Question

Jiminy’s Cricket Farm issued a 30-year, 6 percent semiannual coupon bond 4 years ago. The bond currently sells for 105 percent of its face value. The company’s tax rate is 23 percent. The book value of the debt issue is $60 million. In addition, the company has a second debt issue, a zero coupon bond with 8 years left to maturity; the book value of this issue is $35 million, and the bonds sell for 67 percent of par.

A. What is the company’s total book value of debt?

B. What is the company’s total market value of debt?

C. What is the aftertax cost of debt?

Answer 1

(a) Bond 1: Book Value of Debt = $ 60 million and Bond 2: Book Value of Debt = $ 35 million

Total Book Value of Debt = 60 + 35 = $ 95 million

(b) Bond 1: Face Value = $ 60 million, Price = 105 % of Face Value = 1.05 x 60 = $ 63 million,  Remaining Tenure = 26 years or (26 x 2) = 52 half-years, Coupon Rate = 6 %, Coupon Frequency: Semi-Annual

Semi-Annual Coupon = 0.06 x 60 x 0.5 = $ 1.8 million

Let the yield be y1

Therefore, 63 = 1.8 x (1/y1) x [1-{1/(1+y1)^(52)}] + 60 / (1+y1)^(52)

Using EXCEL's Goal Seek Function/hit and trial method/a financial calculator to solve the above equation, we get:

y1 = 0.028157 or 2.8157 % ~ 2.82 %

Bond 2: Face Value = $ 35 million, Tenure = 8 Years and Price = 67% of Face Value = 0.67 x 35 = $ 23.45 million

Let the yield be y2

Therefore, 23.45 = 35 / (1+y2)^(8)

y2 = [(35/23.45)^(1/8)-1] = 0.0513338 or 5.13338 % ~ 5.13 %

Total Market Value of Debt = 63 + 23.45 = $ 86.45 million

(c) Weighted Average Cost of Debt = 2.82 x [63/(63+23.45)] + 5.13 x [23.45/(63+23.45)] = 3.446599 % ~ 3.45 %

Tax Rate = 23 %

After -Tax cost of debt = (1-0.23) x 3.45 = 2.654 % ~ 2.65 %