Jiminy’s Cricket Farm issued a bond with 25 years to maturity and a semiannual c
ID: 2721137 • Letter: J
Question
Jiminy’s Cricket Farm issued a bond with 25 years to maturity and a semiannual coupon rate of 10 percent 4 years ago. The bond currently sells for 97 percent of its face value. The company’s tax rate is 38 percent. The book value of the debt issue is $45 million. In addition, the company has a second debt issue on the market, a zero coupon bond with 11 years left to maturity; the book value of this issue is $45 million, and the bonds sell for 53 percent of par.
What is the company’s total book value of debt?
What is the company’s total market value of debt?
What is your best estimate of the aftertax cost of debt?
What is the company’s total book value of debt?
What is the company’s total market value of debt?
What is your best estimate of the aftertax cost of debt?
Explanation / Answer
1) Total Book Value of Debt = 45 + 45 = $90 million.
2) Total Market Value of Debt = 45*0.97 + 45*0.53 = 43.65 + 23.85 = $67.5 million
3) After tax cost of debt:
After tax cost of the 25 year 10% bond:
The after tax cost (semi-annual) is the value of i in the following equation:
97 = 100*pvif(i,42) + 5*0.62*pvifa(i,42)
discounting with 3%
pv = 100*0.2890 + 3.1*23.7014 = 28.9 + 73.47 = 102.37
discounting with 4%
pv = 100*0.1926 + 3.1*20.1856 = 19.26 + 62.57 = 81.84
exact value of i = 3 + 5.37/20.53 = 3.26
Annual value = 3.26*2 = 6.52%---after tax cost of the bond.
After tax cost of the Zero coupon bond:
Yield to maturity of the bond is the value of i in the following equation
53*(1+i)^11 = 100; i = (100/53)^1/11 - 1 = 0.059414
After tax cost = 0.059414*0.62 = 0.03684 = 3.68%
3) Best estimate of the after tax cost of debt:
It is the weighted average of the cost of the above two debt instruments using market value weights.
= 6.52*(43.65/67.5) + 3.68*(23.85/67.5) = 4.22 + 1.30 = 5.52%
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