REVIEW OF FORMULAS
REVIEW OF FORMULAS
1. Kd (cost of debt) = Y(1 − T) (11-1)
Y is yield
T is corporate tax rate
2.
Dp is the annual dividend on preferred stock
Pp is the price of preferred stock
F is flotation, or selling, cost
3.
D1 is dividend at the end of the first year (or period)
P0 is the price of the stock today
g is growth rate in dividends
4. Kj (required return on common stock) = Rf + β(Km − Rf) (11-4)
Rf is risk-free rate of return
β is beta coefficient
Km is return in the market as measured by the appropriate index
5.
D1 is dividend at the end of the first year (or period)
P0 is price of the stock today
g is growth rate in dividends
Page 360
6.
Same as above with:
F as flotation, or selling, cost
7.
8.
LIST OF TERMS
cost of capital 341
flotation cost 344
dividend valuation model 345
capital asset pricing model (CAPM) 346
common stock equity 347
optimum capital structure 349
weighted average cost of capital 350
financial capital 351
marginal cost of capital 354
DISCUSSION QUESTIONS
1. Why do we use the overall cost of capital for investment decisions even when only one source of capital will be used (e.g., debt)? (LO11-1)
2. How does the cost of a source of capital relate to the valuation concepts presented previously in Chapter 10? (LO11-3)
3. In computing the cost of capital, do we use the historical costs of existing debt and equity or the current costs as determined in the market? Why? (LO11-3)
4. Why is the cost of debt less than the cost of preferred stock if both securities are priced to yield 10 percent in the market? (LO11-3)
5. What are the two sources of equity (ownership) capital for the firm? (LO11-3)
6. Explain why retained earnings have an associated opportunity cost. (LO11-3)
7. Why is the cost of retained earnings the equivalent of the firm’s own required rate of return on common stock (Ke)? (LO11-3)
8. Why is the cost of issuing new common stock (Kn) higher than the cost of retained earnings (Ke)? (LO11-3)
9. How are the weights determined to arrive at the optimal weighted average cost of capital? (LO11-4)
10. Explain the traditional, U-shaped approach to the cost of capital. (LO11-4)
11. It has often been said that if the company can’t earn a rate of return greater than the cost of capital it should not make investments. Explain. (LO11-2)
12. What effect would inflation have on a company’s cost of capital? (Hint: Think about how inflation influences interest rates, stock prices, corporate profits, and growth.) (LO11-3)
13. What is the concept of marginal cost of capital? (LO11-5)
Page 361
PRACTICE PROBLEMS AND SOLUTIONS
Yield to maturity and cost of debt
(LO11-3)
1. a. A $1,000 par value bond issued by Conseco Electronics has 16 years to maturity. The bond pays $78 a year in interest and is selling for $884. What is the yield to maturity?
b. If the firm is in a 30 percent tax bracket, what is the aftertax cost of the debt?
Weighted average cost of capital
(LO11-1)
2. a. Assume the following capital structure for the Morgan Corp.
| Debt | 35% |
| Preferred stock | 15% |
| Common equity | 50% |
The following facts are also provided:
| Bond yield to maturity | 9% |
| Corporate tax rate | 35% |
| Dividend, preferred stock | $ 8.50 |
| Price, preferred stock | $ 100 |
| Flotation cost, preferred stock | $ 2 |
| Dividend, common stock | $ 1.20 |
| Price, common stock | $ 30 |
| Growth rate, common stock | 9% |
Compute the weighted average cost of capital.
b. If there are $30 million in retained earnings, at what dollar value will the marginal cost of capital go up? If the flotation cost on common stock is $1.50, what will be the cost of new common stock?
Solutions
1. a. Yield to maturity (YTM)
The yield to maturity is 9.21 percent.
b.
| Kd (aftertax cost of debt) | = Y (yield)(1 − T) |
| = 9.21% (1 − 0.30) | |
| = 9.21% (0.70) | |
| = 6.45% |
| FINANCIAL CALCULATOR | |
| Bond YTM | |
| Value | Function |
| 16 | N |
| −884 | PV |
| 78 | PMT |
| 1000 | FV |
| Function | Solution |
| CPT | |
| I/Y | 9.21 |
Page 362
2. a. First compute the cost of the components in the capital structure.
| Dp = | Dividend, preferred stock = $8.50 |
| Pp = | Price, preferred stock = $100 |
| F = | Flotation cost, preferred stock = $2 |
| D1 = | Dividend, common stock = $1.20 |
| P0 = | Price, common stock = $30 |
| g = | Growth rate, common stock = 9% |
Now combine these with the weights in the capital structure to compute the weighted average cost of capital.
b. The marginal cost of capital will go up when there are no longer enough retained earnings to support the capital structure. This is point X.
Solve for X:
At this point, new common stock will be used instead of retained earnings in the capital structure. The cost of the new common stock is:
Kn = Cost of new common stock
The only new term is F:
D1 = $1.20
Page 363
| P0 = | $30 |
| F = | Flotation cost, new common stock $1.50 |
| g = | 9% |
PROBLEMS
Selected problems are available with Connect. Please see the preface for more information.
Basic Problems
Cost of capital
(LO11-2)
1. In March 2010, Hertz Pain Relievers bought a massage machine that provided a return of 8 percent. It was financed by debt costing 7 percent. In August, Mr. Hertz came up with a heating compound that would have a return of 14 percent. The chief financial officer, Mr. Smith, told him it was impractical because it would require the issuance of common stock at a cost of 16 percent to finance the purchase. Is the company following a logical approach to using its cost of capital?
Cost of capital
(LO11-2)
2. Speedy Delivery Systems can buy a piece of equipment that is anticipated to provide an 11 percent return and can be financed at 6 percent with debt. Later in the year, the firm turns down an opportunity to buy a new machine that would yield a 9 percent return but would cost 15 percent to finance through common equity. Assume debt and common equity each represent 50 percent of the firm’s capital structure.
a. Compute the weighted average cost of capital.
b. Which project(s) should be accepted?
Effect of discount rate
(LO11-2)
3. A brilliant young scientist is killed in a plane crash. It is anticipated that he could have earned $240,000 a year for the next 50 years. The attorney for the plaintiff’s estate argues that the lost income should be discounted back to the present at 4 percent. The lawyer for the defendant’s insurance company argues for a discount rate of 8 percent. What is the difference between the present value of the settlement at 4 percent and 8 percent? Compute each one separately.
Aftertax cost of debt
(LO11-3)
4. Telecom Systems can issue debt yielding 9 percent. The company is in a 30 percent bracket. What is its aftertax cost of debt?
Aftertax cost of debt
(LO11-3)
5. Calculate the aftertax cost of debt under each of the following conditions:
| Yield | Corporate Tax Rate | |
| a. | 8.0% | 18% |
| b. | 12.0 | 34 |
| c. | 10.6 | 15 |
Aftertax cost of debt
(LO11-3)
6. Calculate the aftertax cost of debt under each of the following conditions:
| Yield | Corporate Tax Rate | |
| a. | 8.0% | 26% |
| b. | 9.0 | 35 |
| c. | 8.0 | 0 |
Aftertax cost of debt
(LO11-3)
Page 364
7. The Goodsmith Charitable Foundation, which is tax-exempt, issued debt last year at 9 percent to help finance a new playground facility in Los Angeles. This year the cost of debt is 25 percent higher; that is, firms that paid 11 percent for debt last year will be paying 13.75 percent this year.
a. If the Goodsmith Charitable Foundation borrowed money this year, what would the aftertax cost of debt be, based on their cost last year and the 25 percent increase?
b. If the receipts of the foundation were found to be taxable by the IRS (at a rate of 34 percent because of involvement in political activities), what would the aftertax cost of debt be?
Aftertax cost of debt
(LO11-3)
8. Royal Jewelers Inc. has an aftertax cost of debt of 7 percent. With a tax rate of 35 percent, what can you assume the yield on the debt is?
Yield to maturity and cost of debt
(LO11-3)
9. Airborne Airlines Inc. has a $1,000 par value bond outstanding with 25 years to maturity. The bond carries an annual interest payment of $88 and is currently selling for $950. Airborne is in a 40 percent tax bracket. The firm wishes to know what the aftertax cost of a new bond issue is likely to be. The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar.
a. Compute the yield to maturity on the old issue and use this as the yield for the new issue.
b. Make the appropriate tax adjustment to determine the aftertax cost of debt.
Yield to maturity and cost of debt
(LO11-3)
10. Russell Container Corporation has a $1,000 par value bond outstanding with 30 years to maturity. The bond carries an annual interest payment of $105 and is currently selling for $880 per bond. Russell Corp. is in a 40 percent tax bracket. The firm wishes to know what the aftertax cost of a new bond issue is likely to be. The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar.
a. Compute the yield to maturity on the old issue and use this as the yield for the new issue.
b. Make the appropriate tax adjustment to determine the aftertax cost of debt.
Changing rates and cost of debt
(LO11-3)
11. Terrier Company is in a 40 percent tax bracket and has a bond outstanding that yields 10 percent to maturity.
a. What is Terrier’s aftertax cost of debt?
b. Assume that the yield on the bond goes down by 1 percentage point, and due to tax reform, the corporate tax rate falls to 25 percent. What is Terrier’s new aftertax cost of debt?
c. Has the aftertax cost of debt gone up or down from part a to part b? Explain why.
Real-world example and cost of debt
(LO11-3)
12. KeySpan Corp. is planning to issue debt that will mature in 2035. In many respects, the issue is similar to currently outstanding debt of the corporation.
a. Using Table 11-3, identify the yield to maturity on similarly outstanding debt for the firm in terms of maturity.
Page 365
b. Assume that because the new debt will be issued at par, the required yield to maturity will be 0.15 percent higher than the value determined in part a. Add this factor to the answer in a. (New issues sold at par sometimes require a slightly higher yield than older seasoned issues because there are fewer tax advantages and more financial leverage that increase company risk.)
c. If the firm is in a 30 percent tax bracket, what is the aftertax cost of debt?
Cost of preferred stock
(LO11-3)
13. Medco Corporation can sell preferred stock for $90 with an estimated flotation cost of $2. It is anticipated the preferred stock will pay $8 per share in dividends.
a. Compute the cost of preferred stock for Medco Corp.
b. Do we need to make a tax adjustment for the issuing firm?
