compounded annually over the first seven years, and 10% compounded annually over the final three years. (Round to the nearest hundred dollars) [$5400] 8. Order the investment criteria of accounting rate of return (ARR), discounted payback period (DPP) and net present value (NPV) from the most desirable to the least desirable? [NPV, DPP, ARR] 9. GJ Inc. is considering an investment proposal that will yield cash flows of $ per year in years 1 through 4, $ per year in years 5 through 9, and $ in year 10. This project will cost the firm $ today. Assuming that money flows uniformly during the year and the firm's cost of capital is 10 percent, the payback period (PP) for this proposal is: [4.9 years] 10. What is the discounted payback period (DPP) of the following project if the cost of capital is 14%? [4.6 years] Year Time Cash Flow -$

4 11. A corporation plans to purchase an asset costing $ for the purpose of reducing its production costs. This purchase will generate taxable income of $3750 in each of years 1 and 2 following the asset s acquisition, and $4750 in each of years 3 and 4. The expected salvage value of the asset at the end of its four-year life is $5000. The corporation pays 40% of its taxable income in taxes and requires an 8% return on investment. Determine the accounting rate of return (ARR) of the project. [34 %] 12. A project that requires an initial investment (i.e. at time 0) of $ will begin production in three year s time. Once in production, the project will generate cash flows of $1200 per year over a thirty-year period, and of $500 per year thereafter. The cost of capital is 10%. Determine the present value of the production period cash flows at the time of the initial investment. (Round to the nearest hundred dollars) [$8700] 13. Referring back to the information given in question 12 above, what would the project's cash flows beyond the 30-year production period need to be in order to break-even (i.e. yield a rate of return of 10%)? (Round to the nearest ten dollars) [$4650] 14. Consider the following two mutually exclusive alternatives which have common benefits: Alternative A B Immediate investment ($) Life (yrs) 8 8 Salvage value ($) Annual maintenance expense ($) Using a cost of capital of 10 percent, the incremental benefit-cost ratio of choosing alternative B over alternative A is: [0.49 or 0.52] 15. A firm needs $165 million to finance a project. If external financing is used, the firm will incur issuing expenses of 8% for equity (i.e. it will realize 92% of the value issued) and 2.5% for debt. Given that the project is to be financed with 60% equity and 40% debt, how much funds must the firm raise in order to finance the project? [$175.2 million] PART 2. Full-solution Problems 16. BJ Industries has 6.5 million common shares (par value of $5) outstanding with a market price of $14 per share. The company also has outstanding preferred shares with a market value of $10 million, and bonds, each with a face value $1000 and priced at 90% of par on the market. The before-tax cost of existing preferred equity is 10% and that of existing debt is 7.25%. BJ's tax rate is 34% Given that BJ s current common dividend is $1 and that dividends are expected to grow at an annual rate of 6%, determine BJ s cost of existing common equity. [13.6 %] 16.2 Assuming now that BJ s cost of existing common equity is 14%, determine the company s after-tax cost of capital (WACC). [12.0 %] 2

5 17. Complete the following table, rounding each missing value to the nearest whole amount. (Values given are in bold characters) Output Total Cost Fixed Cost Variable Cost Average Cost Incremental Cost Average Fixed Cost Average Variable Cost TEST # 1 FALL '04 PART 1. Multiple-choice Problems and Statements 1. You have just won a lottery prize. You can choose to receive a lump-sum payment of $ today, or an annual payment of $ at the end of each of the next 20 years. The interest rate that makes you indifferent between the two options is 2.91 percent (at two decimal precision), and at higher interest rates, you should choose the lump-sum payment. A) True B) False.2. You are considering two bonds identical in every respect except for coupon frequency bond A pays interest annually, and bond B pays interest semi-annually. If the bonds have the same market price, the yield-to-maturity on bond A is greater than that on bond B. A) True B) False 3. Six years ago, Marti deposited $3500 in an bank account. No other deposits or withdrawals have been made since. Today the account is worth $ What annual interest rate did Marti earn thus far? [13.30 %] 4. Today, Richard is investing $1000 at an annual interest rate of 5% for five years. One year ago, Richard invested $1000 at 6.25% for six years. How much money will Richard have saved in total five years from now if both investments compound interest annually? [$ ] 5. Sampson Inc. invested $ in a project that earned an annual interest rate of 8.25%. Sampson sold the project for $ How much sooner could Sampson have sold the project if they only wanted $3 million while maintaining the same interest rate? [2.69 years] 6. J&J Enterprises wants to issue 20-year, $1000 face value, zero-coupon bonds (i.e. the bonds do not pay any annual interest). If the bonds are to have a yield to maturity of 8%, how many bonds must J&J sell to raise a minimum of $2 million? (Ignore any issuing costs) [9322 ] 3

6 7. The bonds of Microhard Inc. carry a 10% annual coupon (i.e. interest paid once per year), have a face value of $1000, and mature in four years. Bonds of equivalent risk have a yield of 15%. Microhard is having is having liquidity problems and has asked its bondholders to accept the following arrangement: the firm would make the next three coupon payments at half the scheduled amount, and make the final coupon payment in an amount of $250. If this plan is accepted by the bondholders and the required yield is maintained at 15%, what will be the market price of the bonds? [$ ] 8. The annual maintenance costs on equipment you have just purchased are expected to be $500, $700, $1400, and $1400, respectively, over the next four years. At an annual interest rate of 10%, what equal annual sum is equivalent to these costs (assume end-of-period convention and round to the nearest ten dollars)? [$960] 9. A firm has a current ratio of 2.1. If dividends payable are paid using the cash account, the current ratio will: [B] A) remain unchanged B) increase C) decrease 10. A firm has a current ratio of 2.1. If dividends payable are paid from a line of credit (i.e. a short-term bank loan), the quick ratio will: [A] A) remain unchanged B) increase C) decrease 11. All other things held constant, which of the following transactions will cause a firm s current ratio (presently at 1.2) to increase? [C or D] A) some accounts payable are paid using the firm s line of credit B) fixed assets are purchased using a long-term bank loan C) accounts payable are paid with funds from the cash account D) a sale is made but not immediately paid by the client E) none of the transactions above will cause the current ratio to increase 12. George Inc. s annual income statement indicates sales of $ The firm s balance sheet shows an accounts receivable balance of $ What is George Inc. s average collection period? [44 days] 13. Bernard Inc. has a cost of goods sold of $ on sales of $ The firm s balance sheet shows total assets of $ and an inventory balance of $ What is Bernard Inc. s inventory turnover ratio? [7.0 times ] 14. Shaw Inc. has an average quarterly net income of $50 000, average accounts receivable of $ , average quarterly sales of $ and average total assets of $ What is Shaw s return on total assets? [8 %] 15. An asset costs $ and has a salvage value of $ at the end of its 5-year life. Determine the asset s accounting book value after two years of use using straight-line depreciation. [$40 000] PART 2. Full-solution Problems 16. Your firm is considering a three-year project that will cost $ today, and another $ at the end of each 6-month period over the first two years. Also, the project will return $5000 at the end of each quarter of the three-year project life, and an extra $ will be received at the end of the project, three years from now. Illustrate these monetary flows in two diagrams, using periods of 3 months (quarters). 4

7 16.1 First, show each monetary flow element separately. $ t=0 $ $ t=1 t=2 t=3 $ Second, show only the net monetary flow at the end of each period. $ t=0 $ $ t=1 t=2 t=3 $ BJ Mining Inc. is interested in obtaining estimates of the supply and demand functions for coal, both assumed to be linear. The firm's research department informs you that at the current market equilibrium price (P) and quantity (Q) of $41 per tonne and 1206 tonnes per week, respectively, the price elasticity of supply is approximately 1.7, and the price elasticity of demand is approximately The supply curve: Q = a + β P (Note: β is the slope) The demand curve: Q = c - δ P (Note: - δ is the slope) 17.1 Estimate the linear supply and demand functions (i.e. determine the values of the constants a, β, c and δ). [-844, 50, 2231 and 25, respectively] 17.2 What impact would a 10% increase in demand at all price levels have on the equilibrium price and quantity? [New demand function: Q = P; new market equilibrium at P=42.56 and Q=1284] 5

8 17.3 If the government refused to let BJ Mining raise the price of coal when demand increases as in 17.2 above, what shortage would be created? [At P=41, Q D = and Q S =1206; there is a shortage of 120.6, a value equal to the 10 percent increase in demand at the previous market equilibrium price] TEST # 2 WINTER '04 PART 1. Multiple-choice Problems Use the following information to answer questions 1 to 7. A plant with a maximum production capacity of units per year has a linear cost function. The constant selling price is $800 per unit. 1. At an annual production rate of 8000 units, the average fixed cost is $200 and the average production cost is $600. What are the annual fixed costs? [$ } 2. At an annual production rate of 8000 units, the annual fixed costs are $ and the average production cost is $600. What is the marginal cost? [$350] 3. At an annual production rate of 8000 units, the annual fixed costs are $ and the average variable cost is $380. What is the break-even rate of production at a constant selling price of $800 per unit? [3810] 4. At an annual production rate of 8000 units, the marginal cost is $350 and the annual fixed costs are $ What is the contribution margin at a constant selling price of $800 per unit? [$450] 5. At an annual production rate of 8000 units, the average fixed cost is $200 and the average variable cost is $380. What is the average fixed cost at an annual production rate of ? [$160] 6. At an annual production rate of 8000 units, the average fixed cost is $200 and the average variable cost is $380. What are the annual fixed costs at an annual production rate of ? [$ ] 7. At an annual production rate of 8000 units, the annual fixed costs are $ and the average variable cost is $380. By how much must the plant change its annual fixed costs to achieve a break-even rate of 3000 units at a constant selling price of $800 per unit? [$ decrease] Use the following information to answer questions 8 to 12. Montreal Dance Studios (MDS) has the following capital structure, which it considers optimal: 60% Debt 10% Preferred equity 30% Common equity This year, MDS expected net income is $ Its established dividend payout ratio is 40% of income available to common, the corporate income tax rate is 45%, and investors expect earnings and dividends to grow at a constant annual rate of 10%. MDS just paid a dividend (D 0 ) of $3.60 per common share, and its stock has a current market price of $50 per share. Government of Canada Savings Bonds now have a coupon rate of 8%. The following conditions would apply to new security offerings made by MDS: Common shares: New common shares would have an after-tax issuing cost of 10% of the market price. Preferred shares: New preferred shares could be sold to the public at a price of $90 per share with a annual dividend of $10. Before-tax issuing costs of $6 per share would be incurred. 6

9 Debt: New bonds could be sold with a yield-to-maturity of 12% (with interest paid once a year). Issuing costs on bonds are negligible. 8. What is MDS cost of funds associated with its existing common equity? [17.9%] 9. What is MDS cost of funds obtained by issuing new common shares? [18.8%] 10. What is MDS cost of funds obtained by issuing new preferred shares? [11.5%] 11. What is MDS cost of funds obtained by issuing new bonds? [6.6%] 12. What is MDS cost of funds associated with retained earnings? [17.9%] 13. A share with a current market price of $20.00 has just paid a quarterly dividend of $0.20. Share price and dividends are expected to grow at an annual rate of 8% (effective annual growth rate). Assuming that both the share and the dividend have the same growth rate per quarter, determine the cost of common equity? [12.4%] 14. Suppose a firm invests $6000 in a project. The net income from the project is $1000, $1250, and $1400 in each of the three years of the project's life. The initial cost is depreciated to zero by the straight-line method over 3 years. What is the accounting rate of return of the project? [40.6%] PART 2. Multiple-choice Statements 15. Which one of the following statements is true? [C] A) If a firm issues new common stock below the par value of its current common stock, the wealth of its common shareholders would probably be reduced. B) The current dividend yield (D 0 / P) plus the expected annual growth rate in dividends equals the cost of capital associated with issuing new common equity. C) Firms should assess and make decisions about projects using their own cost of capital. D) If a firm is planning to issue only common shares to raise funds for a project, the cost of capital associated with the new shares will be the same as that of its retained earnings. E) none of the statements are true. 16. When determining the cost of capital, the financing sources that should be included are: [D] A) accounts payable and accruals B) short-term debt (i.e. short-term bank loans) C) net income available to common shareholders before corporate taxes have been paid D) long-term debt, preferred shares, common shares and retained earnings. E) all of the choices given above 17. The internal rate of return (IRR) is that discount rate which equates the present value of expected future cash flows with: [B] A) the present value of net returns B) the immediate capital investment C) the present value of future receipts D) the depreciated value of the old assets less the cost of the new assets E) none of the choices given above 18. When projects are mutually exclusive, [B] A) they can only be accepted if capital funds are limited B) the selection of one alternative excludes the selection of other alternatives C) the selection of one is not affected by either the selection or rejection of another 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 7

10 19. Which one of the following statements is true? [C] A) The NPV criterion assumes that the cash inflows are reinvested at the internal rate of return. B) The IRR criterion assumes that the cash inflows are reinvested at the NPV rate of return. C) The NPV criterion assumes that the cash inflows are reinvested at the discount rate used to determine the NPV. D) The IRR criterion assumes that the cash inflows are reinvested at the cost of capital. E) none of the choices given above 20. Which of the following statements is true regarding the use of the discounted payback period criterion? [C] A) An advantage of this criterion is the fact that the maximum acceptable period is arbitrarily set. B) If a project recovers the initial investment on a discounted basis, then it must have a positive NPV. C) When comparing projects, this criterion is superior to the payback period. D) The discounted payback period is much simpler to calculate than the payback period. E) Time value of money concepts are ignored in the calculation of the discounted payback period. PART 3. Full-solution Problems 21. Consider a project with a preproduction period of one year and a time distribution of cash flows as shown below Given a cost of capital of 10%, determine the payback period of the project. [2.75 years] 21.2 Given a cost of capital of 10%, determine the net present value of the project. [$ ] 21.3 Given a cost of capital of 10%, determine the internal rate of return of the project. [22.3 %] 21.4 Given a cost of capital of 10%, determine present value ratio of the project. [0.428] 21.5 Given a cost of capital of 10% and assuming that the positive cash flows are full benefits, determine the benefit-cost ratio of the project. [1.428] 21.6 Given a cost of capital of 10%, determine the discounted payback period of the project. [3.43 years] 8

11 TEST # 1 WINTER '04 PART 1. Multiple-choice Problems Use the following information to answer questions 1 to 3. The demand function for books is: The supply function for books is: Q D = P Q S = 5 P 1. What is the equilibrium quantity of books sold? [100] 2. If P=$15, which of the following statement is true? [There is a shortage of 30 books.] 3. If P=$22, which of the following statement is true? [There is a surplus of 12 books.] 4. In the following diagram, the demand at point A is: [infinitely elastic] Price X A 0.25 X B Y Y Quantity 5. In the diagram above, the demand at point B is: [inelastic, but not completely inelastic] Use the following information to answer questions 6 to 8. An asset costs $ and has an estimated salvage value of $5000 at the end of its useful life of 5 years. 6. Using the straight-line method to fully depreciate the asset over its useful life, the depreciation charge for tax purposes in the first year of ownership of the asset is: [$6000] 7. Using the declining-balance method with an annual depreciation rate of 20%, the book value of the asset after three years of ownership is: [$15 360] 8. Using the unit-of-production method and assuming a constant annual production rate, the depreciation charge for accounting purposes in the second year of ownership of the asset is: [$5000] 9

12 Use the following financial statements to answer questions 9 to 15. Marble Comics Group Year-end Balance Sheets ($ millions) Cash Accounts payable Accounts rec Notes payable Inventory Current liabilities Current assets Long-term debt Net fixed assets Common stock Retained earnings Total Assets Total Liab. & Equity Income Statement ($ millions) Net sales 905 Less: Cost of goods sold 522 Less: General & admin. expenses 93 Less: Depreciation 110 EBIT 180 Less: Interest on long-term debt 61 Earnings before taxes 119 Less: Taxes 30 Net income What is Marble Comics' debt ratio at the end of 1999? [0.70 ] 10. Marble Comics' times-interest-earned ratio is: [2.95 ] 11. The profit margin of Marble Comics Group is: [19.9% ] 12. What is Marble Comics' return on equity for 1999? [21.3% ] 13. What is the greatest use of funds for Marble Comics' Corp. during 1999? [C] A) increase in accounts receivable [decrease; source] B) decrease in accounts payable [increase; source] C) acquisition of more fixed assets [212; use] D) dividends [56; use] E) sale of inventory [source] 14. What is the net cash flow from operating, investment and financial activities in 1999? [$60] 15. What is the cash flow from investment activities in 1999? [$212] 16. At an effective annual interest rate of 20 percent, how many years will it take a given amount to triple in value? (Round to the nearest year) [6 years] 17. A lottery you have won offers the payoff options shown below. Which one would you choose given an annual interest rate of 10%? [2] 1. $ today; [PV=$ ] 10

13 2. $ paid at the beginning of each year, with the first payment today, over a period of four years; [PV=$ ] 3. An annual perpetuity of $55 000; [PV=$ ] 4. An annual perpetuity growing at 6% per year; with the first payment of $ one year from today. [PV=$ ] 18. Mr. AA borrowed $ for a nine-month period at a nominal annual rate of 11%. What is his interest cost expressed as an effective annual rate if interest is compounded quarterly? [11.46 %] 19. What is the present value of a stream of end-of-year monetary flows consisting of a negative flow of $100 per year for each of the next 3 years, and a positive flow of $300 per year in years 4 through 7, if the appropriate discount rate is 10%? [$466] 20. The current market price of V Corporation's bonds is $ A 10 percent coupon rate is paid semi-annually, and the face value is $1000. What is the yield to maturity (stated as a nominal annual rate) if the bonds mature 10 years from today? [6 %] 21. Assume the same bond as in question 20. Two years later, the market value of the bond is such that its yield to maturity is now 12%. What effect will this have on its market value? [The market price of the bond will decrease to about $899.] PART 2. Full-solution Problem 22. Find the value of X on the monetary flow diagram shown below, assuming that the down-pointing arrows are deposits into a savings account and the up-pointing arrows are withdrawals that deplete the account entirely by time 5. The interest rate paid per period by the savings account is variable as shown on the diagram. [$699.20] X X X 8% 10% 12% 14% 16% $500 $500 $500 TEST # 2 FALL '03 PART 1. Multiple-choice Problems and Statements Use the following information to answer questions 1 to 3. A fiberglass boat producer has the following production variables: Fixed Cost (FC) $ per month; constant unit variable cost (vc) $320; selling price (p) $

14 1. Determine the contribution margin if the fixed cost is reduced to $10 000, the unit variable cost is increased to $520, and the selling price is increased to $700. [$180] 2. By how much must the fixed cost be reduced if the break-even rate is to be 30 units per month? [$9600] 3. Which statement(s) is/are correct when the situation in question 1 above is compared to the original situation? [B] I. More flexible operation II. Less risk III. Lower profit growth A) I B) I & II C) II & III D) I, II & III E) None of the choices given above 4. The theory of the business firm makes the following assumption(s): [B] I. Limited resources II. Perfect market competition (producer is small relative to total market) III. Conditions of certainty (all variables are unknown at the present and for future time periods) A) I B) II C) II & III D) I, II & III E) None of the choices given above 5. A project with an initial investment of $ has expected cash flows of $3000 per year for 5 years. The discount rate is %. The project s NPV is and its IRR is. [$0.764; 15.2 %] 6. The Carnation Chemical Company is investing in an incinerator to dispose of PCB waste. The incinerator costs $1.5 million and will generate annual cash flows of $1 million for the next 3 years. At the end of 3 years, the incinerator will be worthless and must be disposed of at a cost of $ The internal rate of return of this project is: [34.6 %] 7. You have a choice between two projects. Project 1 pays $ back at the end of one period on an investment of $ Project 2 pays back $6 500 at the end of one period on an investment of $ If the objective is to maximize wealth, which project should be chosen and what problem must you be concerned with in this choice? [C] A) Project 1; discount rate. B) Project 2; discount rate. C) Project 1; project scale (i.e. size of investment). D) Project 2; project scale. E) Project 1, timing of cash flows. 8. Which of the following correctly orders the investment rules of accounting rate of return (ARR), discounted payback period (DPP), and net present value (NPV) from the most desirable to the least desirable? [NPV, DPP, ARR] 9. GJ Inc. has been presented with an investment opportunity that will yield cash flows of $ per year in years 1 through 4, $ per year in years 5 through 9, and $ in year 10. This pro- 12

15 ject will cost the firm $ today, and the firm's cost of capital is 10 percent. Assume that cash flows occur uniformly during the year, i.e. 1/365th of the annual value each day. The payback period for this investment is: [4.9 years] 10. What is the discounted payback period of the following project if the required return on investment is 14%? [4.4 years] Year-end Time Cash Flow -$ Given the opportunity to invest in bonds from the list below, which one(s) would you purchase? Assume that you require at least a 7% (effective) return on investment. [Bonds B and C] Bond Face Value Annual Coupon Rate Maturity Market Price ($) (%) (yrs) ($) A B C The potential owner/managers of the yet to be formed new In-Line Blade Company are evaluating a prospect for the business. New equipment is expected to cost $5.5 million and have annual aftertax cash flows of $ over the first two years, $ over the following two years, and starting in the fifth year, $ per year indefinitely. The owners require a 15% rate of return. What is the net present value of the project to In-Line Blade Company, and should they go forward with the investment? [$ ; yes] Use the following information to answer questions 13 and 14. Consider the following two mutually exclusive alternatives which have common benefits: Alternative A B Immediate investment ($) Life (yrs) 8 8 Salvage value ($) Annual maintenance expense ($) Using a cost of capital of 10 percent, the equivalent annual cost (i.e. ordinary annuity) of alternative A is: [$1863] 14. Using a cost of capital of 10 percent, the incremental benefit-cost ratio of choosing alternative B over alternative A is: [0.49 or 0.52] PART 2. Full-solution Problems 15. JLP Industries has 6.5 million common shares ($5 par value) outstanding with a market price of $14 per share. The company also has outstanding preferred stock with a market value of $10 million, and bonds, each with a face value $1000, but selling at 90% of par on the market. The before-tax cost of common equity is 14%, that of preferred equity is 10%, and that of debt is 7.25%. If JLP's tax rate is 34%, what is its after-tax WACC? [12.0 %] 16. A firm needs to raise $165 million for a project. If external financing is used, the firm faces issuing expenses of 8% for equity (i.e. it only realizes 92% of the value issued) and 2.5% for debt. Given that the project is to be financed with 60% equity and 40% debt, how much funds must the firm raise in order to finance the project? [$175.2 million] 13

16 TEST # 1 FALL '03 PART 1. Multiple-choice Problems and Statements Use the following information to answer questions 1 to 3. The demand function for pencils (the type used to answer multiple-choice exams) is given by [ Q = P ] in which Q is the quantity demanded in units and P is the price/pencil in dollars. The bookstore selling price is $0.30/pencil. 1. The elasticity at P=0 is: [0] 2. The elasticity at P=$0.30/pencil is: [1.5] 3. What would be the total producer income if the market equilibrium was at P=$0.24/pencil? [$624] 4. A process with a linear production cost function has an annual fixed cost of $ , and an average production cost of $25 at a production rate of 8000 units per year. The constant unit variable cost of the process is: [$10] 5. [ Q = 210 S + 90 S 2-10 S 3 ] is a production function in which Q represents the output in hundreds of units per year and S represents the input in thousands of units per year. The average product at an annual input rate of 4000 units is: [41] Use the following financial statements to answer questions 6 to 11. Bo Knows Profit Corporation Income Statement for 1999 Sales $ 8800 Less: Costs 5600 Depreciation 900 EBIT 2300 Less: Interest 350 EBT 1950 Less: Taxes 550 Net Income 1400 Dividends 900 Addition to retained earnings 500 Bo Knows Profit Corporation Balance Sheet for End of Year 1998, Cash Accounts payable Accounts receivable Notes payable Inventory Current liabilities Current assets Long-term debt Net fixed assets Common stock (1998: 50 shares) Retained earnings Total Assets $3910 $5310 Total Liab. & Equity $3910 $5310 Note: Assume that the additional common stock was issued at the end of

17 6. What was the greatest source of funds for Bo Knows Profit Corp. during 1999? [B] A) Sale of inventory [240] B) Increase in long-term debt [615] C) Acquisition of more fixed assets [use] D) Increase in notes payable [200] E) Increase in common stock [100] 7. What was the greatest use of funds for Bo Knows Profit Corp. during 1999? [C] A) Increase in accounts receivable [200] B) Decrease in accounts payable [15] C) Acquisition of more fixed assets [2400] D) Dividends [900] E) Sale of inventory [source] 8. If you prepare a statement of cash flow for 1999, what is the positive flow of cash from operating activities? (Consider only inflows) [$2540 ] 9. If you prepare a statement of cash flow for 1999, what is the negative flow of cash due to operating activities? (Consider only outflows) [-$215 ] 10. What is the cash flow from investment activities in 1999? [-$2400 ] 11. If the firm s price/earnings ratio is currently 2.0, what is the approximate market price per share? [$56 ] 12. Which of the following statements is/are accurate? [D] All else being the same, i. present values increase as the discount rate increases. ii. present values increase the further away in time the future value. iii. present values are always smaller than future values when both the interest rate and the number of compounding periods are positive. A) I only B) I and II only C) II only D) III only E) II and III only 13. A bond sold five weeks ago for $1100. The bond is worth $1050 in today's market. Assuming no changes in risk, which of the following is true? [D] A) The face value of the bond must be $1100. B) The bond must be within one year of maturity. C) Interest rates must be lower now than they were five weeks ago. D) The bond's current yield has increased from five weeks ago. E) The coupon payment of the bond must have increased. 14. In her will, your aunt left you the sum of $5000 per year forever with payments starting immediately. However, the news is better. She has specified that the payments should grow at 5% per year to maintain purchasing power. Given an annual interest rate of 12%, what is the present value today of the inheritance? [$80 000] 15. Joe, a freshman in college, needs $ at his graduation in 4 years time to buy the car of his dreams. Given that his investments earn 6% interest per year, 15

18 i) What lump-sum (single deposit) must he invest today to have the desired amount at graduation? [$ ] ii) If he invested once a year beginning today and up until the end of the 4 years, what constant amount must he deposit to have the desired amount at graduation? [$ ] 16. Mr Miser, who is 35 years old, has just inherited $ and decided to use this windfall towards his retirement. He places the money in a bank, which promises a return of 6% per year until his planned retirement at age 65. If his funds earn 6% interest compounded continuously, how much will he have at retirement? [$ ] 17. Which of the following amounts is closest to the present value of a bond that pays an annual coupon of 5% and has a face value of $ The interest is paid semi-annually and the face value is returned at the end of two years. [Cannot determine the present value without a discount rate] 18. Suppose three zero coupon bonds (bonds that pay no interest) with face values of $1000 each and maturity dates of 1 year, 2 years and 3 years, respectively. The current prices of the 1-year, 2-year and 3-year bonds are $826.45, $ and $640.66, respectively. The yield to maturity of the 1- year bond as well as that of the 2-year bond are: [21% ; 18%] 19. If a company is currently paying a $0.40 dividend on its shares and that this dividend is expected to grow at an annual rate of 7% over the next 6 years and at 4% thereafter, the dividend expected at the end of year 8 is: [$ 0.65] 20. Which of the following amounts is closest to the value today of a bond that pays a coupon of $55 every 6 months assessed at a semi-annual interest rate of 5%? The face value is $1000 and the bond matures in 3 years. There are exactly six months before the first interest payment. [$1025] TEST # 2 WINTER '03 PART 1. True or False Statements 1. If a firm's annual cash flow is negative, then total dividends must have exceeded the amount of new equity sold by the firm during the year. 2. If uses of funds are greater than sources of funds in a firm s Statement of Changes in Financial Position, then the business incurred a loss over the relevant operating period. 3. Whereas depreciation is used to write off tangible fixed assets such as equipment, amortisation is used to write off intangible assets. 4. The objective of a sinking fund is to accumulate funds to pay off a future cash obligation. 5. The periodical interest payment paid by a bond is called the bond's yield-to-maturity. 6. For income tax purposes, preferred stock is treated like debt rather than like common stock. 7. A firm that only accepts projects for which the IRR is equal to the firm's cost of capital will neither create nor destroy wealth for its shareholders. 8. When multiple IRRs exist, a project must have a negative NPV at the highest IRR. 9. In the theory of the business firm, the maximum profit per period is achieved at the production rate at which marginal cost equals average cost. 16

19 10. In general, the current level of dividends on common stock can be ignored for the purpose of estimating the cost of preferred stock. PART 2. Multiple-choice Statements 11. The balance sheet identity states that: [B] A) Current assets + Fixed assets = Total assets B) Assets = Liabilities + Shareholders' equity C) Current liabilities + Long-term debt = Total liabilities D) Common stock + Retained earnings = Shareholders' equity E) Cash flow = Market value Book value 12. Which of the following assets is generally considered to be the least liquid? [C] A) Plant and equipment B) Inventory C) Goodwill D) Cash E) Accounts receivable 13. An increase in the financial leverage of a firm as a result of an increase in long-term debt the potential reward to stockholders while the risk of financial distress or bankruptcy. [C] A) decreases; decreasing B) increases; decreasing C) increases; increasing D) decreases; increasing E) does not affect; increasing 14. Suppose that you have the 1999 income statement for a firm, along with the 1998 and 1999 yearend balance sheets. How would you calculate net capital spending (purchases of fixed assets less disposals) in 1999? [A] A) Net fixed assets (1999) minus net fixed assets (1998) plus 1999 depreciation B) Net fixed assets (1998) minus net fixed assets (1999) plus 1999 depreciation C) Net fixed assets (1998) plus net fixed assets (1999) minus 1999 depreciation D) Net fixed assets (1999) minus net fixed assets (1998) plus 1999 taxes paid E) Net fixed assets (1999) plus net fixed assets (1998) minus 1999 taxes paid 15. ABC Corporation reported retained earnings of $400 in its 1998 year-end balance sheet. In 1999, the company reported a loss of $40, and it paid out a dividend of $60. What will retained earnings be in ABC's 1999 year-end balance sheet? [$300] 16. The Total Asset Turnover ratio is determined as follows: [A] A) Net sales divided by average total assets B) Net income divided by average total assets C) Net sales divided by average fixed assets D) Cost of goods sold divided by average inventory E) Average total assets divided by net sales multiplied by 365 days 17. The payback period rule can be best stated as: {A] 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 E) None of the choices above 17

20 18. The discount rate that makes the present value of all the positive cash flows of a project exactly equal to the present value of all its negative cash flows is the: [B] A) Payback period B) Internal rate of return C) Accounting rate of return D) Present value ratio E) Discounted payback period 19. The present value ratio rule can be best stated as: [A] A) A project is acceptable if its PVR is greater than zero B) A project is acceptable if its PVR is greater than one C) A project is acceptable if its PVR is greater than the internal rate of return D) A project is acceptable if its PVR is less than the net present value E) None of the choices above 20. Which one of the following statements is correct? [C] A) The IRR is the most important project evaluation criterion B) The accounting rate of return is preferable to the PVR C) The assessment of the discounted payback period requires the use of a discount rate D) In the selection of the most economical project among a series of mutually exclusive projects using an incremental analysis approach, the IRR criterion is better than the PVR criterion E) The payback period criterion is preferable to the discounted payback period criterion PART 3. Multiple-choice Problems 21. Suppose that a firm has 10.4 million shares of common stock outstanding with a par value of $1 per share. The current market price per share is $12. The firm has outstanding long-term debt with a face value of $56 million selling at 102% of face value. What capital structure weight would you use for debt when calculating the firm's WACC? [0.314] 22. Suppose a firm invests $6000 in a project. The net income from the project is $1000, $1250, and $1400 in each of the three years of the project's life. The initial cost is depreciated to zero by the straight-line method over 3 years. What is the accounting rate of return of the project? [40.56 %] 23. You are considering a project with cash flows as shown below. You require a return on investment of 10%, a payback period of less than three years and a discounted payback period of less than four years. Should you invest in this project? [D] Time Cash Flow ($) A) Yes, because the payback period is 2.5 years B) Yes, because the discounted payback period is slightly above three years C) Yes, because both the payback and the discounted payback periods are less than the required values D) No, because the NPV is negative E) No, because the project has a large negative cash flow at the end of its life Use the following information to answer questions 24 to 29. Floyd Clymer is the CFO of Mid-America Mustang, a manufacturer of parts for classic automobiles. Floyd is considering the purchase of a two-tonne press which will allow the firm to stamp out automobile fenders. The equipment costs $ The project is expected to produce an after-tax cash flow of $ over the first year, increasing by $ annually; and eventually reach $ in year 5. Liquidation of the equipment will net the firm $ at the end of five years, resulting in a cash flow of $ Floyd s required return on investment is 15%. 18

21 24. What is the payback period for the proposed investment? [3.4 years] 25. Assuming that the sale of the equipment at the end of five years would net the firm $ instead of $10 000, what would be the payback period? [3.4 years] 26. What is the project's discounted payback period? [4.7 years] 27. What is the project's net present value? [$13 853] 28. What is the project's present value ratio? [0.06] 29. Assuming that the required return on investment is 15%, what is the project's internal rate of return? [17.1 %] PART 4. Full-solution Problems 1. A business firm subject to a corporate income tax rate of 45 percent has a capital structure with the following characteristics: Equity with a before-tax cost of 14% Long-term debt with a before-tax cost of 9% Debt to equity ratio of 3:5 Determine the firm s after-tax cost of capital. [10.6 %] 2. A manufacturing company is planning to add a new item to its production line. The plant's capacity for this product is units per year. The annual fixed cost of the new process is $3.1 million and the variable costs are $350 per unit for any amount produced up to a level of per year, and $300 per unit for that part of the production that exceeds units per year. The selling price set by the firm is $600 per unit. According to a market survey, the demand for the product at this price level is units per year. 2.1 What is the marginal cost at a production rate of units per year? [$300] 2.2 Determine the break-even production rate. [ uniys] 2.3 Under the company s current production line capacity, how many units should be produce per year? Determine the annual before-tax profit generated by the sale of the new item at this production rate. [ units per year; $ ] TEST # 1 WINTER '03 PART 1. True or False Statements 1. Suppose that AMR Inc. holds a patent on a new anti-cholesterol drug. This patent is considered an intangible asset. 2. If a firm uses part of the cash it received from the payment of an account receivable to buy inventory and leaves the rest in its cash account, its current ratio will remain unchanged. 3. If a firm uses cash to purchase inventory, its quick ratio will increase. 19

22 4. You hold a winning ticket from your provincial lottery. It entitles the bearer to receive payments of $ at the end of each of the next 20 years. Given what you know about the time value of money, you should be able to sell this ticket for no less than $1 million in the open market. 5. If the rate of interest at which you can invest money is 0%, the value today of $1 to be received at some time in the future is less than $1. PART 2. Multiple Choice Statements 6. The financial statement showing a firm's accounting value on a particular date is the: [B] A) Income statement B) Balance sheet C) Statement of cash flow D) Tax reconciliation statement E) Shareholders' equity sheet 7. A(n) asset is one that can be converted quickly into cash without significant loss in value. [D] A) current B) fixed C) intangible D) liquid E) long-term 8. Balance sheet assets. [D] I. are always equal to total liabilities plus shareholders' equity. II. represent items acquired with the use of the firm's assumed liabilities and equity. III. are listed in order of increasing liquidity. A) I only B) II only C) III only D) I and II only E) II and III only 9. Which of the following is not a current asset? [C] A) Inventory B) Cash on hand C) Patents D) Accounts receivable E) Marketable securities 10. XYZ Company had a net income of $40 million in The firm paid no dividends. If there were no further changes to the stockholders' equity accounts, then by $40 million. [B] A) common stock increased B) retained earnings increased C) total shareholders' equity decreased D) common stock decreased E) the market value of the firm's stock decreased PART 3. Multiple-choice Problems 11. If current assets = $95, net fixed assets = $250, long-term debt = $40, and shareholders equity = $200, what is the value of current liabilities if it is the only other item on the balance sheet? [$105] 20

23 12. At the end of 1998, Jordan Company's balance sheet showed current assets = $800, net fixed assets = $1500, intangible assets = $300, current liabilities = $600, and long-term liabilities = $1400. What is the value of the shareholders' equity account? [$600 ] 13. In 1999, Spend-it Corporation reported a net income of $200 and paid a $40 dividend. Spend-it's December 31, 1998 balance sheet reported the following items: common stock = $220, capital surplus = $180, retained earnings = $300. What is the value of the retained earnings account in the December 31, 1999 balance sheet? [$460] 14. If total assets = $550, net fixed assets = $375, current liabilities = $140, shareholders equity = $265, long-term debt = $145, and current assets is the only remaining account in the balance sheet, what is the value of working capital? [$35] 15. In 1889, Vincent Van Gogh's painting, "Sunflowers", sold for $125. One hundred years later it sold for $36 million. Had the painting been purchased by your great-grandfather and passed on to you (to sell in 1989), what annual interest rate would your family have earned on the original investment? [13.4 % ] 16. What is the future value equivalent (at time 4) of the following monetary flows? Assume an annual interest rate of 8%. [$173] Time Monetary Flow $1000 -$1000 $1000 -$ The monthly mortgage payment on your house is $ It is a 30-year mortgage carrying an annual interest rate of 7.8% compounded monthly. How much did you borrow? [$ ] 18. If the following bonds are identical except for the coupon rate, what is the market price of bond B? [$901.04] Bond A Bond B Face value $1000 $1000 Semi-annual coupon $45 $35 Years to maturity Market price $ ? 19. In 1555, King Henry borrowed 100 from his bankers, agreeing to repay 7 percent of the amount borrowed at each fair (there were four fairs per year) until he had made a total of 60 payments. At this time, the loan would be considered repaid. What effective annual interest rate were the bankers charging? [30.44 %] PART 4. Full-solution Problems 1. The aggregate demand function of a manufacturer is represented by the equation: Q = P in which Q is the annual quantity demanded and P is the price per unit in dollars. 1.1 Determine the price elasticity of demand when P=20. [ or indeterminate] 1.2 If the price is lowered from $15/unit to $10/unit, determine the direction (+ or -) and magnitude of change in total consumer expenditure. [increased by $375] 1.3 At what price is total consumer expenditure maximized? [$10] 21