Jiminy's Cricket Farm issued a 30-year, 7.2 percent semiannual bond 9 years ago. The bond currently sells for 85.5 percent of its face value. The book value of this debt issue is $107 million. In addition, the company has a second debt issue, a zero coupon bond with 12 years left to maturity; the book value of this issue is $66 million, and it sells for 61 percent of par. The company’s tax rate is 30 percent.
I need to find market value and aftertax cost of debt
.
Market Value of 30-year, 7.2 percent semiannual bond: $91.66 million
Aftertax Cost of Debt: 5.04%
To find the market value and after-tax cost of debt, we need to calculate the market value of each debt issue and then calculate the after-tax cost of each issue.
1. Market Value of the 30-year, 7.2% semiannual bond:
The bond is currently selling for 85.5% of its face value. We need to find the market value of the bond. Given that the face value is not provided, we'll assume it is $100 (par value). The bond has a remaining term of 21 years (30 years - 9 years). The bond makes semiannual coupon payments, so there will be 2 * 21 = 42 coupon payments left.
To calculate the market value, you can use the following formula:
Market Value = (Coupon Payment * (1 - (1 + r)^-n) / r) + (Face Value / (1 + r)^n)
Where:
Coupon Payment = Bond's coupon rate * Face Value / 2 = 7.2% * $100 / 2 = $3.60
r = Semiannual discount rate = (1 + Annual Market Interest Rate)^(1/2) - 1 = (1 + 0.072)^(1/2) - 1 ≈ 3.52%
n = Number of semiannual periods remaining = 42
Market Value = ($3.60 * (1 - (1 + 0.0352)^(-42)) / 0.0352) + ($100 / (1 + 0.0352)^42)
2. Market Value of the zero coupon bond:
The bond sells for 61% of par value. The book value is given as $66 million. We can assume the par value is $100. The bond has a remaining term of 12 years.
To calculate the market value, you can use the formula:
Market Value = Face Value * Selling Price
Market Value = $100 * 0.61
3. After-tax cost of debt:
The after-tax cost of debt is the effective interest rate paid on the bond after considering the tax savings associated with interest expense. To calculate it, we need to multiply the pre-tax cost of debt by (1 - tax rate).
After-tax Cost of Debt = Pre-Tax Cost of Debt * (1 - Tax Rate)
Now, let's calculate the values using the given information:
- Assume the face value of the bonds is $100.
- Assume the tax rate is 30%.
1. Market Value of the 30-year, 7.2% semiannual bond:
Market Value = ($3.60 * (1 - (1 + 0.0352)^(-42)) / 0.0352) + ($100 / (1 + 0.0352)^42)
2. Market Value of the zero coupon bond:
Market Value = $100 * 0.61
3. After-tax cost of debt:
After-tax Cost of Debt = Pre-Tax Cost of Debt * (1 - Tax Rate)
By plugging in the appropriate values into the formulas, you can calculate the market value and after-tax cost of debt.
To find the market value of the semiannual bond, we need to calculate the present value of its cash flows. Here are the steps:
Step 1: Determine the face value of the bond.
The face value is not provided in the question, so we cannot calculate the market value unless we assume a face value for the bond.
Step 2: Calculate the semiannual coupon payment.
The coupon payment can be calculated by multiplying the face value by the semiannual interest rate. Given that the bond has a 7.2% semiannual interest rate, divide this by 2 to get the semiannual coupon rate.
Step 3: Determine the number of remaining coupon payments.
Since the bond was issued 9 years ago and has a 30-year maturity, there are 21 years (30 - 9) left until maturity. As the bond pays semiannual coupons, multiply this by 2 to get the total number of remaining coupon periods.
Step 4: Calculate the present value of the cash flows.
To calculate the present value, we need to discount each semiannual coupon payment and the face value at the current discount rate. The discount rate varies depending on market conditions and the risk of the bond.
Once we have the market value of the semiannual bond, we can calculate the after-tax cost of debt using the following formula:
After-tax cost of debt = Yield to maturity (market rate) * (1 - Tax rate)
Without knowing the face value of the bond and the prevailing market rate, we cannot provide an exact calculation. However, this step-by-step guide outlines the necessary calculations to find the market value and after-tax cost of debt.