Suspect Corp. issued a bond with a maturity of 30 years and a semiannual coupon rate of 6 percent 4 years ago. The bond currently sells for 95 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 15 years left to maturity; the book value of this issue is $50 million and the bonds sell for 54 percent of par. The company’s tax rate is 40 percent. Required:a. What is the company’s total book value of debt?b. What is the company’s total market value of debt? c. What is your best estimate of the aftertax cost of debt?

Answer and Explanation:

The computation of each point is shown below:-

But before that we need to do the following calculations

First Issue of Bonds:

Face Value = $45,000,000

Market Value = 95% × $45,000,000

= $42,750,000

Annual Coupon Rate = 6%

Semiannual Coupon Rate = 3%

= 3% × $45,000,000

= $1,350,000

Time to Maturity = 26 years

Semiannual Period to Maturity = 52

Let semiannual YTM be i%

$42,750,000 = $1,350,000 × PVIFA(i%, 52) + $45,000,000 × PVIF(i%, 52)

N = 52

PV = -42750000

PMT = 1350000

FV = 45000000

I = 3.20%

Semiannual YTM = 3.20%

Annual YTM = 2 × 3.20%

Annual YTM = 6.40%

Before-tax Cost of Debt = 6.40%

After-tax Cost of Debt = 6.40% × (1 - 0.40)

= 3.84%

Second Issue of Bonds:

Face Value = $50,000,000

Market Value = 54% × $50,000,000

= $27,000,000

Time to Maturity = 15 years

Semiannual Period to Maturity = 30

Let semiannual YTM be i%

$27,000,000 = $50,000,000 × PVIF(i%, 30)

Using a financial calculator:

N = 30

PV = -27000000

PMT = 0

FV = 50000000

I = 2.075%

Semiannual YTM = 2.075%

Annual YTM = 2 × 2.075%

= 4.15%

Before-tax Cost of Debt = 4.15%

After-tax Cost of Debt = 4.15% × (1 - 0.40)

= 2.49%

a. The total book value of debt is

Total Book Value of Debt = $45,000,000 + $50,000,000

= $95,000,000

b. The total market value of debt is

Total Market Value of Debt = $42,750,000 + $27,000,000

= $69,750,000

c. The estimate of the aftertax cost of debt is

Weight of first Issue of Debt is

= $42,750,000 ÷ $69,750,000

= 0.6129

Weight of second issue of Debt

= $27,000,000 ÷ $69,750,000

= 0.3871

So,  

Estimated After-tax Cost of Debt is

= 0.6129 × 3.84% + 0.3871 × 2.49%

= 3.32%

explanation: doctrine of respondeat superior is a legal doctrine that is commonly used in tort. this principle makes an employer or principal legally responsible for the wrongful acts done by an employee or agent, if such acts occur within the scope of the employment or agency.

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