6.3 Cost of Capital - New Flashcards
The FLF Corporation is preparing to evaluate capital expenditure proposals for the coming year. Because the firm employs discounted cash flow methods, the cost of capital for the firm must be estimated. The following information for FLF Corporation is provided:
* The market price of common stock is $60 per share.
* The dividend next year is expected to be $3 per share.
* Expected growth in dividends is a constant 10%.
* New bonds can be issued at face value with a 10% coupon rate.
* The current capital structure of 40% long-term debt and 60% equity is considered to be optimal.
* Anticipated earnings to be retained in the coming year are $3 million.
* The firm has a 40% marginal tax rate.
The after-tax cost to FLF Corporation of the new bond issue is
A. 4%
B. 10%
C. 6%
D. 14%
C. 6%
Because the bonds are issued at their face value, the pretax effective rate is 10%. However, interest is deductible for tax purposes, so the government absorbs 40% of the cost, leaving 6% after-tax cost.
Williams, Inc., is interested in measuring its overall cost of capital and has gathered the following data. Under the terms described as follows, the company can sell unlimited amounts of all instruments.
* Williams can raise cash by selling $1,000, 8%, 20-year bonds with annual interest payments. In selling the issue, an average premium of $30 per bond would be received, and the firm must pay flotation costs of $30 per bond. The after-tax cost of funds is estimated to be 4.8%.
* Williams can sell 8% preferred stock with a par value of $100 for $105 per share. The cost of issuing and selling the preferred stock is expected to be $5 per share.
* Williams’ common stock is currently selling for $100 per share. The firm expects to pay cash dividends of $7 per share next year, and the dividends are expected to remain constant. The stock will have to be underpriced by $3 per share, and flotation costs are expected to amount to $5 per share.
* Williams expects to have available $100,000 of retained earnings in the coming year; once these retained earnings are exhausted, the firm will use new common stock as the form of common stock equity financing.
* Williams’ preferred capital structure is
- Long-term debt 30%
- Preferred stock 20%
- Common stock 50%
The cost of funds from retained earnings for Williams, Inc, is
A. 7.6%
B. 8.1%
C. 7.4%
D. 7.0%
D. 7.0%
Because retained earning is internally generated (that is, no issue costs are involved), its cost is simply the component cost of common stock, i.e., the next dividend divided by the market price ($7 / $100 = 7.0%)
A firm has sold 1,000 shares of $100 par, 8% preferred stock at an issue price of $92 per share. Stock issue costs were $5 per share. The firm pays taxes at the rate of 40%. What is the firm’s cost of preferred stock capital?
A. 8.00%
B. 8.70%
C. 8.25%
D. 9.20%
D. 9.20%
Because the dividends on preferred stock are not deductible for tax purposes, the effect of income taxes is ignored. Thus, the relevant calculation is to divide the $8 annual dividend by the quantity of funds received from the issuance. In this case, the funds received equal $87 ($92 proceeds - $5 issue costs). Thus, the cost of capital is 9.2% ($8 / $87).
The theory underlying the cost of capital is primarily concerned with the cost of
A. Long-term funds and old funds.
B. Short-term funds and old funds.
C. Long-term funds and new funds.
D. Short-term funds and new funds.
C. Long-term funds and new funds.
The theory underlying the cost of capital is based primarily on the cost of long-term funds and the acquisition of new funds. The reason is that long-term funds are used to finance long-term investments. For an investment alternative to be viable, the return on the investment must be greater than the cost of the funds used. The objective in short-term borrowing is different. Short-term loans are used to meet working capital needs and not to finance long-term investments.
Rogers, Inc., operates a chain of restaurants located in the Southeast. The company has steadily grown to its present size of 48 restaurants. The board of directors recently approved a large-scale remodeling of the restaurants, and the company is now considering two financing alternatives.
* The first alternative would consist of
o Bonds that would have a 9% coupon rate and reissued at their base amount would net $19.2 million after a 4% flotation cost
o Preferred stock with a stated rate of 6% that would yield $4.8 million after a 4% flotation cost
o Common stock that would yield $24 million after a 5% flotation cost
* The second alternative would consist of a public offering of bonds that would have a 9% coupon rate and an 11% market rate and would net $48 million after a 4% flotation cost.
Rogers’ current capital structure, which is considered optimal, consists of 40% long-term debt, 10% preferred stock, and 50% common stock. The current market value of the common stock is $30 per share, and the common stock dividend during the past 12 months was $3 per share. Investors are expecting the growth rate of dividends to equal the historical rate of 6%. Rogers is subject to an effective income tax rate of 40%.
The after-tax weighted marginal cost of capital for Rogers’ second financing alternative consisting solely of bonds would be
A. 5.13%
B. 5.40%
C. 5.63%
D. 6.60%
C. 5.63%
Annual cash interest is $4,500,000 {[$48,000,000 ÷ (1.0 – .04 flotation cost)] × .09}. The cost of the new bonds equals the annual cash interest divided by the net issue proceeds, times one minus the tax rate, or 5.63% [($4,500,000 ÷ $48,000,000) × (100% – 40%)].
A corporation has sold $50 million of $1,000 par value, 12% coupon bonds. The bonds were sold at a discount and the corporation received $985 per bond. If the corporate tax rate is 40%, the after-tax cost of these bonds for the first year (rounded to the nearest hundredth percent) is
A. 7.31%
B. 12.00%
C. 7.09%
D. 4.87%
A. 7.31%
Interest is 12%, and the annual interest payment on one bond is $120. Thus, the effective rate is 12.18% ($120 ÷ $985). Reducing this rate by the 40% tax savings lowers the cost to 7.31%.
DQZ Telecom is considering a project for the coming year that will cost $50 million. DQZ plans to use the following combination of debt and equity to finance the investment.
- Issue $15 million of 20-year bonds at a price of $101, with a coupon rate of 8%, and flotation costs of 2% of par.
- Use $35 million of funds generated from earnings.
- The equity market is expected to earn 12%. U.S. Treasury bonds are currently yielding 5%. The beta coefficient for DQZ is estimated as .60. DQZ is subject to an effective corporate income tax rate of 40%.
Assume that the after-tax cost of debt is 7% and the cost of equity is 12%. Determine the weighted-average cost of capital to DQZ.
A. 9.50%
B. 8.50%
C. 6.30%
D. 10.50%
D. 10.50%
The 7% debt cost and the 12% equity cost should be weighted by the proportions of the total investment represented by each source of capital. The total project costs $50 million, of which debt is $15 million, or 30% of the total. Equity capital is the other 70%. Consequently, the weighted-average cost of capital is 10.5% [(30% × 7%) + (70% × 12%)].
A company is planning to issue additional shares of common stock in a public offering. The current market price of the company’s stock is $38, and the dividend for the past year was $2.25. A well-known investment advisory firm forecasts dividend growth of 8%, and an investment banker estimates that the flotation costs would be 6% of the issue price. What cost of equity should the company use in its cost of capital calculation?
A. 14.8%
B. 13.9%
C. 14.3%
D. 14.0%
A. 14.8%
.
The next dividend that the company will pay is $2.43 ($2.25 × 1.08). The net issue proceeds are $35.72 [$38 × (1 – .06)] after taking the flotation costs into account. Therefore, the cost of capital is 14.8% [($2.43 ÷ $35.72) + .08].
A corporation is selling $25 million of cumulative, non-participating preferred stock. The issue will have a par value of $65 per share with a dividend rate of 6%. The issue will be sold to investors for $68 per share, and issuance costs will be $4 per share. The cost of preferred stock to the corporation is
A. 5.74%
B. 6.09%
C. 5.42%
D. 6.00%
B. 6.09%
Cost of capital for its new preferred stock is calculated as follows:
Cost of new preferred stock = Dividend ÷ Net issue proceeds
= ($65 x 6%) ÷ ($68-4)
= $3.90 ÷ $64
= 6.09%
A firm’s new financing will be in proportion to the market value of its current financing shown below.,
Carrying amount ($000 omitted)
Long term debt: $7,000
Preferred stock (100,000 shares): 1,000
Common stock (200,000 shares): 7,000
The firm’s bonds are currently selling at 80% of par, generating a current market yield of 9%, and the corporation has a 40% tax rate. The preferred stock is selling at its par value and pays a 6% dividend. The common stock has a current market value of $40 and is expected to pay a $1.20 per share dividend this fiscal year. Dividend growth is expected to be 10% per year, and floatation costs are negligible. The firm’s weighted-average cost of capital is (round calculations to tenths of a percent)
A. 9%
B. 13%
C. 8.13%
D. 9.6%
D. 9.6%
The first step is to determine the component costs of each form of capital.
Multiplying the current yield of 9% times one minus the tax rate (1.0 - .40 = .60) results in an after-tax cost of debt of 5.4% (9% x 0.60). Since the preferred stock is trading at par, the component cost is 6% (the annual dividend rate). The component cost of common equity is calculated using the dividend growth model, which combines the dividend yield with the growth rate. Dividing the $1.20 dividend by the $40 market price produces a dividend yield of 3%. Adding the 3% dividend yield and the 10% growth rate gives a 13% component cost of common equity.
Once the costs of the three types of capital have been computed, the next step is to weight them according to their current market values. The market value of the long-term debt is 80% of its carrying amount, or $5,600,000 ($7,000,000 x 80%). The $1,000,000 of preferred stock is selling at par. The common stock has a current market value of $8,000,000 (200,000 shares x $40).
Long-term debt $5,600,000 x 5.4% = $302,400
Preferred stock 1,000,000 x 6.0% = 60,000
common stock 8,000,000 x 13.0% = 1,040,000
Totals: 14,600,000 / $1,402,400
Thus, the weighted-average cost of capital is 9.6% ($1,402,000 / $14,600,000).
A profitable firm is reviewing alternatives to raise additional capital. It estimates that it can issue debt at a yield of 6% or, alternatively, issue preferred shares at a yield of 7%. If the firm’s marginal income tax rate is 37%, what would be the cost for each alternative?
A. Debt: 3.78%, preferred shares: 7.00%
B. Debt: 6.00%, Preferred shares: 4.41%
C. Debt: 3.78%, preferred shares: 4.41%
D. Debt: 6.00%, preferred shares: 7.00%
A. Debt: 3.78%, preferred shares: 7.00%
The cost of the debt would be 3.78% [6% x (1 - .37)] since interest payments are tax-deductible by the firm. The preferred shares would cost 7%.
Rogers, Inc., operates a chain of restaurants located in the Southeast. The company has steadily grown to its present size of 48 restaurants. The board of directors recently approved a large-scale remodeling of the restaurants, and the company is now considering two financing alternatives.
* The first alternative would consist of
o Bonds that would have a 9% coupon rate and reissued at their base amount would net $19.2 million after a 4% flotation cost
o Preferred stock with a stated rate of 6% that would yield $4.8 million after a 4% flotation cost
o Common stock that would yield $24 million after a 5% flotation cost
* The second alternative would consist of a public offering of bonds that would have a 9% coupon rate and an 11% market rate and would net $48 million after a 4% flotation cost.
Rogers’ current capital structure, which is considered optimal, consists of 40% long-term debt, 10% preferred stock, and 50% common stock. The current market value of the common stock is $30 per share, and the common stock dividend during the past 12 months was $3 per share. Investors are expecting the growth rate of dividends to equal the historical rate of 6%. Rogers is subject to an effective income tax rate of 40%.
Assuming the after-tax cost of common stock is 15%, the after-tax weighted marginal cost of capital for Roger’s first financing alternative consisting of bonds, preferred stock, and common stock would be
A. 7.285%
B. 8.725%
C. 11.700%
D. 10.375%
D. 10.375%
Because the bonds would incur a 4% flotation cost, their face amount must be $20,000,000 ($19,000,000 / .96). The before-tax rate of return on the debt is therefore .09375 [($20,000,000 x 9%) / $19,200,000]. The preferred stock will yield $4,800,000 after subtracting the 4% floatation cost, so it must sell for $5,000,000 ($4,800,000 / .96). The annual dividend on the preferred stock is $300,000 ($5,000,000 x 6%). Consequently, the cost of capital raised by issuing preferred stock is 6.25% ($300,000 dividend / $4,800,000 net issuance price). The after-tax weighted marginal cost of capital for Roger’s first financing alternative is therefore calculated as follows:
Long term debt 40% x 9.375% x (1.0 - 4.0) = 2.250%
Preferred stock 10% x 6.25% = .625%
Common stock 50% x 15% = 7.500%
A preferred stock is sold for $101 per share, has a face value of $100 per share, underwriting fees of $5 per share, and annual dividends of $10 per share. If the tax rate is 40%, the cost of funds (capital) for the preferred stock is
A. 10.4%
B. 4.2%
C. 6.25%
D. 10.0%
A. 10.4%
The cost of capital for new preferred stock is equal to the dividend on the stock divided by the net issue proceeds [$10 / ($101 - $5) = 10.4%]. Because dividends on preferred stock are not deductible for tax purposes, the income tax rate is irrelevant.
Vivid, Inc., has determined that it needs $10,000,000 of funding to expand its operations into a foreign country. Its capital structure consists of 10% long-term debt, 20% preferred stock, 40% common stock, and 30% retained earnings. Vivid issued new debt and collected $40,000 of proceeds. The yearly interest rate is 12%. The cost of retained earnings is expected to be 13.5%, and the cost of new common stock is expected to be 17%. Vivid also can sell $200 par value preferred stock that pays a 15% dividend and has a $10 floatation cost. What is the weighed average cost of new capital? (Round numbers to three decimal places, e.g., 0.1547 = 15.5%)
A. 14.1%
B. 15.3%
C. 15.8%
D. 17%
B. 15.3%
The cost of new capital is the ratio of what a firm must pay to what it receives. The cost of new capital is calculated as follows:
Long term debt 10% x 12.0% (A) = 1.2%
Preferred stock 20% x 15.8% (B) = 3.2%
Common stock 40% x 17.0% = 6.8%
Retained earnings 30% x 13.5% = 4.1%
= 15.3%
(A) (1) $40,000 proceeds x .12 interest rate = $3,800 annual interest
(2) $4,800 annual interest / $40,000 net proceeds = 12%
(B) (1) $200 par value x .15 dividend rate = $30 dividend
(2) $30 dividend / ($200 par value - $10 floatation cost) = 15.8%
Williams, Inc., is interested in measuring its overall cost of capital and has gathered the following data. Under the terms described as follows, the company can sell unlimited amounts of all instruments.
* Williams can raise cash by selling $1,000, 8%, 20-year bonds with annual interest payments. In selling the issue, an average premium of $30 per bond would be received, and the firm must pay flotation costs of $30 per bond. The after-tax cost of funds is estimated to be 4.8%.
* Williams can sell 8% preferred stock with a par value of $100 for $105 per share. The cost of issuing and selling the preferred stock is expected to be $5 per share.
* Williams’ common stock is currently selling for $100 per share. The firm expects to pay cash dividends of $7 per share next year, and the dividends are expected to remain constant. The stock will have to be underpriced by $3 per share, and flotation costs are expected to amount to $5 per share.
* Williams expects to have available $100,000 of retained earnings in the coming year; once these retained earnings are exhausted, the firm will use new common stock as the form of common stock equity financing.
* Williams’ preferred capital structure is
Long-term debt 30%
Preferred stock 20%
Common stock 50%
If Williams, Inc., needs a total of $1,000,000, the firm’s weighted-average cost of capital would be
A. 6.5%
B. 6.8%
C. 27.4%
D. 4.8%
B. 6.8%
Because Williams can sell unlimited amounts of all of its instruments, it can maintain its preferred capital structure. The cost of new debt is given as 4.8%. The cost of new preferred stock is 8.0% (8% dividend / $100 net issue proceeds). The common equity component will amount to $500,000 (%1,000,000 capital needed x 50% common stock). Retained earnings are available to cover $100,000 (10% of the total), so new common stock will have to be issued to cover the 40%. The cost of new common stock is 7.6% ($7 dividend / $92 net issue proceeds).
New long-term debt 30% x 4.8% = 1.44%
New preferred stock 20% x 8.0% = 1.60%
New common stock 40% x 7.6% = 3.04%
Retained earnings 10% x 7.0% = 0.70%
Total = 6.78%
The FLF Corporation is preparing to evaluate capital expenditure proposals for the coming year. Because the firm employs discounted cash flow methods, the cost of capital for the firm must be estimated. The following information for FLF corporation is provided:
* The market price of common stock is $60 per share.
* The dividend next year is expected to be $3 per share.
* Expected growth in dividends is a constant 10%.
* New bonds can be issued at face value with a 10% coupon rate.
* The current capital structure of 40% long-term debt and 60% equity is considered to be optimal.
* Anticipated earnings to be retained in the coming year are $3 million.
* The firm has a 40% marginal tax rate.
The maximum capital expansion that FLF Corporation can support in the coming year without resorting to external equity financing is
A. $3 million.
B. $5 million.
C. $2 million.
D. Cannot determine from the information given.
B. $5 million.
The current optimal capital structure is 40% debt and 60% equity. The $3 million to be retained earnings in the coming year represents the equity portion of the maximum new capital outlay. To retain the optimal capital structure, $2 million of debt must be added to the $3 million of retained earnings. Hence, the maximum capital expansion is $5 million.
DQZ Telecom is considering a project for the coming year that will cost $50 million. DQZ plans to use the following combination of debt and equity to finance the investment.
- Issue $15 million of 20-year bonds at a price of $101, with a coupon rate of 8%, and flotation costs of 2% of par.
- Use $35 million of funds generated from earnings.
- The equity market is expected to earn 12%. U.S. Treasury bonds are currently yielding 5%. The beta coefficient for DQZ is estimated as .60. DQZ is subject to an effective corporate income tax rate of 40%.
The before-tax cost of DQZ’s planned debt financing, net of flotation costs, in the first year is
A. 8.08%
B. 11.80%
C. 10.00%
D. 7.92%
A. 8.08%
The cost of new debt equals the annual interest divided by the net issue proceeds. The annual interest is $1.2 million ($15,000,000 x .08 coupon rate). The proceeds amount to $14,850,000 [($15,000,000 x 1.01) market price - ($15,000,000 x .02) flotation costs]. Thus, the company is paying $1.2 million annually for the use of $14,850,000, a cost of 8.08% ($1,200,000 / $14,850,000).
Williams, Inc., is interested in measuring its overall cost of capital and has gathered the following data. Under the terms described as follows, the company can sell unlimited amounts of all instruments.
* Williams can raise cash by selling $1,000, 8%, 20-year bonds with annual interest payments. In selling the issue, an average premium of $30 per bond would be received, and the firm must pay flotation costs of $30 per bond. The after-tax cost of funds is estimated to be 4.8%.
* Williams can sell 8% preferred stock with a par value of $100 for $105 per share. The cost of issuing and selling the preferred stock is expected to be $5 per share.
* Williams’ common stock is currently selling for $100 per share. The firm expects to pay cash dividends of $7 per share next year, and the dividends are expected to remain constant. The stock will have to be underpriced by $3 per share, and flotation costs are expected to amount to $5 per share.
* Williams expects to have available $100,000 of retained earnings in the coming year; once these retained earnings are exhausted, the firm will use new common stock as the form of common stock equity financing.
* Williams’ preferred capital structure is
- Long-term debt 30%
- Preferred stock 20%
- Common stock 50%
The cost of funds from the sale of common stock for Williams, Inc., is
A. 8.1%
B. 7.0%
C. 7.4%
D. 7.6%
D. 7.6%
According to the dividend growth model, the cost of new (external) common equity is the next dividend divided by the net issue proceeds plus the dividend growth rate. Since flotation costs are incurred when issuing new stock, they must be deducted from the market price to arrive at the amount of capital the corporation will actually receive. Accordingly, the $100 selling price is reduced by the $3 discount and the $5 flotation costs to arrive at the $92 to be received for the stock. Because the dividend is not expected to increase in future years, no growth factor is included in the calculation. Thus, the cost of the common stock is 7.6% ($7 dividend / $92 net issue proceeds).
A firm has total capital of $100 million, and its weighted-average cost of capital is 12%. A new project has been proposed that will require additional capital of $10 million. The firm estimates that the additional capital can be raised at a pre-tax cost of 10%. The marginal income tax rate is 36%. What discount rate should the firm use in evaluating the new project?
A. 10.00%
B. 7.56%
C. 12.00%
D. 6.40%
C. 12.00%
The weighted-average cost of capital should be used it is known. A lower marginal rate for debt will lead to greater risk to shareholders, which will lead to a higher cost for common equity. Thus, the firm should invest in projects that have an expected return that is greater than the 12% weighted-average cost of capital.
