Al Imam Mohammad Ibn Saud Islamic University (IMSIU) College of Economics and Administrative Sciences Department of Finance and Investment Fin 382: Corporate finance Level 6: (Finance & Investments; Businss Banking) Dr. Nader Naifar

Textbook: Jonathan Berk, Peter DeMarzo and Jarrad Harford (2012) "Fundamentals of Corporate Finance”, 2 Edition, Pearson Education Limited. The cost of Capital Exercise 1

(The weighted Average Cost of Capital)

MV Corporation has debt with Market value of $100 million, common equity with a book value of $100 million, and preferred stock worth $20 million outstanding. Its common equity trades at $50 per share, and the firm has 6 million shares outstanding. What weights should MV Corporation use in its WACC? Solutions Value of debt: $100 million Value of preferred stock: $20 million Market value of common equity: $50 per share  6 million shares  $300 million

Total market value of firm: $100 + 20 +300 = $420 million Weights for WACC calculation: 100  23.81% 420 20 Preferred Stock  4.76% 420 300 Common Equity  71.43% 420 Debt

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Exercise 2

(The weighted Average Cost of Capital)

Book Co. has 1 million shares of common equity with a par (book) value of $1, retained earnings of $30 million, and its shares have a market value of $50 per share. It also has debt with a par value of $20 million that is trading at 101% of par. a- What is the market value of its equity? b- What is the market value of its debt? c- What weights should it use in computing its WACC? Solutions a- MV equity: 1 million shares  $50 per share = $50 million b- MV debt: 101% of par  $20 million par = $20.2 million c- Equity weight: $50 million/($50 million +$20.2 million) =0.712×100=71.2% Debt weight: $20.2 million/($50 million + $20.2 million) =0.288×100=28.8%

Exercise 3

(The firm's costs of debt and equity capital)

Avicorp has a $10 million debt issue outstanding, with a 6% coupon rate. the face value equal to $100 per bond. The debt has semi-annual coupons, the next coupon is due in six months, and the debt matures in five years. It is currently priced at 95% of par value. a- What is Avicorp’s pre-tax cost of debt? b- If Avicorp faces a 40% tax rate, what is its after-tax cost of debt? Solutions a- The pre-tax cost of debt is the YTM on the outstanding debt issue. We solve for the 6-month YTM on the bond, and then compute the annual rate:

3.6%×2=7.2%

The pre-tax cost of debt is 3.6044% every 6 months, or 7.2% per year. b- After-tax cost of debt = 7.2%×(1-0.4)=4.4%

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Exercise 4

(The firm's costs of debt and equity capital)

Mackenzie Company has a price of $36 and will issue a dividend of $2 next year. It has a beta of 1.2, the risk-free rate is 5.5%, and it estimates the market risk premium to be 5%. a. Estimate the equity cost of capital for Mackenzie. b. Under the CGDM, at what rate do you need to expect Mackenzie’s dividends to grow to get the same equity cost of capital as in part (a)? Solutions

a. Using the Capital Asset Pricing Model, re  5.5%  1.2  5%  11.5%

b.

2 0.115  g 0.115  g  0.0556 g  5.944% 36 

Mackenzie’s cost of equity using the CAPM is 11.5%, which would require a dividend growth rate of 5.944% to result in the same cost of equity using CGDM.

Exercise 5

(The weighted Average Cost of Capital)

Growth Company’s current share price is $20 and it is expected to pay a $1 dividend per share next year. After that, the firm’s dividends are expected to grow at a rate of 4% per year. a. What is an estimate of Growth Company’s cost of equity? b. Growth Company also has preferred stock outstanding that pays a $2 per share fixed dividend. If this stock is currently priced at $28, what is Growth Company’s cost of preferred stock? c.

Growth Company has existing debt issued three years ago with a coupon rate of 6%. The firm just issued new debt at par with a coupon rate of 6.5%. What is Growth Company’s pre-tax cost of debt?

d. Growth Company has 5 million common shares outstanding and 1 million preferred shares outstanding, and its equity has a total book value of $50 million. Its liabilities have a market value of $20 million. If 3

Growth Company’s common and preferred shares are priced as in parts (a) and (b), what is the market value of Growth Company’s assets? e.

Growth Company faces a 35% tax rate. Given the information in parts (a) – (d), and your answers to those problems, what is Growth Company’s WACC?

Solutions

a. $20 

1 re  0.04

re  9%

b. $28 

2 rps

rps  7.143%

c. The pre-tax cost of debt is the firm’s YTM on current debt. Since the firm recently issued debt at par, then the coupon rate of that debt must be equal to the YTM of the debt. Thus, the pre-tax cost of debt is 6.5%. d. Market value of debt = $20 million Market value of preferred stock = $28 per share  1 million preferred shares = $28 million Market value of equity = $20 per share  5 million shares outstanding = $100 million Market value of assets = $20 + 28 + 100 = $148 million 20   28  (7.143%)   100  (9%)  8.003%  (6.5%)(1  35%)       148   148   148 

WACC 

The calculation leads to a WACC of 8.003%.

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Exercise 6

(The weighted Average Cost of Capital)

McNabb Construction Company is trying to calculate its cost of capital for use in making a capital budgeting decision. Mr. Reid, the vice- president of finance, has given you the following information and has asked you to compute the weighted average cost of capital. - The company currently has outstanding a bond with a 9.5 percent coupon rate and another bond with a 7.8 percent rate. The firm has been informed by its investment banker that bonds of equal risk and credit rating are now selling to yield 10.5 percent. - The common stock has a price of $98.44 and an expected dividend (D 1) of $3.15 per share. The historical growth pattern (g) for dividends is as follows: $2.00; 2.24; 2.51; 2.81. Compute the historical growth rate, round it to the nearest whole number, and use it for g. - The preferred stock is selling at $90 per share and pays a dividend of $8.50 per share. The corporate tax rate is 30 percent. The flotation cost is 2 percent of the selling price for preferred stock. The optimum capital structure for the firm is 30 percent debt, 10 percent preferred stock, and 60 percent common equity in the form of retained earnings. Question: Compute the cost of capital for the individual components in the capital structure, and then calculate the weighted average cost of capital Solutions Kd = Yield (1 – T) = 10.5% (1 – .30) = 10.5% (.70) = 7.35% Kp = Dp/(Pp – F) = $8.50/($90 – $1.80) = $8.50/$88.20 = 9.64% Ke = (D1/P0) + g D1 = $3.15 P0 = $98.44 g = 12% (see below) $24/2.00 = 12% $27/2.24 = 12.05% $30/2.51 = 11.95% g = 12% Ke = (D1/P0) + g = $3.15/$98.44 + 12% = 3.20% + 12% = 15.20%

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Bring the above values together to compute the weighted average cost of capital Cost Weighted (aftertax) Weights Cost Debt (Kd).............................................. 7.35% 30% 2.205% Preferred stock (Kp) ........................ 9.64 10% .964 Common equity (Ke) (retained earnings) ....................... 15.20 65% 9.120 Weighted average cost 12.289% of capital (Ka) ................................... 12.29%

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