Question

Masterson, Inc., has 7 million shares of common stock outstanding. The current share price is $83, and the book value per share is $8. The company also has two bond issues outstanding. The first bond issue has a face value of $140 million, has a coupon rate of 6 percent, and sells for 94 percent of par. The second issue has a face value of $125 million, has a coupon rate of 5 percent, and sells for 105 percent of par. The first issue matures in 25 years, the second in 8 years.

Suppose the most recent dividend was $4.95 and the dividend growth rate is 4.9 percent. Assume that the overall cost of debt is the weighted average of that implied by the two outstanding debt issues. Both bonds make semiannual payments. The tax rate is 24 percent. What is the company’s WACC? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Solution:

Formula of WACC:
WACC = Weight of debt x Cost of debt x (1-tax rate)    +    Weight of equity x Cost of equity
In this formula we have five variables: Weight of debt, Cost of debt, tax rate, Weight of equity and Cost of equity. Out of these we have been provided with the tax rate of 24% or 0.24 and we need to find remaining four variables.
Weight of debt and Weight of equity:
Total amount of debt = Face value of first bond + Face value of second bond = $140 million + $125 million = $ 265 million		.
Total amount of equity = Number of shares of common stock outstanding x Current share price = $7 million x $83 = $ 581 million
Weight of debt = Total amount of debt / (Total amount of debt + Tptal amount of equity) = 265 /(265+581) = 0.31323877
Weight of equity = Total amount of equity / (Total amount of debt + Tptal amount of equity) = 581 /(265+581) = 0.68676123
Cost of debt:
First bond (semi-annual payments)
Nper = 25 x 2 = 50 (indicates the number of periods till maturity)
FV = 140 million (indicates the face value of bonds)
PMT = 140 million x (6%/2) = 140 million x 3% = 4.2 million (indicates semi-annual interest payment)
PV = 94% of par = 94% x 140 million = 131.6 million (indicates the current selling price)
Rate = ? (indicates semi-annual yield to maturity)
Rate = using excel formula, Rate(Nper,PMT,PV,FV) = Rate(50,4.2,-131.6,140) = 3.244116%
Annual yield to maturity = Rate x 2 = 3.244116% x 2 = 6.488231%
Second bond (semi-annual payments)
Nper = 8 x 2 = 16 (indicates the number of periods till maturity)
FV = 125 million (indicates the face value of bonds)
PMT = 125 million x (5%/2) = 125 million x 2.5% = 3.125 million (indicates semi-annual interest payment)
PV = 105% of par = 105% x 125 million = 131.25 million (indicates the current selling price)
Rate = ? (indicates semi-annual yield to maturity)
Rate = using excel formula, Rate(Nper,PMT,PV,FV) = Rate(16,3.125,-131.25,125) = 2.128005%
Annual yield to maturity = Rate x 2 = 2.128005% x 2 = 4.256010%
Cost of debt = Weighted average of that implied by the two outstanding debt issues = (140 x 6.488231% + 125 x 4.256010%) / (140+125) = 5.435297%
Cost of equity:
Using Gordon growth formula: Current stock price = Current dividend x (1+growth rate) / (Cost of equity - growth rate)
On putting values we get,
83 = 4.95 x (1+4.9%) / (Cost of equity - 4.9%)
83 = 4.95 x (1+0.049) / (Cost of equity - 0.049)
83 = 5.19255 / (Cost of equity - 0.049)
Cost of equity - 0.049 = 5.19255 / 83
Cost of equity - 0.049 = 0.0625608
Cost of equity = 0.0625608 + 0.049 = 0.11156084 or 11.156084%
WACC:
WACC = Weight of debt x Cost of debt x (1-tax rate)    +    Weight of equity x Cost of equity
WACC = 0.31323877 x 5.435397% x (1-0.24)    +    0.68676123 x 11.156084% = 8.9555009%
WACC = 8.96% (answer)

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