A corporation has 12,000,000 shares of stock outstanding at price of $40 per sha

Question

A corporation has 12,000,000 shares of stock outstanding at price of $40 per share. They just paid a dividend of $3 and the dividend is expected to grow by 4% per year forever. The stock has a beta of .9 the current risk free rate is 3%, and the market risk premium is 7%. The corporation also has 400,000 bonds outstanding with a price of $950 per bond. the bond has a coupon rate of 6% with semiannual interest payments, a face value of 1,000, and 13 years to go until maturity. The company plans on issuing ne debt until they reach their targetdebt ratio of 70%. They expecttheir cost of debt to be 9% and their cost of equity to be 13% under the new capital structure. The tax rate is 40%

1. What is the CAPM required return on the corpartion's stock? a. 8.4% b 9.3% c10.3 d11.2

2. What is the expected return on the corporation's stock? a. 10.4 % b. 11.3 c. 11.8 d. 12.6

3. what is the relevant yield on the company's debt? a. 6.6 b. 7.1 c. 7.8 d. 8.25

4. What perecent of their current market value capital structure is made of debt? a. 25 b. 38 c 44 d 56

5. what is their WACC using their target capital structure and expected cost of debt and equity? a. 7.7 b 8.2 c. 8.9 d. 9.4

6. Given the new cost of debt, what should be the new price of the bond? a. 775 b. 850 c. 911 d. 1,025

7. Given the new cost of equity, what should be the price of the stock? a. 23.75 b. 28.50 c. 34.67 d. 44.25

Explanation / Answer

1. Cost of equity calculation:

= risk free rate+beta*(market premium)

= 3%+0.9*7% = 3%+6.3% = 9.3%

2. Expected return on corporation's stock:

Using the dividend discount model, we calculate the Present value (PV) of future dividends growing at 4%

Now, price = dividend/(rate of return - growth rate)

40 = 3/(r-4%)

r-4% = 0.075

or r = 0.075+0.04. or r = 0.115 or 11.5%

3. Relevant yield = annual interest/price

annual interest = 6% of 1,000 being paid semi-annually: Total interest being paid = 30+30 =

Yield = 60/950 = 6.32% Please note that this is the current yield and not Yield to maturity

4. Market value of equity = no. of shares*price per share

= 12,000,000*40 = $480,000,000

Market value of debt = no. of bonds*price per bond

= 400,000*950 = $380,000,000

Total capital = equity+debt = 480,000,000+380,000,000 = 860,000,000

% of debt in capital = 380,000,000/860,000,000 = 44%

5. Debt = 70% of capital. equity = 30% of capital

WACC = weight of debt*its cost after tax+weight of equity*its cost

= 0.7*(9%*(100%-40%))+0.3*13%

= 3.8%+3.9% = 7.7%

7. new cost of equity = 13%

stock price using dividend discount model:

dividend/(cost of equity - growth rate)

3/(13% - 4%)

= 3/0.09 = 33.33

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