AAA has only stock and bonds in its capital structure. Balance sheet information: Long term debt (par value--NOT number of bonds) = $20,000,000, Common equity and retained earings = $17,000,000, and Shares of stock outstanding = 1,000,000. Bond information: Bond price ($1,000 par value per bond) = $1,250.00, bond annual coupon rate with semiannual payments = 7.0%, and bond maturity = 10 years. Stock information: Stock price = $40.00, beta = 1.25, recent dividend (D0) = $3.00, dividend growth rate = 4.00%. Other information: risk free rate = 4.0%, the market risk premium = 6.5%, tax rate = 40.0%. Find the company's after-tax required return on debt
To calculate the after-tax required return on debt, we will first need to find the coupon payment and the yield to maturity of the bond.
1. Calculate the coupon payment:
The annual coupon payment can be calculated by multiplying the par value of the bond by the annual coupon rate:
Coupon payment = Bond par value × Annual coupon rate
Coupon payment = $1,000 × 7% = $70
2. Calculate the yield to maturity (YTM) of the bond:
The yield to maturity represents the overall return on the bond if held until maturity. We can use the bond price, coupon payment, and maturity period to calculate the YTM. However, since the bond pays semiannual coupons, we need to adjust the period rate accordingly. The formula to calculate YTM is:
Bond price = Coupon payment × [1 − (1 + YTM)-n] / YTM + par value / (1 + YTM)-n
Here, n represents the number of periods until maturity.
In this case, the bond price is $1,250, the coupon payment is $70, the par value is $1,000, and the maturity period is 10 years. Since the bond pays semiannual coupons, the number of periods is 2 × 10 = 20.
Using this information, we can use trial and error or Excel to find the YTM. In this example, the YTM is approximately 5.99%.
3. Calculate the after-tax required return on debt:
The after-tax required return on debt can be calculated using the following formula:
After-tax required return on debt = YTM × (1 − Tax rate)
Here, the tax rate is 40%.
After-tax required return on debt = 5.99% × (1 − 0.40)
After-tax required return on debt = 5.99% × 0.60
After-tax required return on debt = 3.59%
Therefore, the company's after-tax required return on debt is 3.59%.
To find the after-tax required return on debt, we need to calculate the yield to maturity, and then adjust it for the tax rate.
1. Calculate the annual coupon payment:
The coupon rate is 7.0%, and since the coupon payment is semiannual, we need to divide it by 2.
Coupon Payment = (Coupon Rate / 2) * Par Value
Coupon Payment = (7.0% / 2) * $1,000 = $35.00
2. Determine the number of periods:
The bond has a maturity of 10 years, and since the coupon payment is semiannual, the number of periods will be 10 * 2 = 20.
3. Calculate the yield to maturity (YTM):
To find the yield to maturity (rate of return) on the bond, we can use a financial calculator or Excel's RATE function. Given the bond price is $1,250.00, the coupon payment is $35.00, the par value is $1,000, and the number of periods is 20, we can calculate the YTM.
YTM = RATE(N, PMT, PV, FV)
YTM = RATE(20, 35, -1250, 1000)
YTM ≈ 2.26%
4. Calculate the after-tax required return on debt:
The tax rate is 40%, so we need to adjust the YTM for the tax benefit obtained from the interest expense deduction.
After-Tax Required Return on Debt = YTM * (1 - Tax Rate)
After-Tax Required Return on Debt = 2.26% * (1 - 0.40)
After-Tax Required Return on Debt ≈ 1.356%
Therefore, the company's after-tax required return on debt is approximately 1.356%.