Question

Jiminy’s Cricket Farm issued a 30-year, 4.5 percent semiannual bond three years ago. The bond currently sells for 104 percent of its face value. The company’s tax rate is 22 percent. a. What is the pretax cost of debt? Jiminy’s Cricket Farm issued a 30-year, 4.5 percent semiannual bond three years ago. The bond currently sells for 104 percent of its face value. The company’s tax rate is 22 percent. a. What is the pretax cost of debt? b. What is the aftertax cost of debt?

Answer 1

a. The pretax cost of debt for Jiminy's Cricket Farm is 2.25 percent.

b. The aftertax cost of debt for Jiminy's Cricket Farm is 1.76 percent.

Step-by-step explanation:

a. The pretax cost of debt can be calculated using the formula:

Pretax Cost of Debt = Annual Interest Payment/Current Market Price

In this case, the bond has a 4.5 percent annual coupon rate, and since it is a semiannual bond, the semiannual interest payment can be calculated as 4.5%/2. Therefore, the annual interest payment is 2 × 4.5\%/2. The current market price is given as 104 percent of face value, so in decimal form, it is 104/100 times the face value. Plugging these values into the formula gives the pretax cost of debt.

b. The aftertax cost of debt is determined by adjusting the pretax cost of debt for taxes. The formula is:

Aftertax Cost of Debt = Pretax Cost of Debt × (1 - Tax Rate)

With the given tax rate of 22 percent, plugging this into the formula along with the pretax cost of debt gives the aftertax cost of debt. This reflects the actual cost to the company after considering the tax shield provided by the deductibility of interest payments.

Answer 2

Jiminy's Cricket Farm's pretax cost of debt is the yield to maturity on the bond, while the aftertax cost of debt accounts for the company's tax rate. Bond prices fluctuate with market interest rates; they fall when market rates rise and increase when market rates fall.

Step-by-step explanation:

To calculate the pretax cost of debt for Jiminy’s Cricket Farm, we need to find the yield to maturity (YTM) on the bond, which is the interest rate that equates the present value of all future cash flows from the bond (coupons and principal) with the current price of the bond. Since the bond sells for 104 percent of its face value and has a coupon rate of 4.5 percent paid semiannually, the calculation involves solving for YTM in the bond pricing formula, which can be done using a financial calculator or software designed for such calculations.

The aftertax cost of debt is calculated by multiplying the pretax cost of debt by one minus the tax rate. Therefore, if the pretax cost of debt is found to be Y%, the aftertax cost of debt would be Y% * (1 - 0.22).

Using similar logic, we can discuss the scenario described in the example where a local water company issued a $10,000 ten-year bond at an interest rate of 6% and you are thinking about buying this bond one year before the end of the ten years, but interest rates are now 9%. The price of the bond would be lower than its face value as it offers a lower interest rate than the current market rate. Conversely, if interest rates had fallen, the bond would sell for more than its face value. This is because the bond's fixed interest payments are more attractive when compared to the new lower market rates.

Considering the provided examples, if the market interest rate rises from 3% to 4% a year after Ford issues the bonds, the value of the bond will decrease because new bonds in the market would be offering a higher interest rate, making the existing bonds with lower interest rates less attractive.