Question

The current stock price for a company is $42 per share, and there are 6 million shares outstanding. This firm also has 230,000 bonds outstanding, which pay interest semiannually. If these bonds have a coupon interest rate of 9%, 10 years to maturity, a face value of $1,000, and an annual yield to maturity of 7.8%, what is the percent market value of debt for this firm? (Answer to the nearest hundredth of a percent, but do not use a percent sign).

Answer 1

Bonds:

Face Value = $1,000

Annual Coupon Rate = 9%
Semiannual Coupon Rate = 4.5%
Semiannual Coupon = 4.5% * $1,000
Semiannual Coupon = $45

Annual YTM = 7.8%
Semiannual YTM = 3.9%

Time to Maturity = 10 years
Semiannual Period to maturity = 20

Current Price = $45 * PVIFA(3.9%, 20) + $1,000 * PVIF(3.9%, 20)
Current Price = $45 * (1 - (1/1.039)^20) / 0.039 + $1,000 / 1.039^20
Current Price = $1,082.27

Number of bonds outstanding = 230,000

Value of Debt = Current Price * Number of bonds outstanding
Value of Debt = $1,082.27 * 230,000
Value of Debt = $248,922,100

Equity:

Number of shares outstanding = 6,000,000
Current price = $42

Value of Equity = Number of shares outstanding * Current price
Value of Equity = 6,000,000 * $42
Value of Equity = $252,000,000

Market Value of the Firm = Value of Debt + Value of Equity
Market Value of the Firm = $248,922,100 + $252,000,000
Market Value of the Firm = $500,922,100

Weight of Debt = Value of Debt / Market Value of the Firm
Weight of Debt = $248,922,100 / $500,922,100
Weight of Debt = 0.4969 or 49.69%