Question

Jiminy’s Cricket Farm issued a bond with 20 years to maturity and a semiannual coupon rate of 5 percent 2 years ago. The bond currently sells for 96 percent of its face value. The company’s tax rate is 21 percent. The book value of the debt issue is $55 million. In addition, the company has a second debt issue on the market, a zero coupon bond with 8 years left to maturity; the book value of this issue is $30 million, and the bonds sell for 67 percent of par. a. What is the company’s total book value of debt? (Enter your answer in dollars, not millions of dollars, e.g. 1,234,567.) b. What is the company’s total market value of debt? (Enter your answer in dollars, not millions of dollars, e.g. 1,234,567.) c. 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.)

Answer 1

Answer:

a.- 85 millions

b.- 71.8 millions

c.- 3.92%

Explanation:

bonds book value of debt: 55,000,000

zero cuopon book value:  30,000,000  

total book value of the debt 85,000,000

market value of the bonds:

55,000,000 x 94% = 51,700,000

market value of the zero coupon:

30,000,000 x 67% = 20,100,000

Total market vale of the debt 71,800,000

Cost of debt:

We will calculate each debt coponent rate;

zero coupon:

$20.1 \times (1+r)^{8} =30$

$r= \sqrt[8]{\frac{30}{20.1}}-1$

r =

bond rate (approximation of the YTM)

$YTM = \frac{C + \frac{F-P}{n }}{\frac{F+P}{2}}$

C= 50 (1,000 bond x 5% / 2 payment per year)

F= 1000

P= 940 (94% of the face value)

n= 40  ( 20 years and 2 payment per year)

YTM= 5.3092784%

To calculate an estimated cost of debt for the whole firm, we will weight each debt rate by their influence in the compay's total debt:

0.051333842 x 20.1/71.8  + 0.053092784 x 51.7/78 =

0.014370616   +  0.035190986  =  0.049561602

Finally, we apply the tax shield:

0.049561602 x ( 1 - 0.21) = 0,03915366558 = 3.92%