Question

Jiminy’s Cricket Farm issued a bond with 30 years to maturity and a semiannual coupon rate of 10 percent 4 years ago. The bond currently sells for 94 percent of its face value. The company’s tax rate is 38 percent. The book value of the debt issue is $50 million. In addition, the company has a second debt issue on the market, a zero coupon bond with 14 years left to maturity; the book value of this issue is $50 million, and the bonds sell for 54 percent of par.

What is the company’s total book value of debt? (Enter your answer in dollars, not millions of dollars, e.g. 1,234,567.)

Total book value $

What is the company’s total market value of debt? (Enter your answer in dollars, not millions of dollars, e.g. 1,234,567.)

Total market value $

What is your best estimate of the aftertax cost of debt? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Cost of debt %

Answer 1

Debt 1 Book Value = BV(D1) = $ 50 million and Debt 2 Book Value = BV(D2) = $ 50 million

Total Book Value of Debt = BV(D1) + BV(D2) = 50 + 50 = $ 100 million

Market Value of Debt = MV(D1) = 0.94 x BV(D1) = 50 x 0.94 = $ 47 million

Market Value of Debt = MV(D2) = 0.54 x BV(D2) = 50 x 0.54 = $ 27 million

Total Market Value of Debt = MV(D1) + MV(D2) = 47 + 27 = $ 74 million

Debt 1:

Remaining Tenure = 26 Years or 52 years, Annual Coupon Rate = 10 % per annum payable semi-annually, Face Value of Debt = $ 50 million, Market Value = 94% of Par Value = 0.94 x 50 = $ 47 million

Semi-Annual Coupon = 0.1 x 50 x 0.5 = $ 2.5 million

Let the yield to maturity be 2R

Therefore, 47 = 2.5 x (1/R) x [1-{1/(1+R)^(52)}] + 50 / (1+R)^(52)

Using EXCEL's Goal Seek Function to solve the above equation, we get:

R = 0.0534 or 5.34 % per half - year

Therefore, Yield to Maturity of Debt1 = YTM1 = 5.34 x 2 = 10.68 %

Debt 2:

Bond Tenure = 14 years, Bond Par Value = $ 50 million, Bond Market Value = 54 % of Par Value = 0.54 x 50 = $ 27 million

Let the bond's yield to maturity be R

Therefore, 27 = 50 / (1+R)^(14)  

Using EXCEL's Goal Seek Function to solve the above equation, we get:

R = 0.045 or 4.5 % per annum

Therefore, Yield to Maturity = YTM2 = 4.5 %

Weighted Average Cost of Debt = r(d) = Weighted Average Value of the two debt's YTM = YTM 1 x Debt 1 Proportion + YTM 2 x Debt Proportion = 10.68 x (47/74) + 4.5 x (27/74) = 8.4251 %

Tax Rate = t = 38 %

After Tax Cost of Debt = (1-t) x r(d) = (1-0.38) x 8.4251 = 5.224 % or 5.22% approximately