Question

Suppose your company needs to raise $54 million and you want to issue 25-year bonds for this purpose. Assume the required return on your bond issue will be 4.8 percent, and you're evaluating two issue alternatives: A semiannual coupon bond with a coupon rate of 4.8 percent and a zero coupon bond. Your company's tax rate is 25 percent. Both bonds will have a par value of $1,000. a-1. How many of the coupon bonds would you need to issue to raise the $54 million? a-2. How many of the zeroes would you need to issue? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b-1. In 25 years, what will your company's repayment be if you issue the coupon bonds? (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, e.g., 1,234,567.) b-2. What if you issue the zeroes? (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, e.g., 1,234,567.) C. Calculate the aftertax cash flows for the first year for each bond. (Do not round intermediate calculations and enter your answers in dollars, not millions of dollars, e.g., 1,234,567.)

Answer 1

Part (a - 1)

Coupon rate = desired return, hence bond will be issued at par i.e. @ $ 1,000 per bond.

Hence, number of bond required = 54,000,000 / 1,000 = 54,000

Part (a - 2)

Price of a zero coupon bond = P = 1,000 / (1 + r/2)ⁿ = 1,000 / (1 + 4.8% / 2)^{2 x 25} = $ 305.49

Hence, number of bonds required = 54,000,000 / 305.49 = 176,763.09

Part (b - 1)

In 25 years, the repayment = Principal + last coupon amount = 54,000,000 x (1 + 4.8% / 2 ) =  55,296,000

Part (b - 2)

The repayment = Number of bonds x face value = 176,763.09 x 1,000 = $  176,763,093

Part (c - 1)

Coupon bond

After tax cash flows = - Post tax interest = - 54,000,000 x 4.8% x (1 - 25%) = - 1,944,000 (and it's an outflow and hence the negative sign)

Zero Coupon Bond

Price today = 305.49 (calculated earlier)

Price after 1 year = = 1,000 / (1 + 4.8% / 2)^{2 x 24} = $ 320.33

Hence, interest in first year = 320.33 - 305.49 = 14.84

Hence, total tax shield on interest = 14.84 x 176,763.09 (number of bonds) x 25% (tax rate) = $ 655,776 (and note that this is an inflow)