Question

Pearce’s Cricket Farm issued a 30-year, 8% semiannual bond 4 years ago. The bond currently sells for 94% of its face value. The company’s tax rate is 35%. Assume the par value of the bond is $1,000.

a. What is the pre-tax cost of debt? (Do not round intermediate calculations. Round the final answer to 3 decimal places.)

Pre-tax cost of debt             %

b. What is the after-tax cost of debt? (Do not round intermediate calculations. Round the final answer to 3 decimal places.)

After-tax cost of debt             %

c. Which is more relevant, the pre-tax or the after-tax cost of debt?

• After-tax cost of debt

• Pre-tax cost of debt

Answer 1

Solution

a. Pre tax debt = Yield to maturity of the bond

Current price of the bond=Present value of coupon payments+Present value of face value

Current price of the bond=Present value of annuity of coupon payments+Face value/(1+r)^n

Current price of the bond=Semi annual coupon payment*(((1-((1/(1+r)^n)))/r))+Face value/(1+r)^n

Where

r= semi annual rate of discounting

n= Number of periods to maturity-Since 4 years alraedy gone so number of periods=26*2=52 semiannual periods

Face value=1000

Semi annual coupon payment=$40

Current price of bond=94% of Face value=940

Putting value in above formula

940=40*(((1-((1/(1+r)^52)))/r))+1000/(1+r)^52

Solving we get r=.0429

Therefore YTM=2*r=.0429*2

=0.0858

Pre tax cost of debt=8.58%

b. After tax cost of debt=Pre tax cost of debt*(1-tax rate)

=8.58*(1-.35)

=5.577% (After tax cost of debt

c. After tax cost of debt is more relevant as that is the actual cost of debt to company

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