Question

What are the following values?

Jiminy's Cricket Farm issued a 30-year, 5.9 percent semiannual bond 7 years ago. The bond currently sells for 107.7 percent of its face value. The book value of this debt issue is $145 million. In addition, the company has a second debt issue, a zero coupon bond with 11 years left to maturity; the book value of this issue is $85 million, and it sells for 61.8 percent of par. The company’s tax rate is 25 percent.

What is the total book value of debt?
What is the total market value of debt?
What is the aftertax cost of the 5.9 percent coupon bond?
What is the aftertax cost of the zero coupon bond?
What is the aftertax cost of debt?

Note: Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to the nearest whole number, e.g., 1,234,567.

Answer 1

1. Total book value of debt: 684600

2.Total market value of debt: 79.25

3. After-tax cost of the 5.9% coupon bond: 0.0033

4. After-tax cost of the zero coupon bond: 0.00112

5. After-tax cost of debt: 0.00224.

To solve this problem, we will first find the values of the bonds and then calculate the after-tax costs of the bonds.

Face value of the 5.9% coupon bond:

FV = 1000000 * (1 - y^n)

FV = 100000 * (1 - (0.059 * 7)^9)

FV = 100000 * (1 - (0.059 * 532.1)

FV = 100000 * (1 - 31.64)

FV = 100000 * 0.6836

FV = 683600

Face value of the zero coupon bond:

FV_z = 100000 * (1 - y^n)

FV_z = 100000 * (1 - (0.000 * 11)^11)

FV_z = 100000 * (1 - 0.000)

FV_z = 100000 * 0.000

FV_z = 100

Total book value of debt:

TBV = FV + FV_z

TBV = 683600 + 100

TBV = 684600

Total market value of debt:

TMV = PV * (1 - t)

TMV = 107.7 * (1 - 0.25)

TMV = 107.7 * 0.75

TMV = 79.25

After-tax cost of the 5.9% coupon bond:

ATC = (C / FV) * (1 - T)

ATC = (30 / 683600) * (1 - 0.25)

ATC = 0.00445 * 0.75

ATC = 0.0033

After-tax cost of the zero coupon bond:

ATC_z = (PV_z / FV_z) * (1 - T)

ATC_z = (100 / 683600) * (1 - 0.25)

ATC_z = 0.000156 * 0.75

ATC_z = 0.00112

After-tax cost of debt:

ATC_d = (ATC + ATC_z) / 2

ATC_d = (0.0033 + 0.00112) / 2

ATC_d = 0.00224

In summary:

Total book value of debt: 684600

Total market value of debt: 79.25

After-tax cost of the 5.9% coupon bond: 0.0033

After-tax cost of the zero coupon bond: 0.00112

After-tax cost of debt: 0.00224