Mathematics

Sheet 1

Book Value versus Market Value
Filer Manufacturing has 8.3 million shares of common stock outstanding. The current share price is $53, and the book value per share is $4. Filer Manufacturing also has two bond issues outstanding. The first bond issue has a face value of $70 million and a coupon rate of 7 percent and sells for 108.3 percent of par. The second issue has a face value of $60 million and a coupon rate of 7.5 percent and sells for 108.9 percent of par. The first issue matures in 8 years, the second in 27 years.
a. What are Filer’s capital structure weights on a book value basis?
b. What are Filer’s capital structure weights on a market value basis?
c. Which are more relevant, the book or market value weights? Why?
Shares of common stock outstanding 8,300,000
Current share price $53
Book value per share $4
Number of bond issues outstanding 2
First bond issue face value $70,000,000
First bond issue coupon rate 7.0%
First bond issue sells for what percent of par? 108.3%
Second bond issue face value $60,000,000
Second bond issue coupon rate 7.5%
Second bond issue sells for what percent of par? 108.9%
First bond issue matures in how many years? 8
Second bond issue matures in how many years? 27
a. The book value of equity is the book value per share times the number of shares, and the book value of debt is the face value of the company’s debt, so:
Equity = $33,200,000
Debt = $130,000,000
So, the total book value of the company is:
Book Value = $163,200,000
And the book value weights of equity and debt are:
Equity/Value = 0.2034
Debt/Value = 0.7966
b. The market value of equity is the share price times the number of shares, so:
S = $439,900,000
Using the relationship that the total market value of debt is the price quote times the par value of the bond, we find the market value of debt is:
B = $141,150,000
This makes the total market value of the company:
V = $581,050,000
And the market value weights of equity and debt are:
S/V = 0.7571
B/V = 0.2429
c. The market value weights are more relevant.
PART 2
Calculating the WACC
In the previous problem, suppose the company’s stock has a beta of 1.2. The risk-free rate is 3.1 percent, and the market risk premium is 7 percent. Assume that the overall cost of debt is the weighted average implied by the two outstanding debt issues. Both bonds make semiannual payments. The tax rate is 35 percent. What is the company’s WACC?
The company’s stock has a beta of 1.2
Risk-free rate 3.1%
Market risk premium 7%
Tax rate 35%
First, we will find the cost of equity for the company. The information provided allows us to solve for the cost of equity using the CAPM, so:
RS = .031 + 1.2(.07) = .1150, or 11.50%
RS =

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