Prof. Q. MA, HA222 Spring 2007
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Chapter 15
EQ # 1: Cost of Equity – DGM
1.1. A firm is expected to pay a dividend of $3.50 per share in one year. This dividend, along with the
firm’s earnings, is expected to grow at a rate of 7% forever. If the current market price for a share is
$70, what is the cost of equity?
Solution: R=D1/P0 + g = 3.5 /70 + 7 = 12%
1.2. Given the following information, what is the average annual dividend growth rate?
D
1998
=$1.70, D
1999
=$1.80, D
2000
=$2.05, D
2001
=$2.18, D
2002
=$2.39, D
2003
=$2.65.
Solution: g1999 = 1.80/1.70 – 1 = 5.88%; similarly, g2000=13.89, g2001=6.34%, g2002=9.63% and
g2003=10.88%. The average is what we want: 9.32%.
EQ # 2: Cost of Equity – SML
The cost of equity for a firm will increase, all else the same, with a decrease in the:
[c]
a. Amount of systematic risk.
b. Reward for bearing systematic risk.
c. Pure time value of money (if the firm has an equity beta greater than one).
d. Pure time value of money (if the firm has an equity beta less than one).
e. Pure time value of money (if the firm has an equity beta equal to one).
EQ # 3: Cost of Debt:
3.1. The long-term debt of your firm is currently selling for 119% of its face value. The issue matures in
12 years and pays an annual coupon of 7.5%. What is the cost of debt?
[5.32%]
Solution: Without loss of generality, assuming par value of the bond is 1000, then bond price=1190,
coupon = 75, time to maturity is 12, we are asked to get yield to maturity. Using bond pricing formula
& trial and error or using financial calculator to solve for yield to maturity.
3.2. A firm sold a 10-year bond issue 3 years ago. The bond has a 6.55% annual coupon and a $1,000 face
value. If the current market price of the bond is $961.64 and the tax rate is 35%, what is the after-tax
cost of debt?
Solution: Par=1000, price=961.64, coupon=65.5, time to maturity is 10 – 3 = 7 years, solve for yield to
maturity, 7.268%. The after-tax cost of debt is 7.268% x (1 – 35%) = 4.724%.
3.3. A bond issue sells for $775. The coupon rate is 7%, the bonds mature in 20 years, and interest is paid
semiannually. The tax rate is 35%. What is the after-tax cost of debt?
Solution: par value is 1000, price is 775, period (6-month) coupon is 70/2 = 35, number of periods in
maturity 20 x 2 = 40, we solve for period yield to maturity as 4.77%, so the annual yield is 4.77% x 2 =
9.54% and the after-tax cost of debt is 6.20%.
EQ # 4: Cost of Preferred Stock
A company’s preferred stock pays an annual dividend of $7.00 per share. When issued, the shares sold for
their par value of $100 per share. What is the cost of preferred stock if the current price is $130 per
share?
[P0=130=D/R = 7/R, R=7/130 = 5.35%]
EQ # 5: Capital Structure Weight
5.1. Given the following information, what is the value of the firm?