Question

Zero Coupon Bonds. Suppose your company needs to raise $40 million and you want to issue 20-year bonds for this purpose. Assume the required return on your bond issue will be 5.7 percent, and you’re evaluating two issue alternatives a 5.7 percent semiannual coupon bond and a zero coupon. Your company’s tax rate is 21 percent.

            a. How many of the coupon bonds would you need to issue to raise the $40 million? How many of the zeros would you need to issue?

            b. In 20 years, what will your company’s repayment be if you issue the coupon bonds? What if you issue the zeros?

Answer 1

a. required return on coupon bond is 5.7% which is equal to coupon rate of 5.7% semiannual coupon bond. so, bond will be issued at par value of $1,000. coupon bonds usually have par value of $1,000 and if required return and coupon rate of the bond are same then bond's par value and current price are same.

no. of coupon bonds needed to be issued = amount to be raised/market price of the bond = $40,000,000/$1,000 = 40,000

You would need to issue 40,000 coupon bonds to raise the $40 million.

Zero coupon bonds don't pay any coupon and are issued at discount to their par value. so we need to calculate market price of zero coupon bond. we can use financial calculator for calculation of market price with below keystrokes:

N = maturity = 20; I/Y = required return = 5.7%; PMT = coupon payment = $0; FV = par value = $1,000 > CPT = compute > PV = market price = $329.99

Calculator will show PV as negative value as it's a cash outflow.

no. of zero coupon bonds needed to be issued = amount to be raised/market price of the bond = $40,000,000/$329.99 = 121,216

You would need to issue 121,216 zeros.

b. Company's repayment if coupon bonds are issued = par value of bonds or principal repayment + coupon payment on bonds

Company's repayment if coupon bonds are issued = $40,000,000 + ($40,000,000*5.7%) = $40,000,000 + $2,280,000 = $42,280,000

In 20 years, your company’s repayment will be $42,280,000 if you issue the coupon bonds.

Company's repayment if zero coupon bonds are issued = no. of zero coupon bonds issued*par value of zero coupon bond = 121,216*$1,000 = $121,216,000

In 20 years, your company’s repayment will be $121,216,000 if you issue the zero coupon bonds.