Jiminy\'s Cricket Farm issued a 30-year, 7.2 percent semiannual bond 5 years ago

Question

Jiminy's Cricket Farm issued a 30-year, 7.2 percent semiannual bond 5 years ago. The bond currently sells for 89.5 percent of its face value. The book value of this debt issue is $99 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 $69 million, and it sells for 57 percent of par. The company’s tax rate is 40 percent.

What is the total book value of debt? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars (e.g., 1,234,567).)

What is the total market value of debt? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars (e.g., 1,234,567).)

What is the aftertax cost of the 7.2 percent coupon bond? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

What is the aftertax cost of the zero coupon bond? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

What is the aftertax cost of debt? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

What is the total book value of debt? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars (e.g., 1,234,567).)

Explanation / Answer

The book value of debt is the total par value of all outstanding debt, so:

BVD = $99,000,000 + 69,000,000

BVD = $168,000,000

To find the market value of debt, we find the price of the bonds and multiply by the number of bonds. Alternatively, we can multiply the price quote of the bond times the par value of the bonds. Doing so, we find:

MVD = .895($99,000,000) + .570($69,000,000)

MVD = $127,935,000

The YTM of the zero coupon bonds is (Remember, even on zero coupon bonds, for consistency, the “payments” are assumed to be semiannual):

PZ = $570 = $1,000(PVIFRr%,16)

R = .03576 or 3.576%

Which means the YTM is: YTM = 3.576% × 2

YTM = 7.15%

So, the aftertax cost of the zero coupon bonds is:

RZ = .0715(1 – .40)

RZ = .0429 or 4.29%

The aftertax cost of debt for the company is the weighted average of the aftertax cost of debt for all outstanding bond issues. We need to use the market value weights of the bonds. The total aftertax cost of debt for the company is

The after tax interest rate of 30 year bond is

=0.720(1-.40)

= 0.0432 or 4.32%

: RD = .0432[(0.895)($99,000,000)/$ 127,935,000] + .0429[(.570)($69,000,000)/$ 127,935,000]

RD = (.0432 *0.692578) + (.0429*0.307422)

RD = 0.029919+0.013188

RD = .043108 or 4.31%

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