1.You invest $1,000 in a certificate of deposit that matures after 10 years and pays 5 percent interest, which is compounded annually until the certificate matures.
a. How much interest will the saver earn if the interest is left to accumulate?
b. How much interest will the saver earn if the interest is withdrawn each year?
c. Why are the answers to a and b different?
2. A self-employed person deposits $3,000 annually in a retirement account (called a Keogh account) that earns 8 percent.
a. How much will be in the account when the individual retires at the age of 65 if the savings program starts when the person is age 40?
b. How much additional money will be in the account if the saver defers retirement until age 70 and continues the contributions?
c. How much additional money will be in the account if the saver discontinues the contributions at age 65 but does not retire until age 70?
3. A 45-year-old woman decides to put funds into a retirement plan. She can save $2,000 a year and earn 9 percent on this savings. How much will she have accumulated if she retires at age 65? At retirement how much can she withdraw each year for 20 years from the accumulated savings if the savings continue to earn 9 percent?
5. If a father wants to have $100,000 to send a newborn child to college, how much must he invest annually for 18 years if he earns 9 percent on his funds? (Any current student who subsequently becomes a parent and wants to send a child to college should make this calculation early in the child's life.)
6. A widow currently has a $93,000 investment yielding 9 percent annually. Can she withdraw $16,000 a year for the next 10 years?
7. An investment generates $10,000 per year for 25 years. If you can earn 10 percent on other investments, what is the current value of this investment? If its current price is $120,000, should you buy it?
12. You are 25 years old and inherit $65,000 from your grandmother. If you wish to purchase a $100,000 yacht to celebrate your 30th birthday, what compound annual rate of return must you earn?
13. An investment offers to pay you $10,000 a year for five years. If it costs $33,520, what will be your rate of return on the investment?
3. Fill in the blanks (_________) with the correct entries.
Assets &nbs p; Liabilities and Stockholders' Equity
Current asset   ; Current liabilities
Cash $ 250,000 Accounts payable $ 620,000
Accounts receivable (_________ less)
allowance for doubtful
accounts of $20,000) 1,320,000
Notes payable to banks 130,000
; Accrued wages _________________________
&nb sp; Taxes owed 100,000
Total current liabilities $1,250,000
Total current assets ____________________ Long-term debt _________________________
Plant and equipment Preferred stock 1,000,000
($2,800,000 less accumulated Common stock ($1 par, 750,000 shares
depreciation _________) 2,110,000 authorized, 700,000 outstanding) _________
Total assets $5,390,000 Retained earnings _____________________
&nb sp; Total stockholders' equity $3,140,000
Total liabilities and equity __________________
8. Given the following information, compute the current and quick ratios:
Accounts receivable 357,000
Current liabilities 498,000
Long-term debt 610,000
9. If a firm has sales of $25,689,000 a year, and the average collection period for the industry is 45 days, what should this firm's accounts receivable be if the firm is comparable to the industry?
11. A firm with sales of $500,000 has average inventory of $200,000. The industry average for inventory turnover is four times a year. What would be the reduction in inventory if this firm were to achieve a turnover comparable to the industry average?
3. Jersey Mining earns $9.50 a share, sells for $90, and pays a $6 per share dividend. The stock is split two for one and a $3 per share cash dividend is declared.
a. What will be the new price of the stock?
b. If the firm's total earnings do not change, what is the payout ratio before and after the stock split?
4. Firm A had the following selected items on its balance sheet:
Cash $ 28,000,000
Common stock ($50 par; 2,000,000 shares outstanding) 100,000,000
Additional paid-in capital 10,000,000
Retained earnings 62,000,000
How would each of these accounts appear after:
a. a cash dividend of $1 per share?
b. a 5 percent stock dividend (fair market value is $100 per share)?
c. a one-for-two reverse split?
5. Jackson Enterprises has the following capital (equity) accounts:
Common stock ($1 par; 100,000 shares outstanding) $100,000
Additional paid-in capital 200,000
Retained earnings 225,000
The board of directors has declared a 20 percent stock dividend on January 1 and a $0.25 cash dividend on March 1. What changes occur in the capital accounts after each transaction if the price of the stock is $4?
7. What effect will a two-for-one stock split have on the following items found on a firm's financial statements?
1. earnings per share $4.20 2. total equity $10,000,000
3. long-term debt $4,300,000 4. additional paid-in capital $1,534,000
5. number of shares outstanding 1,000,000 6. earnings $4,200,000
1. The dividend-growth model may be used to value a stock:
What is the value of a stock if:
a. What is the value of this stock if the dividend is increased to $3 and the other variables remain constant?
b. What is the value of this stock if the required return declines to 7.5 percent and the other variables remain constant?
c. What is the value of this stock if the growth rate declines to 4 percent and the other variables remain constant?
d. What is the value of this stock if the dividend is increased to $2.30, the growth rate declines to 4 percent, and the required return remains 10 percent?
2 Last year Artworks, Inc. paid a dividend of $3.50. You anticipate that the company's growth rate is 10 percent and have a required rate of return of 15 percent for this type of equity investment. What is the maximum price you would be willing to pay for the stock?
3. An investor with a required return of 14 percent for very risky investments in common stock has analyzed three firms and must decide which, if any, to purchase. The information is as follows:Firm
Firm A B C
Current Earnings $2.00 $3.20 $7.00
Current dividend $1.00 $3.00 $7.50
Expected annual growth in dividends and earnings 7% 2% -1%
Current market price $23 $47 $60
a. What is the maximum price that the investor should pay for each stock based on the dividend-growth model?
b. If the investor does buy stock A, what is the implied percentage return?
c. If the appropriate P/E ratio is 12, what is the maximum price the investor should pay for each stock? Would your answers be different if the appropriate P/E were 7?
d. What does stock C's negative growth rate imply?
5. Jersey Jewel Mining has a beta coefficient of 1.2. Currently the risk-free rate is 5 percent and the anticipated return on the market is 11 percent. JJM pays a $4.50 dividend that is growing at 6 percent annually.
a. What is the required return for JJM?
b. Given the required return, what is the value of the stock?
c. If the stock is selling for $80, what should you do?
d. If the beta coefficient declines to 1.0, what is the new value of the stock?
e. If the price remains $80, what course of action should you take given the valuation in (d)?
7. The security market line is estimated to be
You are considering two stocks. The beta of A is 1.4. The firm offers a dividend yield during the year of 4 percent and a growth rate of 7 percent. The beta of B is 0.8. The firm offers a dividend yield during the year of 5 percent and a growth rate of 3.8 percent.
a. What is the required return for each security?
b. Why are the required rates of return different?
c. Since A offers higher potential growth, should it be purchased?
d Since B offers higher dividend yield, should it be purchased?
e. Which stock(s) should be purchased?
1. A $1,000 bond has a coupon of 6 percent and matures after 10 years.
a. What would be the bond's price if comparable debt yields 8 percent?
b. What would be the price if comparable debt yields 8 percent and the bond matures after five years?
c. Why are the prices different in a and b?
d. What are the current yields and the yields to maturity in a and b?
2. a. A $1,000 bond has a 7.5 percent coupon and matures after 10 years. If current interest rates are 10 percent, what should be the price of the bond?
b. If after six years interest rates are still 10 percent, what should be the price of the bond?
c. Even though interest rates did not change in a and b, why did the price of the bond change?
d. Change the interest rate in a and b to 6 percent and rework your answers. Even though the interest rate is 6 percent in both calculations, why are the bond prices different?
4. Blackstone, Inc. has a five-year bond outstanding that pays $60 annually. The face value of each bond is $1,000, and the bond sells for $890.
a. What is the bond's coupon rate?
b. What is the current yield?
c. What is the yield to maturity?
9. A bond has the following features:
* Coupon rate of interest: 8%
* Principal: $1,000
* Term to maturity: 10 years
a. What will the holder receive when the bond matures?
b. If the current rate of interest on comparable debt is 12 percent, what should be the price of this bond? Would you expect the firm to call this bond? Why?
c. If the bond has a sinking fund that requires the firm to set aside annually with a trustee sufficient funds to retire the entire issue at maturity, how much must the firm remit each year for 10 years if the funds earn 9 percent annually and there is $10 million outstanding?
1. Big Oil Inc. has a preferred stock outstanding that pays a $9 annual dividend. If investors' required rate of return is 13 percent, what is the market value of the shares? If the required return declines to 11 percent, what is the change in the price of the stock?
2. What should be the prices of the following preferred stocks if comparable securities yield 7 percent? Why are the valuations different?
1. MN Inc., $8 preferred ($100 par)
2. CH Inc., $8 preferred ($100 par) with mandatory retirement after 20 years
4. You are considering purchasing the preferred stock of a firm but are concerned about its capacity to pay the dividend. To help allay that fear, you compute the times-preferred-dividend-earned ratio for the past three years from the following data taken from the firm's financial statements:
Year X1 X2 X3
Operating Income 12000000 15000000 17000000
Interest 3000000 5900000 11000000
Taxes 4000000 5400000 4000000
Preferred dividends 1000000 1000000 1500000
Common dividends 3000000 2000000 -
What does your analysis indicate about the firm's capacity to pay preferred stock dividends?
2. The management of a firm wants to introduce a new product. The product will sell for $4 a unit and can be produced by either of two scales of operation. In the first, total costs are
In the second scale of operation, total costs are
a. What is the break-even level of output for each scale of operation?
b. What will be the firm's profits for each scale of operation if sales reach 5,000 units?
c. One-half of the fixed costs are noncash (depreciation). All other expenses are for cash. If sales are 2,000 units, will cash receipts cover cash expenses for each scale of operation?
d. The anticipated levels of sales are
Year Unit Sales
If management selects the scale of production with higher fixed cost, what can it expect in years 1 and 2? On what grounds can management justify selecting this scale of operation? If sales reach only 5,000 a year, was the correct scale of operation chosen?
3. A firm has the following total revenue and total cost schedules:
a. What is the break-even level of output? What is the level of profits at sales of 9,000 units?
b. As the result of a major technological breakthrough, the total cost schedule is changed to:
4. The manufacturer of a product that has a variable cost of $2.50 per unit and total fixed cost of $125,000 wants to determine the level of output necessary to avoid losses.
a. What level of sales is necessary to break even if the product is sold for $4.25? What will be the manufacturer's profit or loss on the sales of 100,000 units?
b. If fixed costs rise to $175,000, what is the new level of sales necessary to break even?
c. If variable costs decline to $2.25 per unit, what is the new level of sales necessary to break even?
d. If fixed costs were to increase to $175,000, while variable costs declined to $2.25 per unit, what is the new break-even level of sales?
1. HBM, Inc. has the following capital structure:
Preferred stock 20,000
Common stock 240,000
The common stock is currently selling for $15 a share, pays a cash dividend of $0.75 per share, and is growing annually at 6 percent. The preferred stock pays a $9 cash dividend and currently sells for $91 a share. The debt pays interest of 8.5 percent annually, and the firm is in the 30 percent marginal tax bracket.
a. What is the after-tax cost of debt?
b. What is the cost of preferred stock?
c. What is the cost of common stock?
d. What is the firm's weighted-average cost of capital?
2. Sun Instruments expects to issue new stock at $34 a share with estimated flotation costs of 7 percent of the market price. The company currently pays a $2.10 cash dividend and has a 6 percent growth rate. What are the costs of retained earnings and new common stock?
3. A firm's current balance sheet is as follows:
a. What is the firm's weighted-average cost of capital at various combinations of debt and equity, given the following information?
Debt/Assets After-Tax Cost of Debt Cost of Equity Cost of Capital
0% &nbs p; 8% 12% ?
& nbsp; 10 8 12 ?
20 &nb sp; 8 12 ?
30 8 13 ?
40 &n bsp; 9 14 ?
50   ; 10 15 ?
60 &nbs p;12 16 ?
b. Construct a pro forma balance sheet that indicates the firm's optimal capital structure. Compare this balance sheet with the firm's current balance sheet. What course of action should the firm take?
c. As a firm initially substitutes debt for equity financing, what happens to the cost of capital, and why?
d. If a firm uses too much debt financing, why does the cost of capital rise?
1. You purchase machinery for $23,958 that generates cash flow of $6,000 for five years. What is the internal rate of return on the investment?
2. The cost of capital for a firm is 10 percent. The firm has two possible investments with the following cash inflows:
Year 1 $300 $200
2 200 200
3 100 200
a. Each investment costs $480. What investment(s) should the firm make according to net present value?
b. What is the internal rate of return for the two investments? Which investment(s) should the firm make? Is this the same answer you obtained in part a?
c. If the cost of capital rises to 14 percent, which investment(s) should the firm make?
3. A firm has the following investment alternatives:
A B C
Year 1 &nb sp; $1,100 $3,600 —
2 1,100 & nbsp; — —
3 1,100 — $4,562
Each investment costs $3,000; investments B and C are mutually exclusive, and the firm's cost of capital is 8 percent.
a. What is the net present value of each investment?
b. According to the net present values, which investment(s) should the firm make? Why?
c. What is the internal rate of return on each investment?
d. According to the internal rates of return, which investment(s) should the firm make? Why?
e. According to both the net present values and internal rates of return, which investments should the firm make?
f. If the firm could reinvest the $3,600 earned in year one from investment B at 10 percent, what effect would that information have on your answer to part e? Would the answer be different if the rate were 14 percent?
g. If the firm's cost of capital had been 10 percent, what would be investment A's internal rate of return?
h. The payback method of capital budgeting selects which investment? Why? (Review Chapter 19, if necessary.)
4. The chief financial officer has asked you to calculate the net present values and internal rates of return of two $50,000 mutually exclusive investments with the following cash flows:
Project A Cash Flow Project B Cash Flow
Year 1 $10,000 $ 0
2 25,000 22,000
3 30,000 48,000
If the firm's cost of capital is 9 percent, which investment(s) would you recommend? Would your answer be different if the cost of capital were 14 percent?
7. An investment with total costs of $10,000 will generate total revenues of $11,000 for one year. Management thinks that since the investment is profitable, it should be made. Do you agree? What additional information would you want? If funds cost 12 percent, what would be your advice to management? Would your answer be different if the cost of capital is 8 percent?
10. (This problem combines material from Chapters 21 and 22.) The financial manager has determined the following schedules for the cost of funds:
Cost of Debt Ratio Cost of Debt Equity
0% 5% 13%
10 5 13
20 5 13
30 5 13
40 5 14
50 6 15
60 8 16
a. Determine the firm's optimal capital structure.
b. Construct a simple pro forma balance sheet that shows the firm's optimal combination of debt and equity for its current level of assets.
Assets $500 Debt —
c. An investment costs $400 and offers annual cash inflows of $133 for five years. Should the firm make the investment?
d. If the firm makes this additional investment, how should its balance sheet appear?
Asset — Debt —
e. If the firm is operating with its optimal capital structure and a $400 asset yields 20.0 percent, what return will the stockholders earn on their investment in the asset?
11. Investments Quick and Slow cost $1,000 each, are mutually exclusive, and have the following cash flows. The firm's cost of capital is 10 percent.
Year 1 $1,300 $386
2 — 386
3 — 386
4 — 386
a. According to the net present value method of capital budgeting, which investment(s) should the firm make?
b. According to the internal rate of return method of capital budgeting, which investment(s) should the firm make?
c. If Q is chosen, the $1,300 can be reinvested and earn 12 percent. Does this information alter your conclusions concerning investing in Q and S? To answer, assume that S's cash flows can be reinvested at its internal rate of return. Would your answer be different if S's cash flows were reinvested at the cost of capital (10 percent)?
3. a. What is the EOQ for a firm that sells 5,000 units when the cost of placing an order is $5 and the carrying costs are $3.50 per unit?
b. How long will the EOQ last? How many orders are placed annually?
c. As a result of lower interest rates, the financial manager determines the carrying costs are now $1.80 per unit. What are the new EOQ and annual number of objects?
4. Given the following information:
Annual sales in units 30,000
Cost of placing an order $60.00
Per-unit carrying costs $ 1.50
Existing units of safety stock 300
a. What is the EOQ?
b. What is the average inventory based on the EOQ and the existing safety stock?
c. What is the maximum level of inventory?
d. How many orders are placed each year?
14. What is the effective, compound rate of interest you earn if you enter into a repurchase agreement in which you buy a Treasury bill for $76,789 and agree to sell it after a month (30 days) for $77,345? What is the compound rate of interest you pay if you sell a Treasury bill for $76,789 and repurchase it after 30 days?
2. Tinker, Inc. finances its seasonal working capital need with short-term bank loans. Management plans to borrow $65,000 for a year. The bank has offered the company a 3.5 percent discounted loan with a 1.5 percent origination fee. What are the interest payment and the origination fee required by the loan? What is the rate of interest charged by the bank?
5. An individual wishes to borrow $10,000 for a year and is offered the following alternatives:
a. a 10 percent loan discounted in advance
b. an 11 percent straight loan (i.e., interest paid at maturity). Which loan is more expensive?
6. Which of the following terms of trade credit is the more expensive?
a. A 3 percent cash discount if paid on the 15th day with bill due on the 45th day (3/15, net 45)
b. A 2 percent cash discount if paid on the 10th day with the bill due on the 30th day (2/10, net 30)
9. If $1 million face amount of commercial paper (270-day paper) is sold for $982,500, what is the simple rate of interest being paid? What is the compound annual rate?
11. Bank A offers the following terms for a $10 million loan:
* interest rate: 8 percent for one year on funds borrowed
* fees: 0.5 percent of the unused balance for the unused term of the loan Bank B offers the following terms for a $10 million loan:
* interest rate: 6.6 percent for one year on funds borrowed
* fees: 2 percent origination fee
• Which terms are better if the firm intends to borrow the $10 million for the entire year?
• If the firm plans to use the funds for only three months, which terms are better?