Shanken Corp. issued a 18-year, 8 percent semiannual bond 3 years ago. The bond
ID: 2788211 • Letter: S
Question
Shanken Corp. issued a 18-year, 8 percent semiannual bond 3 years ago. The bond currently sells for 92 percent of its face value. 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 12 years left to maturity; the book value of this issue is $35 million and the bonds sell for 51 percent of par. The company’s tax rate is 40 percent. What is your best estimate of the aftertax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Explanation / Answer
Lets assume par value per bond is 1000
Cost of debt = interest+(par value-market value)/years to maturity / (par value+ market value)/2
40+(1000-920)/30 / (1000+920)/2
42.666/960 = .044444
annual before tax cost of debt = .04444*2*100 = 8.888%
After tax cost of debt = 8.88*(1-tax rate) = 8.88*(1-.4) = 5.33%
2- cost of capital of zero coupon bond = (face value/market value)^(1/n) -1
(35/17.85)^(1/12) -1 = 1.057716-1 = .05771
before tax cost of debt = .05771*(1-tax rate) = .05771*.6*100 = 3.4629%
overall cost of debt on the basis of book value
Book value
weight
cost of debt
weight*cost of debt
coupon bond
45
0.5625
5.33
2.998125
zero coupon bond
35
0.4375
3.46
1.51375
80
overall cost of debt
sum of weight*cost of debt
4.511875
overall cost of debt on the basis of market value
Book value
weight
cost of debt
weight*cost of debt
coupon bond
41.4
0.698734
5.33
3.724253
zero coupon bond
17.85
0.301266
3.46
1.04238
59.25
overall cost of debt
sum of weight*cost of debt
4.766633
overall cost of debt on the basis of book value
Book value
weight
cost of debt
weight*cost of debt
coupon bond
45
0.5625
5.33
2.998125
zero coupon bond
35
0.4375
3.46
1.51375
80
overall cost of debt
sum of weight*cost of debt
4.511875
overall cost of debt on the basis of market value
Book value
weight
cost of debt
weight*cost of debt
coupon bond
41.4
0.698734
5.33
3.724253
zero coupon bond
17.85
0.301266
3.46
1.04238
59.25
overall cost of debt
sum of weight*cost of debt
4.766633
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