A company is issuing $1,000 bonds at par value. The coupon rate (and yield to maturity) on the bonds is 8 percent (with annual payments) and the bonds will mature in 10 years. The bonds can be called at a call premium of 5 percent above face value after 3 years. What is the after-tax yield to call for an investor with a 31 percent tax rate?

Question

Quizplus · Accepted Answer

To solve this problem, we need to calculate the yield to call after 3 years, taking into account the call premium and the investor's tax rate.

1. Calculate the price of the bond after 3 years:
The bond will have 7 years left until maturity after 3 years.
Using the formula for the present value of a bond:
PV = C x [(1 - (1 + r)-n) / r] + FV / (1 + r)n
Where PV is the present value of the bond, C is the annual coupon payment, r is the semi-annual yield to maturity, n is the number of semi-annual periods remaining until maturity, and FV is the face value of the bond.
PV = 40 x [(1 - (1 + 0.04)-14) / 0.04] + 1,000 / (1 + 0.04)14
PV = $1,061.69

2. Calculate the after-tax yield to call:
The call price is 1.05 x $1,000 = $1,050.
Since the investor will receive $1,050 in 3 years, we can calculate the semi-annual yield to call using the following formula:
Yield to call = [(Call price - Purchase price) / (Purchase price x Number of periods)] x (1 - Tax rate)
Yield to call = [(1,050 - 1,061.69) / (1,061.69 x 6)] x (1 - 0.31)
Yield to call = -0.005
Yield to call (annualized) = -0.01 or -1%
(Note: A negative yield to call means that the bond is not callable at a profit for the investor)

3. Calculate the after-tax yield to maturity:
Using the same formula as step 1:
PV = 40 x [(1 - (1 + r)-20) / r] + 1,000 / (1 + r)20
Solving for r with a financial calculator or Excel, we get r = 3.3% (semi-annual yield to maturity).
The annual yield to maturity is 2 x 3.3% = 6.6%

4. Compare the after-tax yield to maturity with the yield to call:
Since the yield to call is negative, the investor should hold the bond to maturity to achieve the after-tax yield of 6.6%.

Therefore, the best choice is C.

A Company Is Issuing $1,000 Bonds at Par Value