Question

Zero Coupon Bonds Suppose your company needs to raise $30 million and you want to issue 30-year bonds for this purpose. Assume the required return on your bond issue will be 8 percent, and you’re evaluating two issue alternatives: An 8 percent semiannual coupon bond and a zero coupon bond. Your company’s tax rate is 35 percent.

a. How many of the coupon bonds would you need to issue to raise the $30 million? How many of the zeroes would you need to issue?

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b. In 30 years, what will your company’s repayment be if you issue the coupon bonds? What if you issue the zeroes?

Answer 1

Bond valuation calculates the present value of bond considering the maturity of bond and interest rate. The formula to calculate the present value of bond is as follows:

The company needs to raise $30 million for which 30-year bond is to be issued. The required return or interest rate is 8% or 0.08. The bond is compounded semi-annually. There are two alternatives to raise the funds. The first is to issue 8% semi-annual coupon bond and the second is to issue zero coupon bond. The tax rate for the firm is 35%. Suppose; the par value of the bond is $1,000.

(a)

Calculate the number of coupon bonds to be issued to raise $30 million:

Step 1: Calculate the current bond price for coupon bond as follows:

The 8% semi-annual coupon bond will have the bond price i.e. the selling price and par value i.e. future value as same i.e. $1,000. This is because; the interest rate and coupon rate is same i.e. 8%.

Step 2: Calculate the number of coupon bonds to be raised as follows:

Therefore, the number of coupon bonds to be raised is .

Calculate the number of zero coupon bonds to be issued to raise $30 million:

Step 1: Calculate the current bond price for zero-coupon bond as follows:

Step 2: Calculate the number of zero-coupon bonds to be raised as follows:

Therefore, the number of zero-coupon bonds to be raised is .

(b)

Calculate the company’s repayment after 30 years for coupon bonds as follows:

Therefore, the company’s repayment after 30 years for coupon bonds is .

Calculate the company’s repayment after 30 years for zero-coupon bonds as follows:

Therefore, the company’s repayment after 30 years for zero-coupon bonds is .