Question

Suppose your company needs to raise $36 million and you want to issue 30-year bonds for this purpose. Assume the required return on your bond issue will be 7 percent and you’re evaluating two issue alternatives: A semiannual coupon bond with a coupon rate of 7 percent and a zero coupon bond. Your company’s tax rate is 22 percent. Assume a par value of $1,000.

a-1.	How many of the coupon bonds would you need to issue to raise the $36 million? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

a-2.	How many of the zeroes would you need to issue? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

b-1.	In 30 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, rounded to the nearest whole number, 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, rounded to the nearest whole number, e.g., 1,234,567.)

      

  

c.	Calculate the firm’s aftertax cash outflows for the first year for each bond. (Enter your answers as positive values. Do not round intermediate calculations and enter your answers in dollars, not millions of dollars, rounded to the nearest whole number, e.g., 1,234,567.)

  
      

Answer 1

a1). The coupon bonds have a coupon rate of 7% which matches the 7% required return, so they will sell at par. The number of bonds that must be sold is the amount needed divided by the bond price,so:

Number of coupon bonds to sell = $36,000,000 / $1,000 = 36,000

a2). Price of zero coupon bonds = $1,000 / 1.035⁶⁰ = $126.93

Number of zero coupon bonds to sell = $36,000,000 / $126.93 = 283,611.27, or 283,611

b1). The repayment of the coupon bond will be the par value plus the last coupon payment times the number of bonds issued. So:

Coupon bonds repayment = 36,000($1,035) = $37,260,000

b2). The repayment of the zero coupon bond will be the par value times the number of bonds issued, so:

Zeroes repayment = 283,611.27($1,000) = $283,611,272.40, or $283,611,272

c). The total coupon payment for the coupon bonds will be the number of bonds times the coupon payment. For the cash flow of the coupon bonds, we need to account for the tax deductibility of the interest payments. To do this, we will multiply the total coupon payment times one minus the tax rate. So:

Coupon bonds = (36,000)($70)(1 - 0.22) = $1,965,600 cash outflow

Note that this is a cash outflow since the company is making the interest payment.

For the zero coupon bonds, the first year interest payment is the difference in the price of the zero at the end of the year and the beginning of the year. The price of the zeroes in one year will be:

P1 = $1,000/1.035⁵⁸ = $135.98

The Year 1 interest deduction per bond will be this price minus the price at the beginning of the year, which we found in part b, so:

Year 1 interest deduction per bond = $135.98 - $126.93 = $9.04

The total cash flow for the zeroes will be the interest deduction for the year times the number of zeroes sold, times the tax rate. The cash flow for the zeroes in Year 1 will be:

Cash flows for zeroes in Year 1 = (283,611)($9.04)(0.22) = $564,102.00