Question

Jiminy's Cricket Farm issued a 20-year, 6 percent semiannual coupon bond 3 years ago. The bond currently sells for 103 percent of its face value. The company's tax rate is 22 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 9 years left to maturity; the book value of this issue is $25 million, and the bonds sell for 64 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 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.) Total book value b. Total market value c. Cost of debt S $ 85.000.000 77,800,000 s

Answer 1

1. The book value of debt is the total par value of all outstanding debt

Total Book value = $60,000,000 + $ 25,000,000 = $85,000,000

2. Market value of first issue of debt = $60 Million * 103% = $61.80 million

Market value of second issue of debt = $25 Million * 64% = $16 million

Total Market value of debt D = $61.80 million + $16 million =$77.80 million Or $77,800,000

3. Before tax cost of debt is bond’s yield to maturity (YTM); therefore we need to find the YTM on both bond issues. We have following formula for calculation of bond’s yield

Bond price P0 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Where

Market Price of the bond P0 = $ 61.80 million

M = value at maturity, or par value = $60 million

C = coupon payment = 6% of $ 60 million = $3,600,000 or $3,600,000/2 = $1,800,000 semiannual payment

n = number of remaining payments = 17 years *2 = 34

i = interest rate, or yield to maturity =?

Now we have,

$61.80 million = $1,800,000 * [1 – 1 / (1+i) ^34] /i + $60 million / (1+i) ^34

We got the value of i = 2.86% semiannual

Therefore, annual YTM of first issue = 2 *2.86% = 5.72%

Tax rate = 22%

Therefore After tax cost of debt = 5.72% *(1-0.22) = 4.46%

Now calculate The YTM of the zero coupon bond

Price of zero coupon bond Pz = $16 million

M = value at maturity, or par value = $25 million

We have n = 9 years

Bond price Pz = M / (1+i) ^n

Or $16 million = $25 million / (1+i) ^9

Or i = 5.08%

So, the after tax cost of the zero coupon bonds = 5.08% (1 – 0.22) = 3.97%

The after tax cost of debt for the company is the weighted average of the after tax cost of debt for all debts. We can use the market value as weights of the bonds.

Overall after-tax cost of debt = ($61.80 million /$77.80 million) * 4.46% + ($16 million /$77.80 million) * 3.97%

= 3.55%+ 0.82%

= 4.36%