MIME 310 ENGINEERING ECONOMY
SAMPLE CLASS TESTS
Department of Mining and Materials Engineering
McGill University
FOREWORD 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.
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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), $15 000 per month; constant average variable cost (vc), $320; selling price (p), $500. 1.
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 $10 000 will generate cash flows of $3000 per year over a 5-year period. The discount rate is 15.235%. 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 $500 000. The internal rate of return (IRR) of this project is: [34.6 %]
7.
Consider a 10-year period characterised by payments of $20 000 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 $30 000 per year in years 1 through 4, $35 000 per year in years 5 through 9, and $40 000 in year 10. This project will cost the firm $150 000 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 0 1 2 3 4 5 ––––––––––––––––––––––––––––––––––––––––––––––––––– Cash Flow -$60 22 22 22 10 10
1
11.
A corporation plans to purchase an asset costing $10 000 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 $10 500 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) [$4650]
14.
Consider the following two mutually exclusive alternatives which have common benefits: Alternative A B —————————————————————————————— Immediate investment ($) 5 000 12 000 Life (yrs) 8 8 Salvage value ($) 850 1 800 Annual maintenance expense ($) 1 000 400 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.
16.
Full-solution Problems
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 25 000 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%.
16.1 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
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
0
40
40
0
-
–
-
0
1
45
40
5
45
5
40
5
2
60
40
20
30
15
20
10
3
79
40
39
26
19
13
13
4
105
40
65
26
26
10
16
5
150
40
110
30
45
8
22
6
200
40
180
33
50
7
27
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 $750 000 today, or an annual payment of $50 000 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 $7403.16. 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? [$2714.99] 5. Sampson Inc. invested $1 325 000 in a project that earned an annual interest rate of 8.25%. Sampson sold the project for $3 713 459. 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 ]
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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? [$828.85 ] 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 $100 000. The firm’s balance sheet shows an accounts receivable balance of $12 000. What is George Inc.’s average collection period? [44 days] 13. Bernard Inc. has a cost of goods sold of $105 000 on sales of $150 000. The firm’s balance sheet shows total assets of $75 000 and an inventory balance of $15 000. 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 $100 000, average quarterly sales of $500 000 and average total assets of $2 500 000. What is Shaw’s return on total assets? [8 %] 15. An asset costs $60 000 and has a salvage value of $10 000 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 $50 000 today, and another $15 000 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 $30 000 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).
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16.1 First, show each monetary flow element separately. $30 000
t=0
$5000
|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|
$15 000 t=1
t=2
t=3
$50 000 16.2 Second, show only the net monetary flow at the end of each period. $35 000
t=0
$5000
|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------| $10 000 t=1
t=2
t=3
$50 000 17. 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 0.85. The supply curve: The demand curve:
Q=a+β•P Q=c-δ•P
(Note: β is the slope) (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 = 2454.1 - 27.5 P; new market equilibrium at P=42.56 and Q=1284]
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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, QD=1326.6 and QS=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 10 000 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? [$1 600 000}
2.
At an annual production rate of 8000 units, the annual fixed costs are $2 000 000 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 $1 600 000 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 $1 600 000. 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 10 000? [$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 10 000? [$1 600 000]
7.
At an annual production rate of 8000 units, the annual fixed costs are $1 600 000 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? [$340 000 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 $200 000. 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 (D0) 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
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 (D0 / 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
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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. 21.
Full-solution Problems
Consider a project with a preproduction period of one year and a time distribution of cash flows as shown below.
0
3000
3000
2
3
4000
4000
4000
4
5
6
1
4000 5000
21.1 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. [$3661.46] 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]
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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: QD = 120 - P The supply function for books is: QS = 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
B
0.25 X
0 5.
0.75 Y
Y
Quantity
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 $30 000 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: [$5000]
9
Use the following financial statements to answer questions 9 to 15. Marble Comics Group Year-end Balance Sheets ($ millions)
Cash Accounts rec. Inventory Current assets Net fixed assets
1998 75 230 240 545 788
1999 135 214 188 537 890
Total Assets
1333
1427
1998 89 227 316 615 55 347 1333 --------
Accounts payable Notes payable Current liabilities Long-term debt Common stock Retained earnings Total Liab. & Equity
1999 110 442 552 440 55 380 1427 ---------
1999 Income Statement ($ millions) Net sales Less: Cost of goods sold Less: General & admin. expenses Less: Depreciation EBIT Less: Interest on long-term debt Earnings before taxes Less: Taxes Net income
905 522 93 110 180 61 119 30 89
9.
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. $500 000 today; [PV=$500 000]
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2. $160 000 paid at the beginning of each year, with the first payment today, over a period of four years; [PV=$558 000] 3. An annual perpetuity of $55 000; [PV=$550 000] 4. An annual perpetuity growing at 6% per year; with the first payment of $22 000 one year from today. [PV=$550 000] 18.
Mr. AA borrowed $95 000 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 $1297.58. 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. 22.
Full-solution Problem
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
0
8%
1
10%
2
12%
$500
X
16%
14%
3
$500
X
4
5
$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) $15 000 per month; constant unit variable cost (vc) $320; selling price (p) $500.
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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. II. III. A) B) C) D) E)
4.
More flexible operation Less risk Lower profit growth I I & II II & III I, II & III None of the choices given above
The theory of the business firm makes the following assumption(s): [B] I. II. III. A) B) C) D) E)
Limited resources Perfect market competition (producer is small relative to total market) Conditions of certainty (all variables are unknown at the present and for future time periods) I II II & III I, II & III None of the choices given above
5.
A project with an initial investment of $10 000 has expected cash flows of $3000 per year for 5 years. The discount rate is 15.235%. 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 $500 000. The internal rate of return of this project is: [34.6 %]
7.
You have a choice between two projects. Project 1 pays $12 000 back at the end of one period on an investment of $10 000. Project 2 pays back $6 500 at the end of one period on an investment of $5 000. 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 $30 000 per year in years 1 through 4, $35 000 per year in years 5 through 9, and $40 000 in year 10. This pro-
12
ject will cost the firm $150 000 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 0 1 2 3 4 5 ––––––––––––––––––––––––––––––––––––––––––––––––––– Cash Flow -$60 22 22 25 10 5
11.
Given the opportunity to invest in bonds from the list below, which one(s) would you purchase? Assume that you require at least a 7% (effective) return on investment. [Bonds B and C] Bond A B C
12.
Face Value ($) 1000 1000 1000
Annual Coupon Rate (%) 4.0 7.5 8.5
Maturity (yrs) 1 17 25
Market Price ($) 990 990 990
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 $400 000 over the first two years, $750 000 over the following two years, and starting in the fifth year, $1 200 000 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? [$646 262; yes]
Use the following information to answer questions 13 and 14. Consider the following two mutually exclusive alternatives which have common benefits: Alternative A B ————————————————————————————————— Immediate investment ($) 5 000 12 000 Life (yrs) 8 8 Salvage value ($) 850 1 800 Annual maintenance expense ($) 1 000 400 13.
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 25 000 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
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 = 5000 - 10 000 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 $120 000, 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 S2 - 10 S3 ] 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 Less: Costs Depreciation EBIT Less: Interest EBT Less: Taxes Net Income
$ 8800 5600 900 2300 350 1950 550 1400
Dividends Addition to retained earnings
900 500
Bo Knows Profit Corporation Balance Sheet for End of Year 1998, 1999
Cash Accounts receivable Inventory Current assets Net fixed assets
Total Assets
1998
1999
170 500 1240 1910 2000
110 700 1000 1810 3500
$3910
$5310
Accounts payable Notes payable Current liabilities Long-term debt Common stock (1998: 50 shares) Retained earnings Total Liab. & Equity
1998
1999
135 1200 1335 2005 100
120 1400 1520 2620 200
470 $3910
970 $5310
Note: Assume that the additional common stock was issued at the end of 1999.
14
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) B) C) D) E)
I only I and II only II only III only 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 $55 000 at his graduation in 4 years’ time to buy the car of his dreams. Given that his investments earn 6% interest per year,
15
i)
What lump-sum (single deposit) must he invest today to have the desired amount at graduation? [$43 565.15]
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? [$9756.80]
16.
Mr Miser, who is 35 years old, has just inherited $11 000 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? [$66 546.12 ]
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 $10 000. 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, $718.18 and $640.66, respectively. The yield to maturity of the 1year 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
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
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 $1400 in each of the three years of the project's life. The initial cost is depreciated to zero by the straight-line method over 3 years. What is the accounting rate of return of the project? [40.56 %]
23.
You are considering a project with cash flows as shown below. You require a return on investment of 10%, a payback period of less than three years and a discounted payback period of less than four years. Should you invest in this project? [D] Time Cash Flow ($)
0 -100
1 40
2 40
3 40
4 40
5 -50
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 $250 000. The project is expected to produce an after-tax cash flow of $60 000 over the first year, increasing by $10 000 annually; and eventually reach $100 000 in year 5. Liquidation of the equipment will net the firm $10 000 at the end of five years, resulting in a cash flow of $110 000. Floyd’s required return on investment is 15%.
18
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 $100 000 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. 1.
Full-solution Problems
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 15 000 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 10 000 per year, and $300 per unit for that part of the production that exceeds 10 000 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 22 000 units per year.
2.1
What is the marginal cost at a production rate of 12 500 units per year? [$300]
2.2
Determine the break-even production rate. [12 000 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. [15 000 units per year; $900 000]
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
4.
You hold a winning ticket from your provincial lottery. It entitles the bearer to receive payments of $50 000 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. II. III.
are always equal to total liabilities plus shareholders' equity. represent items acquired with the use of the firm's assumed liabilities and equity. are listed in order of increasing liquidity.
A) B) C) D) E)
I only II only III only I and II only 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 1999. 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. 11.
Multiple-choice Problems
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
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 1 2 3 4 —————————————————————————————— Monetary Flow $1000 -$1000 $1000 -$1000
17.
The monthly mortgage payment on your house is $593.90. It is a 30-year mortgage carrying an annual interest rate of 7.8% compounded monthly. How much did you borrow? [$82 500 ]
18.
If the following bonds are identical except for the coupon rate, what is the market price of bond B? [$901.04]
Face value Semi-annual coupon Years to maturity Market price 19.
Bond B $1000 $35 20 ?
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. 1.
Bond A $1000 $45 20 $1098.96
Full-solution Problems
The aggregate demand function of a manufacturer is represented by the equation: Q = 300 - 15 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
2.
Nanotech medical equipment purchased for $120 000 has a salvage value of $20 000 at the end of its 5-year life.
2.1
Determine the equipment’s book value for accounting purposes after two years of use using straight-line depreciation. [$80 000]
2.2
Determine the equipment’s book value for tax purposes after 4 years of use using decliningbalance depreciation with an annual rate of 30%. [$28 812]
TEST # 2 – FALL '02 ——————————————————————————————————————— PART 1.
True or False Statements
1.
The before-tax cost of debt, which is lower than the after-tax cost, is used for the purpose of calculating a firm's cost of capital.
2.
Funds acquired by retaining earnings have no cost because there are no associated dividend nor interest payments, but capital raised by selling new stock or bonds does have a cost.
3.
The cost of capital should reflect the average combined cost of the various sources of long-term funds that a firm uses to finance its assets.
4.
Suppose that a firm has a debt to equity ratio of 10 percent, a current cost of debt of 8 percent, a current cost of equity of 16 percent, and that it is subject to a corporate income tax rate of 40 percent. All other variables remaining constant, an increase in the debt to equity ratio from 10 to 20 percent would decrease the weighted-average cost of capital.
5.
For a fixed nominal interest rate, the greater the number of compounding periods within a year, the greater the future value of a lump sum invested today, and the greater the present value of a lump sum to be received sometime in the future.
PART 2.
Multiple-choice Statements
6.
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 (D0 / P) plus the expected annual growth rate in dividends equals the cost of 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 equity to raise funds for a project, the cost of the new equity will be the same as that of its retained earnings.
7.
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, and common equity E) all of the above
8.
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 initial capital investment C) the present value of future receipts
22
D) the depreciated value of the old assets less the cost of the new assets E) none of the above 9.
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
10.
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 cost of capital. D) The IRR criterion assumes that the cash inflows are reinvested at the cost of capital. E) none of the above
11.
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.
Statements with Missing Words
12.
????? are assets having no physical existence, yet having substantial value to a company. [B] A) Deferred taxes B) Intangibles C) Marketable securities D) Preferred shares E) None of the above
13.
????? represents the amount paid by new shareholders in excess of the par or legal value of the common shares. [D] A) Goodwill B) Market price C) Profit D) Capital surplus E) None of the above
14.
????? appears as a source of funds in the statement of Changes in Financial Position because it is not a cash expense. [C] A) Accumulated depreciation B) A deferred expense C) Depreciation D) A loss on disposal E) None of the above
15.
????? represents the decline in the useful value of an intangible. [C] A) Depreciation B) Accumulated depreciation C) Amortization D) Net loss E) None of the above
23
16.
????? as defined in accounting practice is an indicator of the ability of a business to meet its shortterm financial obligations. [E] A) The debt to equity ratio B) The operating cost ratio C) The profit margin D) The time-interest-earned ratio E) None of the above choices
PART 4. 17.
Multiple-choice Problems
Montreal Dance Studios (MDS) has the following capital structure, which it considers optimal: 60% Debt 10% Preferred shares 30% Common equity This year, MDS has an expected net income of $20 000, its established dividend payout ratio is 40%, 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 (D0) 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 12%. 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. Debt: Debt could be sold with a yield-to-maturity of 12% (with interest paid once a year). Issuing costs on debt are negligible. What are MDS' after-tax costs of debt, retained earnings, new common shares and new preferred shares, respectively? [6.6 %, 17.92 %, 18.80 %, 11.53 %] 18.
XYZ Inc. is considering the following two projects:
• Project X requires an initial investment of $1000 and would provide an annual cash flow of $100 over 100 years
• Project Y requires a capital outlay of $400 and would provide an annual cash flow of $50 over 50 years Compute the internal rate of return for each project and determine which is preferred? [IRRx = 10 %, IRRy = 12.5 %, Accept Y] PART 5. 1.
Full-solution Problems
Consider a project with a time distribution of cash flows as shown below. 2000
3000
3000
4000
4000
1
2
3
4
5
0
8000 24
1.1
Given a cost of capital of 10%, determine the payback period of the project. [3 years]
1.2
Given a cost of capital of 10%, determine the net present value of the project. [$3767.20]
1.3
Given a hurdle rate (MARR) of 12%, determine the internal rate of return of the project. [25.0 %]
2.
McBurger’s maximum production capacity is 5000 cheeseburgers per year (assume a uniform production rate throughout the year). Given fixed costs of $5000 per year, constant variable costs of $3.20 per burger and a selling price of $5 per burger,
2.1
What is the break-even production rate? [2778 units]
2.2
Determine McBurger’s annual profit when production is maximum and the variable costs increase to $4.00 per unit over the last 6 months of the year. [$2000]
TEST #1 – FALL '02 ——————————————————————————————————————— PART 1. 1.
Multiple-choice Problems
Consider the demand curve shown on the diagram below. 80 A -- Q=1607, P=60
PRICE ($/unit)
70 60
B -- Q=1982, P=46
50 40 30 20 1000
1500
2000
2500
3000
3500
QUANTITY ('000 units/yr) 1.1
Determine the arc elasticity between points A and B. [0.79]
1.2
Using the graphical method, approximate the point elasticity at point A. [0.72]
2.
The total cost function of a plant has the following characteristics: Fixed costs of $150 000 per year Constant variable costs of $50 per unit up to and including a production rate of 6000 units per year Constant variable costs of $40 per unit for all units produced above 6000 units per year
2.1
Determine the total costs of production at a rate of 8000 units per year. [$530 000]
25
2.2
Determine the average cost of production at a rate of 9000 units per year. [$63.33]
2.3
Determine the marginal cost at a rate of 10 000 units per year. [$40]
PART 2.
True or False Statements
1.
Two firms have the same current ratio of 0.75 and the same cost of goods sold. However, firm A has a higher inventory turnover ratio than firm B. Therefore, we can conclude that the quick ratio of firm A is lower than that of firm B.
2.
Suppose that two firms with the same amount of total assets pay the same interest rate on their long-term debt and have the same positive (+) return on total assets. However, one firm has a higher debt ratio. Given that neither of the firms have preferred equity, the firm with the higher debt ratio will also have a higher return on common equity.
3.
Suppose a firm wants to maintain a specific times-interest-earned ratio. Given the amount of longterm debt outstanding, the interest rate paid on that debt and the applicable income tax rate, the firm can calculate the amount of net income required to maintain its target times-interest-earned ratio.
4.
If sales decrease (with a proportional decrease in operating expenses excluding interest on longterm debt) and financial leverage increases, then the profit margin will decrease.
5.
An excess of uses of funds over the sources of funds in a firm’s financial statements implies that the firm incurred a loss over the relevant accounting period.
PART 3.
Multiple-choice Problems and Statements
6.
MBI Corp. has a quick ratio of 0.50, a current ratio of 0.75, and current liabilities of $50 000. Given that inventory is the only non-liquid current asset, determine MBI's inventory level. [$12 500]
7.
Con-U Inc.'s monthly credit purchases are $100 000 and its total outstanding accounts payable are $144 000. Determine approximately how many days' purchases remain outstanding (i.e. to be paid). Assume a 365-day year. [44]
8.
B.Y.O.B. & Sober Inc. has a times-interest-earned ratio of 3.33 and is subject to a 50% income tax rate. It also has annual interest expenses of $60 000. If B.Y.O.B. & Sober's Earnings Before Interest and Taxes amount to $200 000, then its net income is: [$70 000]
9.
If a firm's current ratio is greater than unity, then its working capital is: [B] A) zero B) positive C) negative
10.
Which of the following elements is not considered a source of funds? [D] A) a decrease in inventories B) an increase in accounts payable C) the sale of preferred equity D) the redemption of long-term debt E) a decrease in accounts receivables
11.
In a statement of changes in financial position, which of the following elements would be considered a use of funds? [A] A) an increase in fixed assets at cost B) an increase in retained earnings C) a decrease in accounts receivables
26
D) an increase in accounts payable E) a decrease in inventory PART 4.
Multiple-choice Problems
12.
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]
13.
You have just won a lottery that offers a choice among the three following payoffs. Which one would you choose given that your time value of money corresponds to an effective annual interest rate of 10%? [B] 1. $500 000 today [PV=$500 000] 2. $160 000 paid at the beginning of each year (with first payment today) for a total of four years [PV=$557 896] 3. Annual payments forever, growing at 6% per year; the first payment of $22 000 being one year from today [PV=$550 000]
14.
Mr. AA borrowed $95 000 for a nine-month period at a nominal rate of 11% per year. What is the effective annual rate if interest is compounded quarterly? [11.5 %]
15.
What is the present value of a stream of monetary flows consisting of negative end-of-year flows of $100 for each of the next 3 years, and positive end-of-year flows of $300 in years 4 through 7, if the appropriate annual discount rate is 10%? [$466]
16.
The current market price of V Corporation's 10-year bonds is $1297.58. The bonds have a 10 percent coupon rate paid semi-annually, and their face value is $1000. What is their yield to maturity (i.e. earned interest stated as a nominal annual rate) if the bonds mature 10 years from today? [6 %]
17.
Illustrate the monetary flows of question 15 above on the time line below. $300
1 2 3 |––––––––|––––––––|––––––––|––––––––|––––––––|––––––––|––––––––|––––––––| 0 4 5 6 7 $100
PART 5.
Full-solution Problem
You are saving for the college education of your two children. One child will enter college in 5 years’ time, while the other will enter in 7 years’ time. College fees per child are expected to be $10 000 per year. These fees must be paid at the beginning of each year. Assume that each child will be in college for four years. Your plan is to contribute a constant monetary amount to a fund over each of the next 5 years. Your first contribution will be made at the end of this year, and your final contribution will be made on the date at which you make the first fee payment. The fund pays an interest rate of 8 percent per year. What constant monetary amount should you contribute per year to the fund in order to meet the expected costs of your children's education? [$11 324.92]
27
TEST # 2 – WINTER '02 ——————————————————————————————————————— Full-solution Problems 1.
Consider the cash flow diagram shown below.
0
4%
$7000
$7000
$7000
5%
6%
7%
1
2
3
$7000
4
$8000
1.1
Given that the discount rate (i.e. time value of money) varies as indicated in the diagram above, determine the monetary value equivalent at time 2 of all the cash flows. [$18 390]
1.2
Assuming that these cash flows are those of a project, determine its net present value at a constant cost of capital of 12 percent. [$13 261]
2.
NOR.com’s maximum annual production capacity is 1560 switches which are produced at a uniform rate. Given fixed costs of $50 000 per year, constant variable costs of $320 per unit and a selling price of $500 per unit,
2.1
Determine the annual profit if production is maximum and the variable costs increase to $400 per unit over the last 6 months of the year. [$168 400]
2.2
What is the break-even production rate over the first 6 months of the year? [139 units over 6 months]
2.3
What is the annual profit if production is maximum and the fixed costs increase to $150 000 per year while the variable costs decrease to $250 per unit for the full year? [$240 000]
3
BJL Inc. has the following capital structure:
Common stock – market value of $25 million, par value of $20 million, and Ke=19%; Preferred stock – market value of $10 million, par value of $8 million, and Kp=14%; Debt – market value of $40 million, face value of $36 million, and Kd=8% before-tax. 3.1
Using the market values as weights and a corporate income tax rate of 34%, determine BJL’s weighted-average after-tax cost of capital. [11.0%]
3.2
The treasurer of Super Copper Inc. plans to issue 10-year bonds with a face value of $1000 and a $25 coupon every 6 months. The net proceeds per bond is $900 after a discount of $40 and issuing expenses of $60. If the firm is in a 35% income tax bracket, what is the after-tax cost of new debt? [4.15%]
28
4.
Consider the following two mutually exclusive alternatives which have common benefits: Alternative A B ------------------------------------------------------------------------------------------Immediate investment ($) 5 000 10 000 Life (yrs) 5 15 Salvage value ($) 600 1 000 Annual maintenance expense ($) 500 200
4.1
Using the Equivalent Annual Value criterion (i.e. annuity) and a cost of capital of 8 percent, which alternative should be selected? [$1650.20 cost for A and $1331.20 cost for B]
4.2
Determine the present value cost equivalents of the two alternatives using a cost of capital of 16%? [$6351.49 for A and $11 007.20 for B]
TEST # 1 – WINTER '02 ——————————————————————————————————————— PART 1.
Full-solution Problems
1.
In 1555, King Henry borrowed money from his bankers, agreeing to repay 5 percent of the amount borrowed at each fair (there were four fairs per year) until he had made a total of 40 payments. At this time, the loan would be considered repaid. What effective annual interest rate were the bankers charging? [16.67%]
2.
You bought land three years ago for $50 000. It is worth $65 000 today. What annual interest rate did you earn if interest is compounded yearly? [9.14%]
3.
A bond with a face value of $1000 and a coupon rate of 8% payable semi-annually will mature in 10 years. If you want to earn an annual interest rate of 10% (effective annual rate), what maximum amount would you be willing to pay today to purchase this bond? [$889.21]
4.
John is considering working on a one-year project that will cost him $20 000 today. The project will pay him $10 000 at the end of each month for the next 12 months, and cost him another $15 000 at the end of each quarter. An extra $10 000 will be received at the end of the project, one year from now. Illustrate these monetary flows in two diagrams, using monthly periods: i) Show each monetary flow element separately. $10 000 $10 000 t=0 |--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|
$20 000
$15 000 t=3
t=6
t=9
29
t=12
ii) Show only the net monetary flow in each period. $10 000 $5000 t=0 |--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------| $5000 t=3
t=6
t=9
t=12
$20 000 PART 2.
Multiple-choice Problems and Statements
1.
A firm has a current ratio of 1.9. If some of the accounts payable are paid off from the cash account, the current ratio would: [B] A) remain unchanged B) increase C) decrease
2.
A firm has a quick ratio of 1.2. If inventory were purchased for cash, the quick ratio would: [C] A) remain unchanged B) increase C) decrease
3.
All other things held constant, which one of the following transactions will cause a firm’s current ratio that is now greater than 1.0 to increase? [C] A) accounts receivable are collected and the funds received are deposited in the firm’s cash account B) fixed assets are purchased from the cash account C) accounts payable are paid with funds from the cash account D) inventory is purchased on account (i.e. not purchased for cash)
4.
RGB Inc’s income statement indicates a cost of goods sold of $100 000. The balance sheet shows an average accounts payable balance of $12 000. What is RGB’s average days’ payable outstanding? [44 days]
5.
RGB Inc. has a gross profit margin of $45 000 on sales of $150 000. The balance sheet shows total assets of $75 000 with an average inventory balance of $15 000. What is RGB’s total asset turnover ratio? [2]
6.
If RGB Inc. has credit sales of $100 000, average accounts payable of $30 000, and average accounts receivable of $25 000, what is RGB’s average collection period? [91 days]
PART 3. 1.
Full-solution Problems
The production cost function of a firm is given by: TC= 10 + 20 R – 3 R2 + 0.8 R3 in which TC represents the total annual production cost in thousands of dollars and R represents the annual production rate in thousands of units.
1.1
Determine the annual fixed costs associated with the production process. [$10 000]
1.2
Determine the average variable costs at a production rate of 3000 units per year. [$18.20]
30
1.3
Determine the average production costs at a production rate of 6000 units per year. [$32.47]
1.4
Determine the production rate that minimises marginal production costs. [1250 units]
2.
An asset costs $14 000 and has salvage value of $3000 at the end of its 7-year life.
2.1
Determine the asset’s book value after one year using straight-line depreciation. [$12 428.57]
2.2
Determine the asset’s book value after 4 years using declining-balance depreciation with an annual rate of 20%. [$5734.40]
TEST # 2 – FALL '01 ——————————————————————————————————————— PART 1.
True or False Statements
1.1
An annuity can easily be converted into a series of equal beginning-of-period payments by dividing the monetary value of the annuity by (1 + i) in which i represents the interest rate per period.
1.2
The series compound amount factor for an annuity comprised of n payments is in fact the summation of n compound amount factors associated with periods of 1 to n.
1.3
The Theory of the Business Firm assumes perfect market competition, i.e. it assumes that the selling price is independent of the production rate.
1.4
In a non-linear cost function, the average variable cost is not constant.
1.5
In the Theory of the Business Firm, the maximum marginal profit is achieved at the rate associated with the point of inflexion on the total production cost curve.
1.6
A preferred share certificate always indicates a par value, but a common share certificate need not indicate such a value.
1.7
Preferred shares allow the expansion of a company’s equity base without diluting the voting power of the bondholders.
1.8
The overall cost of common equity may be assessed with the ratio of earnings per share to market price.
1.9
The objective of business firms that maintain a particular capital structure over the long-term is to minimise their weighted-average cost of capital.
1.10 The maturity date on a bond specifies the time at which the interest becomes payable. PART 2. Complete the statements below with words or expressions selected from the following list. Note that any word or expression may be used more than once. Return on investment, annual monetary amount, debt to equity ratio, dividends, discount, weightedaverage cost of capital, capital structure, salvage value, effective annual interest rate, financial leverage, interest payments, collateral. 2.1
??? refers to the ability of a business to increase its return on equity by including debt in its capital structure.
31
2.2
The mixture of debt and equity sources of funds in a company’s permanent long-term financial structure is referred to as ??? .
2.3
By convention, the cost of capital is expressed as an ??? .
2.4
Long-term debt is a relatively cheap source of funds for a company because bonds and debentures are a low-risk type of investment from the investors’ point of view, and because ??? are tax deductible.
2.5
Bonds are a form of long-term debt that use specific assets as ???
PART 3.
Full-solution Problems
3.1
The annual fixed costs associated with a production process are $680 000, and the variable cost is $150 per unit for any quantity produced up to 8000 units per year, and $130 for that part of the total annual production that exceeds 8000 units. The constant selling price per unit is $200. Determine the break-even production rate. [12 000 units]
3.2
George bought an apartment building for $400 000 and resold it one year later for $480 000. The purchase was financed with $200 000 of his own money and $200 000 which he borrowed from the bank at an annual interest rate of 10 percent compounded annually. What was his ‘accounting’ return on equity? [30%]
3.3
John’s objective is to accumulate a sum of $35 000 in five years’ time. He now has $10 000 in a bank account that pays an annual interest rate of 7.85 percent compounded semi-annually. What equal annual amount will he have to deposit starting two years from now to meet his objective (he will make four deposits)? [$4506.12]
3.4
Using a minimum acceptable return on investment of 12 percent, determine the present value ratio as well as the payback period of a project that has a one-year preproduction period and the time distribution of cash flows as shown below. [PVR: 0.33; PP: 2.5 years] Year Cash Flow ($)
Time 0 -15 000
1 -25 000
2 15 000
3 15 000
4 20 000
5 25 000
TEST # 1 – FALL '01 ——————————————————————————————————————— PART 1.
True or False Statements
1.1
The theory of production is a microeconomic issue.
1.2
International business relations are a microeconomic issue.
1.3
The demand function expresses the market price of a product as a function of the quantity demanded by consumers.
1.4
At a constant market price, increases in demand for a particular product may be the result of substitution, changes in consumer tastes or good marketing.
1.5
Price elasticity expresses the relative change in quantity as a function of the relative change in price.
1.6
The price elasticity of essential products tends to be less than unity.
32
1.7
A demand function that is quasi-vertical is very elastic.
1.8
Most supply functions are elastic at high price levels and inelastic at low price levels.
1.9
The market equilibrium between supply and demand always occurs at the point at which the price elasticity of demand is unitary.
1.10 The productivity of a process is measured by the average product. 1.11 In a production process, the interval over which the average product increases represents Stage I of production. 1.12 The average cost reflects the economic efficiency of a production process. 1.13 In a linear cost function, both the average fixed cost and the average variable cost are constant. 1.14 Cash and inventory are typical examples of current assets. 1.15 The net income of a business serves two purposes: distribution to the shareholders as dividends and/or an internal source of funds for new and ongoing projects. 1.16 When the inventory account decreases, it receives value. 1.17 An expense incurred to purchase consumable materials is usually referred to as a capital expenditure. 1.18 The income statement establishes the net income of a business over the relevant accounting period. 1.19 The fixed assets of a business are recorded in the balance sheet at their book value, i.e., at their original cost less accumulated depreciation. 1.20 Dividends paid to shareholders and the disposal of fixed assets are typical uses of funds in the statement of changes in financial position. 1.21 The working capital is a measure of activity, i.e., an indication of how well a business uses its resources. 1.22 Leverage is a measure of the extent to which a business is financed by debt as opposed to equity. 1.23 The profit margin is the complement of the operating cost ratio. 1.24 When a used asset is sold for an amount exceeding its purchase price, a capital gain is realised. 1.25 The compensation received by a money lender that forfeits the use of his/her own wealth is known as interest. PART 2. Complete the statements below with words or expressions selected from the following list. Note that any word or expression may be used more than once. Advances in technology, amortisation, average fixed cost, capital surplus, current assets, depreciation, economically efficient, intangibles, inventory, inventory turnover ratio, land, marketable securities, net income, net worth, notes payable, prepaid expenses, profit, shortage, short-term imbalances, source of funds, substitution, surplus, technically efficient, total assets, total consumer expenditure, use of funds.
33
2.1
??? is a factor that may cause a change in demand, i.e. a shift of the curve to the right or to the left.
2.2
??? are assets having no physical existence, yet having substantial value to a company.
2.3
A corporation's ???, obtained by subtracting all liabilities from the value of its assets, represents the total equity interest of the shareholders.
2.4
Depreciation is listed as a ??? in the Statement of Changes in Financial Position.
2.5
A ??? in a free and competitive economic system creates forces that tend to drive the price of a product back up to its equilibrium level.
2.6
The price elasticity of demand can be predicted by observing the change in ??? resulting from a change in price.
2.7
The production function represents all ??? combinations of factor inputs used in the production of goods or services.
2.8
??? include cash and those assets which, in the normal course of business, will be turned into cash in the reasonably near future, generally within one year from the date of the balance sheet.
2.9
The ??? of a manufacturer consists of raw materials used in the product, partially finished goods in process of manufacture and finished goods ready for shipment to customers.
2.10 ??? is not subject to depreciation; thus, its listed value in the balance sheet remains unchanged from year to year. PART 3.
Full-solution Problems
3.1
If a relative increase in price of 5 percent along a demand function causes a relative decrease in quantity of 2 percent, then the price elasticity of demand has an approximate value of... [0.4]
3.2
Given the production function [ Q = 20 S + 10 S2 - S3 ] in which Q is given in thousands of units of output per month and S in thousands of units of input per month, determine the marginal product at an input rate of 3000 units/month. [53]
3.3
Given the cost function [ TC = 50 000 + 40 R ] in which TC is given in $/year and R in units/year, determine the marginal cost at a production rate of 4000 units/year. [40]
3.4
Given the cost function [ TC = 50 000 + 40 R ] in which TC is given in $/year and R in units/year, determine the average fixed cost at a production rate of 5000 units/year. [$10]
3.5
A business receives $10 000 worth of accounts receivable in cash. The company accountant must credit the ??? account and debit the ??? account. [receivables, cash]
3.6
An asset costing $60 000 has an estimated salvage value of $10 000. Using straight-line depreciation with an annual rate of 15 percent, determine the depreciation charge for accounting purposes to be used in the asset’s 7th year of use. [$5000]
3.7
Walter borrowed a principal amount of $500 to be repaid along with all accumulated interest charges in 5 years’ time. If the nominal annual interest rate is 10 percent compounded semiannually, how much does he owe by the end of the period? [$814.45]
3.8
Determine the effective annual interest rate associated with a nominal rate of 12 percent compounded monthly. [12.68%]
34
TEST # 2 – WINTER '01 ——————————————————————————————————————— PART 1.
True or False Statements
1.1
In the theory of supply and demand, the selling price of a product is a function of the quantity supplied to the market.
1.2
In the theory of supply and demand, a shift in the supply schedule to higher levels results in a vertical upward movement of the supply curve.
1.3
Decreased demand for a product may be the result of substitution, a decline in consumer income, or an increase in the cost of raw materials and labour.
1.4
In the theory of supply and demand, total consumer expenditure and total producer sales revenue are equal at the market equilibrium point.
1.5
In a demand or supply function, price elasticity measures how the quantity responds to a change in price.
1.6
The market equilibrium between supply and demand always occurs at the point of unitary elastic demand.
1.7
Because luxury items are expensive, their demand tends to be elastic.
1.8
Fixed resources in a production process should only be considered as such in the short-term, because they become in fact variable in the long-term..
1.9
In a production process, variable resources generally remain constant within a relatively small range of output.
1.10 The average product reflects the productivity of a production process. 1.11 The average cost reflects the economic efficiency of a production process. 1.12 In a linear cost function, both the average fixed cost and the average variable cost are constant. 1.13 The Balance Sheet is the principal accounting instrument for showing the financial position of a company at a given point in time. 1.14 Current assets include cash and those assets which, in the normal course of business, will be turned into cash in the reasonably near future, generally within one year from the date of the Balance Sheet. 1.15 Cash, marketable securities and inventory are typical examples of quick assets. 1.16 Fixed assets are those assets not intended for sale that are used over and over again to manufacture the product, display it, warehouse it and transport it. 1.17 For accounting purposes, depreciation is defined as the decline in the useful value of fixed assets due to wear and tear from use and passage of time. 1.18 Long-term debt represents the total amount of money invested in a business by its owners, i.e. the shareholders’.
35
1.19 Capital surplus represent the amount paid by shareholders’ over the par or legal value of the common share. 1.20 Accumulated retained earnings are undistributed profits reinvested in the business to help it grow. 1.21 Working Capital = Current Assets - Current Liabilities 1.22 The current ratio measures the ability of a firm to meet its short-term debt obligations. 1.23 Capital structure is the mixture of debt and equity sources of funds that are listed on the asset side of the balance sheet. 1.24 The debt to equity ratio is a measure of the liquidity of a business firm. 1.25 The profit margin is the complement of the operating ratio. 1.26 The Income Statement summarizes the sales revenue, other income items and operating expenses of a business firm at a specific point in time. 1.27 Interest on bonds and preferred stock dividends must be paid from net income of a business firm before any dividends can be distributed on common stock. 1.28 The dividend payout ratio represents the proportion of net income paid out in dividends to the stockholders. 1.29 A positive rate of return indicates a profitable project. 1.30 The theory of the business firm is an issue studied in macroeconomics. PART 2. Complete the statements below with words or expressions selected from the following list. Note that any word or expression may be used more than once. Prepaid expenses, inelastic, accumulated, capital surplus, intangibles, shortage, notes payable, capital loss, net worth, profit, inventory turnover ratio, elastic, surplus, amortisation, capital gain, depreciation, source of funds, marketable securities, total fixed cost, net income, average fixed cost, use of funds, business risk, capital gain. 2.1
The approved method for the valuation of fixed assets in the balance sheet is cost less the ??? by the date of the balance sheet.
2.2
??? are assets having no physical existence, yet having substantial value to a company.
2.3
A corporation’s ???, obtained by subtracting all liabilities from the value of its assets, represents the total equity interest of the shareholders.
2.4
Depreciation is listed as a ??? in the Statement of Changes in Financial Position.
2.5
A ??? in a free and competitive economic system creates forces that tend to drive the price of a product back down to its equilibrium level.
2.6
??? is the decline in the useful value of an intangible.
2.7
A ??? is realized when an asset is sold for more than its purchase price.
2.8
Payments made in advance from which a company has not yet received benefits, but for which it will receive benefits within the following year, are listed among current assets as ???.
36
2.9
??? represents the amount paid by stockholders over the par or legal value of the common shares.
2.10 Too high a level of long-term debt in the capital structure of a business firm increases its ???. PART 3. Complete the statements below with words or expressions selected from the following list. Note that any word or expression may be used more than once. Substitution, net income, decline in consumer income, capital gain, short-term imbalance, arc elasticity, marginal elasticity, working capital, intangibles, total consumer expenditure, stage II, technically efficient, production, economically efficient, shareholders’ equity, capital surplus, book value, liquidity, leverage, deferred taxes, fixed, depreciation, capital loss, equivalent. 3.1
??? are non-quantifiable factors that may affect a project now or in the future.
3.2
??? is a factor that may cause an increase or a decrease in demand, i.e. a shift of the demand curve to the right or to the left.
3.3
??? in the market place result from the inability of consumers and/or producers to respond quickly to market changes.
3.4
The elasticity at a particular price on the demand curve can be predicted (i.e. elastic or inelastic) by observing the change in ??? resulting from a change in price.
3.5
The production function represents all ??? combinations of factor inputs used in the production of goods and services.
3.6
The net worth of a business firm consists of the value at par of outstanding common and preferred shares, ??? and accumulated retained earnings.
3.7
Accumulated retained earnings represent that part of ??? not distributed to the shareholders but accumulated and reinvested in the business.
3.8
Shareholders’ Equity is sometimes referred to as the ??? of the firm.
3.9
The difference between the uses and sources of funds in the statement of Change in Financial Position may be explained by the change in ???.
3.10 The acid test ratio is a financial indicator that measures the ??? of a business firm. PART 4.
Full-solution Problems
4.1
For the production function [ Q = 20 S + 10 S2 - S3 ] in which Q is given in thousands of units of output per month and S in thousands of units of input per month, determine the marginal product at an input rate of 2000 units/month. [48]
4.2
For the cost function [ TC = 60 000 + 50 R ] in which TC is given in $/year and R in units/year, determine the average cost at a production rate of 4000 units/year. [$65]
4.3
For the cost function [ TC = 60 000 + 50 R ] in which TC is given in $/year and R in units/year, determine the incremental cost between production rates of 4000 and 4500 units/year. [$50]
4.4
Using straight-line depreciation, determine the annual depreciation charge for accounting purposes associated with an asset costing $45 000, and having an estimated salvage value of $5000 at the end of a period of use of 5 years. [$8000]
37
4.5
Determine the payback period and the net present value associated with a project having the time distribution of cash flows shown below. Use a discount rate of 10 percent. [PP: 2.5 years; NPV:$10 113] Year Cash Flow ($)
Time 0 -25 000
1 10 000
2 10 000
3 10 000
4 15 000
TEST # 1 – WINTER '01 ——————————————————————————————————————— PART 1. Shown below are last year’s demand and supply curves for a particular consumer product on a free and competitive market. At the beginning of this year, stricter environmental regulations resulted in a downward shift in supply of 20 000 units per year at all price levels. However, a vigorous publicity campaign caused an upward shift in demand of 40 000 units per year at all price levels. 40.5 40.0
PRICE ($/unit)
39.5 39.0 38.5 38.0 37.5 37.0 36.5 36.0 200
240
280
320
360
400
440
480
QUANTITY ('000 units/yr) 1.1
Draw the new demand and supply curves on the diagram above.
1.2
Determine graphically the new market equilibrium price and quantity. [P: $38.65; Q: 345 000]
1.3a Determine the direction and magnitude of change, if any, in total consumer expenditure caused by the shift in the demand and supply curves. [+ $329 250] 1.3b Can the change determined in 1.3a above be used to predict the price elasticity of demand in the vicinity of the new market equilibrium point – yes or no? Justify your answer. [No] 1.4
Determine graphically the point elasticity on last year’s demand curve at a price of $38.00. [8.44]
PART 2. The list below contains selected balances from the accounts of ZYZWYX Incorporated as of 31 December, 2000. The company had only common shares outstanding at that time. All values are in ‘000 $. Cash 15 000 Net fixed assets 60 000 Long-term debt 22 000 Accumulated retained earnings 25 000 Accumulated depreciation 20 000
38
Shareholders’ equity Accounts receivable Accounts payable Cost of goods sold Inventory of finished products Taxes payable Deferred taxes Rental expenses
55 000 12 000 16 000 60 000 18 000 4 000 8 000 10 000
Using a proper format, construct ZYZWYX’s Balance Sheet at 31 December, 2000. [Total Assets: $105 000; Total Liabilities: $50 000; Shareholders’ Equity: $55 000] PART 3.
Using the information given in the table below, determine the following elements.
Common shares outstanding (#) Common shares at par ($) Preferred shares at par ($) Shareholders’ Equity Accumulated Retained Earnings
31 December,1999 400 000 2 000 000 500 000 3 600 000 ?
31 December, 2000 500 000 2 500 000 500 000 ? ?
Year 1999 600 000 150 000
Year 2000 800 000 200 000
Net Income Dividend (common and preferred) 3.1
Accumulated Retained Earnings, 31 December, 1999 [$1 100 000]
3.2
Accumulated Retained Earnings, 31 December, 2000 [$1 700 000]
3.3
Shareholders’ Equity, 31 December, 2000 [$4 700 000]
3.4
Book Value per common share, 31 December, 1999 (assume that there are no intangibles) [$7.75]
PART 4. Using all the monetary flows shown in the diagram below and an interest rate of 10 percent per period, determine the following elements.
0
$300
$300
1
2
$400
$400
3
4
$500
$500
5
6
4.1
The present value equivalent at time 0 of all monetary flows. [$1687.01]
4.2
The future value equivalent at time 5 of all monetary flows. [$2717.08]
39
4.3
The beginning-of-period equivalent (there are 6 payments) of all monetary flows. [$352.12]
4.4
The present value equivalent at time 0 of all monetary flows if the interest rate per period is 5 percent over the first three periods and 10 percent over the last three periods. [$1898.92]
PART 5. Equipment that was purchased at a cost of $260 000 has an estimated salvage value of $29 000 at the end of a useful life of 6 years. The rate of usage of the equipment is planned as follows: 1700 hours per year over the first 4 years, and 1600 hours per year over the last two years. 5.1
Using the sum-of-the-years’-digits method, determine the depreciation charge that should be used for accounting purposes in year 4. [$33 000]
5.2
Using the unit of production depreciation method, determine the accounting book value of the asset at the end of its third year of use. [$142 190]
TEST # 2 – FALL '00 ——————————————————————————————————————— PART 1. Four years ago, a company purchased equipment at a price of $240 000 f.o.b. (i.e. excluding shipping charges). Additional expenses incurred to ship and install the equipment in the company plant amounted to $30 000 (these expenses are depreciable as well). At the time of purchase, the salvage value of the equipment, at the end of a useful life of 7 years or an equivalent 18 000 hours of operation, was estimated at $35 000. 1.1
Using sum-of-the-years’-digits depreciation, determine the asset’s current book value. [$85 357.14]
1.2
Given that the equipment was operated for 2000, 2200, 2500 and 2400 hours over year 1, 2, 3 and 4, respectively, and using unit of production depreciation, determine the depreciation charge claimed in its third year of operation. [$32 638.89]
PART 2. 2.1
Given the monetary flow diagram shown below, in which the interest rate per period varies as indicated, determine the future value equivalent at time 5 of all the monetary flows. [$1082.45] $400
$300
0
8%
1
8%
$400
$400
$300
10% 2
$400
$400
10% 3
12% 4
$400
40
12% 5
12% 6
7
2.2
You now have $75 000 in a savings account earning a nominal annual interest rate of 10 percent compounded semi-annually. Your objective is to withdraw a certain amount today and at every sixmonth interval thereafter over the following five-year period (i.e. a total of 11 equal withdrawals) such that there will be a balance of $15 000 remaining in the account in five-years’ time. What amount should you start withdrawing today? [$7543.37]
PART 3. A plant is currently producing 10 000 units per year at an average production cost of $52. If the plant were to produce 12 000 units per year, the total production cost would amount to $600 000. The plant’s production cost function is linear. If the selling price of the product is $75 per unit, determine the plant’s break-even production rate. [3429 units] PART 4.
True or False Statements
4.1
When compounding occurs more that once per year, the effective annual interest rate equal to the nominal annual interest rate.
4.2
Cash flows can be moved from one point in time to another using an interest rate that represents the time value of money without altering their purchasing power.
4.3
The factor (P/A,i,n) is in fact equal to the summation of the factors (P/F,i,k) when k varies from 1 to n.
4.4
The factor (F/A,i,n) is in fact equal to the summation of the factors (F/P,i,k) when k varies from 1 to n.
4.5
In a process in which there is a fixed cost, the average fixed cost is minimised at an indeterminate production rate.
4.6
In a process in which the average variable cost is constant, the marginal cost is constant.
4.7
The theory of the business firm states that annual profit is maximised at the production rate at which average cost is minimised.
4.8
The theory of the business firm assumes that the total revenue is constant.
PART 5. Complete the statements below with words or expressions selected from the following list. Note that any word or expression may be used more than once. Fixed resources, marginal cost, variable resources, purchasing power, simple interest, monetary flow, spending power, compound interest, compounding, disbursement, perfect market competition, earning power, nominal interest rate, average production cost, level of inventory, amortisation, break-even production rate, theory of the business firm, salvage value, production limit, depreciation, non-linear cost, linear cost, affirmative theory, book value. 5.1
With ???, the interest is due at the end of each compounding period.
5.2
In depreciation for accounting purpose, the book value of an asset at the end of its period of use is set equal to its estimated ???.
5.3
It may be possible to decrease the ??? by shifting some of the fixed costs to variable costs
5.4
The ??? represents the tangent of the angle of a ray joining the origin with a point on the total production cost curve.
5.5
The ??? at a particular point in time is the difference between the inflows and outflows of cash that occur at the time.
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5.6
In the theory of the business firm, the selling price is considered independent from the production rate because ??? is assumed.
TEST # 1 – FALL '00 ——————————————————————————————————————— PART 1.
The demand relationship for a commodity id given by: P = 56.2 - 3.2 Q + 0.05 Q2
In which the price P is in $/unit and the quantity Q is in thousands of units per month. The supply relationship for that same commodity is given by: P = 8.24 - 1.24 Q + 0.06 Q2 In which the units are the same. Both functions are valid between 10 000 and 30 000 units per month. 1.1
Find the market equilibrium point (i.e. determine P* and Q*). Hint: Solution to quadratic equation f(x): x = (-b ! SQRT[b2 – 4 a ∗ c]) / 2a. [P*=$10; Q*=22 000]
1.2
Determine the total consumer expenditure at the market equilibrium point (give P, Q and P∗Q) [At P=10 and Q=22 000, P∗ Q= $220 000]
1.3
Is the market equilibrium point determined in 1.1 above the point of maximum total consumer expenditure? Justify your answer. [Below]
1.4
A general economic slowdown shifts the demand curve by 3000 units per months. What is the relationship of the new demand curve? Provide your answer in the form P = a + b∗Q + c∗Q2 for maximum points. [P = 47.05 - 2.9 Q + 0.05 Q2]
PART 2. Lotus Emergis specializes in hardware for data logging and transfer. Some operational data for 1999 are shown below (in ‘000 $): Net sales Component inventory at beginning of 1999 Component inventory at end of 1999 Component purchases in 1999 Labour expenses Marketing expenses Net Fixed Assets at the beginning of 1999 Net Fixed Assets at the end of 1999 Utility expenses Income taxes Administrative expenses Property taxes Retained earnings at the beginning of 1999
9000 2000 1600 3000 2000 4000 2000 3000 300 0 2500 150 (4000)
2.1
Prepare an Income Statement for 1999. [Net Income: ($3350)]
2.2
Determine the level of retained earnings at the end of 1999. [$7 350 000]
2.3
Determine the operating cost ratio and comment. [1.4; too high due to excessive operating expenses]
42
2.4
Determine the fixed asset turnover ratio and comment. [3.6: low, indicating low efficiency of fixed assets]
PART 3.
True or False Statements
3.1
In a demand or supply function, price elasticity measures how the quantity responds to a change in quantity.
3.2
Demand is said to be elastic when the quantity demanded decreases significantly as a result of an increase in price.
3.3
The demand for essential goods tends to be inelastic.
3.4
In a free and competitive market, the equilibrium price is achieved at the point of unitary elastic demand.
3.5
A linear demand function has a constant arc elasticity.
3.6
Contrary to demand functions, supply functions are generally elastic in the low price range and inelastic in the high price range.
3.7
In a production process, fixed resources are said to be constant in the short-term, but become variable in the long-term.
3.8
The demand function [Q = 500 / P2] has a constant price elasticity.
3.9
Stage III in a production process exhibits diminishing total output.
3.10 The average product is a measure of the technical productivity of a process. 3.11 Transactions that are significantly different from customary business activities of a company are usually recorded as extraordinary items in the income statement. 3.12 The value of a fixed assets as displayed in the balance sheet is intended to reflect its market value at present or its replacement cost in the future. PART 4. Complete the statements below with words or expressions selected from the following list. Note that any word or expression may be used more than once. Depreciation, amortisation, advances in technology, an increase in the cost of raw materials, book value, respond rapidly, reduce their cost in response, purchase price, terminal book value, factor inputs, variable resources, more intensive amounts, a fixed amount, outstanding common and preferred shares, common shares, variable cost component, fixed cost component, marginal product remains constant, marginal product becomes negative. 4.1
??? is a factor that may cause an increase in supply, i.e. a right-shift of the supply curve.
4.2
Short-term imbalances in the market place result from the inability of consumers and/or suppliers to ??? to market changes.
4.3
The production function represents all technically efficient combinations of ??? used in the production of goods or services.
4.4
Diminishing marginal returns is typical in any process in which ??? of variable resources are applied to fixed resources.
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4.5
The interval over which the average product decreases while the ??? represents the second stage of production.
4.6
A production cost function generally displays a ??? which remains constant over a relatively wide range of production rates.
4.7
The net worth of a business firm consists of the value at par of ???, capital surplus and retained earnings.
4.8
A capital gain is realized when a used asset is sold for more that its ???.
4.9
For accounting purposes, ??? is defined as the decline in the useful value of fixed assets due to wear and tear from use and passage of time.
4.10 ??? is the decline in the useful value of an intangible.
TEST # 2 – WINTER '00 ——————————————————————————————————————— PART 1. A plant is characterised by the following production function in which R represents the annual input in hundreds of units of labour and Q, the annual output in thousands of units of product: Q = 4 R + 0.2 R2 - 0.004 R3 1.1
Determine the productivity at an input rate of 3000 units per year. [64]
1.2
Determine the incremental product between input rates of 2000 and 4000 units per year. [48]
1.3
Determine the marginal product at an input rate of 3000 units per year. [52]
PART 2. A plant manufacturing construction equipment incurs a fixed annual cost of $500 000. The unit variable cost associated with the process is constant and equal to $250 for production rates up to 4000 units per year, and decreases to $200 per unit for that part of the production that exceeds 4000 units per year. 2.1
Determine the average production cost at a production rate of 3000 units per year. [$416.67]
2.2
Determine the average production cost at a production rate of 5000 units per year. [$340]
2.3
Determine the marginal cost at a production rate of 5000 units per year. [$200]
2.4
Given that the selling price is $300 per unit, determine the break-even production rate. [7000 units]
PART 3.
True or False Statements
3.1
In an S-shaped cost function, the marginal cost is always minimised at a rate below that at which the average cost is minimised..
3.2
In a production process, the average fixed cost is constant over the short-term.
3.3
The accumulated depreciation entry in a balance sheet represents the sum of all the debit entries in the depreciable asset accounts.
3.4
Depreciation is considered a source of cash for a business in the sense that it has been declared as an expense in the income statement, but hasn’t actually been paid out to any outside party.
44
3.5
In the theory of supply and demand, the quantity of product available on the market is a function of the selling price of that product.
3.6
The market equilibrium point never occurs at the point of unitary elasticity of demand.
3.7
Total consumer expenditure is maximised at the market equilibrium point.
3.8
The demand function [Q = 750 / P] has a constant price elasticity of unity.
3.9
The price elasticity of the function [Q = 1250 P + 10 000] is always less than unity.
3.10 In the theory of supply and demand, when total consumer expenditures increase as a result of a increase in price, then demand is elastic. 3.11 Current assets include cash and those assets which, in the normal course of business, will be turned into cash in the reasonably near future, generally within one two years from the date of the balance sheet. 3.12 The sale of a depreciable asset for an amount lower than its purchase price results in a capital loss. PART 4. From the information listed below, construct a Statement of Changes in Financial Position. [Total Sources: $400 000; Total Uses: $280 000; Working Capital increased by $120 000] Net income Dividends on preferred Dividends on common Depreciation Increase in long-term debt Purchase of fixed assets Current assets at beginning of exercise Working capital at beginning of exercise Current assets at end of exercise Current liabilities at end of exercise
270 000 40 000 60 000 100 000 30 000 180 000 420 000 190 000 510 000 200 000
PART 5. Equipment that was purchased at a cost of $260 000 has an estimated salvage value of $60 000 at the end of a useful life of 4 years. The rate of usage of the equipment is planned as follows: 1500 hours per year over the first year, rising at a compound rate of 10 percent per year thereafter. 5.1
Using the declining-balance method with an annual rate of 25 percent, determine the book value of the asset at the end of its third year of use. [$109 687.50]
5.2
Using the unit of production depreciation method, determine the depreciation charge for tax purposes for the asset in its fourth year of use. [$74 565.83]
PART 6. Two year ago, Henry purchased a car worth $25 000. He made a down-payment of $5000 and financed the remainder with a loan from his bank over a period of 36 months. The bank charged a nominal annual rate of 8 percent compounded monthly, and the first payment was due one month following the purchase. If Henry wants to pay the balance of the loan today, what additional amount must he remit, along with this month’s payment? [$7831.45]
45
TEST # 1 – WINTER '00 ——————————————————————————————————————— PART 1.
From the demand curve plotted on the graph below, 75
PRICE ($/unit)
70 Point A: Q=31 750, P=61 65 Point B: Q=33 500, P=57 60
55
50 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
QUANTITY ('000 units/yr) 1.1
Determine the arc elasticity between points A and B. [0.791]
1.2
Determine the point elasticity at B using the graphical estimation method. [1.08]
PART 2. A plant has the following cost function in which R represents the annual production rate in thousands of units and TC, the total annual production cost in thousands of dollars: TC = 20 + 10 R - 2 R2 + R3 2.1
Determine the marginal cost at a production rate of 3000 units per year. [$25]
2.2
Determine the incremental cost between production rates of 2000 and 4000 units per year. [$26]
PART 3.
True or False Statements
3.1
The marginal product equals the average product when the marginal product is maximised.
3.2
The equivalent to the marginal cost in a cost schedule is the incremental cost.
3.3
The accumulated depreciation entry associated with a particular fixed asset that appears in the Balance Sheet represents the sum of all the credit entries in that fixed asset’s account.
3.4
Depreciation is considered a use of cash for a business in the sense that it accounts for the money that was spent to purchase capital assets in the past.
3.5
In the theory of supply and demand, the selling price of a product is a function of the quantity available on the market.
3.6
The market equilibrium point always occurs at the point of unitary elasticity of demand.
3.7
At market equilibrium, total consumer expenditures equal total producer sales revenue.
46
3.8
The demand function [Q = 750 / P] has a constant price elasticity.
3.9
The supply function [Q = 1250 P + 10 000] has a constant price elasticity.
3.10 In the theory of supply and demand, when total consumer expenditures increase as a result of a decrease in price, then demand is elastic. PART 4. Complete the statements below with words or expressions selected from the following list. Note that any word or expression may be used more than once. Substitution, net income, decline in consumer income, capital gain, short-term imbalances, arc elasticity, marginal elasticity, working capital, intangibles, total consumer expenditure, stage II, technically efficient, productive, economically efficient, shareholders’ equity, capital surplus, book value, liquidity, leverage, business risk, deferred taxes, depreciation, capital loss, equivalent. 4.1
??? are non-quantifiable factors that may affect a project now or in the future.
4.2
??? is a factor that may cause a change in demand, i.e. a shift of the curve to the right or to the left.
4.3
??? in the market place result from the inability of consumers and/or suppliers to respond rapidly to market changes.
4.4
The price elasticity of demand can be predicted by observing the change in ??? resulting from a change in price.
4.5
Factor inputs to a production process can either be ??? or variable.
4.6
The production function represents all ??? combinations of factor inputs used in the production of goods or services.
4.7
The net worth of a business consists of the value at par of outstanding common and preferred shares, ??? and accumulated retained earnings.
4.8
Retained earnings represent that part of ??? not distributed to the shareholders but accumulated and reinvested in the business.
4.9
Shareholders’ Equity is also referred to as the ??? of the firm.
4.10 The difference between the uses and sources of funds in the statement of Change in Financial Position may be explained by the change in ???. 4.11 The acid test ratio is a financial indicator that measures the ??? of a business firm. 4.12 Too much debt in the financial structure of a firm increases its ???. 4.13 The ??? taxes entry in the Balance Sheet accounts for the fact that depreciation used in the Income Statement is seldom the same as that used to determine the taxable income. 4.14 A ??? is realised when a used asset is sold for more than its purchase price. 4.15 Monetary values occurring at different points in time are said to be ??? if they have the same earning power.
47
PART 5.
Using the information given in the table below, determine the following elements.
Common shares outstanding (#) Common shares at par ($) Preferred shares at par ($) Shareholders’ Equity Capital Surplus Accumulated Retained Earnings
Net Income Dividend declared and paid
31 December,1998 400 000 2 000 000 500 000 3 500 000 ? 800 000
31 December, 1999 500 000 2 500 000 500 000 ? 300 000 ?
Year 1998 500 000 170 000
Year 1999 600 000 200 000
5.1
Capital Surplus, 31 December, 1998 [$200 000]
5.2
Shareholders’ Equity, 31 December, 1999 [$4 500 000]
5.3
Accumulated Retained Earnings, 31 December, 1999 [$1 200 000]
5.4
Book Value per common share, 31 December, 1999 (assume that there are no intangibles) [$8]
PART 6. Equipment that was purchased at a cost of $160 000 has an estimated salvage value of $20 000 at the end of a useful life of 5 years. The rate of usage of the equipment is planned as follows: 1600 hours per year over the first 3 years, and 1100 hours per year over the last two years. 6.1
Using the sum-of-the-years’-digits method, determine the depreciation charge that should be used for accounting purposes in year 3. [$28 000]
6.2
Using the unit of production depreciation method, determine the accounting book value of the asset at the end of its fourth year of use. [$42 000]
PART 7. A haulage truck costing $250 000 is expected to have a useful life of 5 years after which time it will be sold for $35 000. Annual operating expense of the truck are expected to amount to $40 000 in years 1 to 3, and $50 000 in years 4 and 5. The truck will require maintenance at the end of year 2 and 4, costing $20 000 and $25 000, respectively. Using a time value of money of 12 percent, what minimum annual benefits must the truck yield over its life to justify its purchase? [$116 028]
48