Question

Suppose your company needs to raise $18 million and you want to issue 27-year bonds for this purpose. Assume the required return on your bond issue will be 5 percent, and you're evaluating two issue alternatives: a 5 percent semiannual coupon bond and a zero coupon bond. Your company's tax rate is 31 percent.

a. You will need to issue ............. of the coupon bonds to raise the $18 million. You will need to issue ................ of the zeroes to raise the $18 million.

(Round your answers to the nearest whole number. (e.g., 32))

b. In 27 years, your company's repayment will be $ .............. if you issue the coupon bonds. If you issue the zeroes, your company's repayment will be $ ..................

(Do not include the dollar sign ($). Do not round your intermediate calculations. Round your answers to the nearest whole number. (e.g., 32))

c. Your aftertax cash outflow for the first year will be $ ................. if you issue the coupon bonds, and a cash inflow of $ ....................if you issue the zeroes.

(Do not include the dollar signs ($). Do not round your intermediate calculations. Round your answers to the nearest whole number. (e.g., 32))

Pls try to answer with Excel.

Answer 1

a]

Let us assume the face value of each bond is $1000.

For the coupon bond, the issue price is equal to face value since the required return equals the coupon rate.

Number of coupon bonds to issue = amount to raise / issue price per bond

Number of coupon bonds to issue = $18 million / $1000 = 18,000 bonds

Issue price of each zero bond = present value of face value, discounted at required rate of return for 27 years

Issue price of each zero bond = $1000 / (1 + 5%)²⁷ = $267.85

Number of zero bonds to issue = amount to raise / issue price per bond

Number of zero bonds to issue = $18 million / $267.85 = 67,202 bonds

b]

Repayment of coupon bonds = number of bonds issued * face value per bond

Repayment of coupon bonds = 18,000 * $1000 = $18 million

Repayment of zero bonds = number of bonds issued * face value per bond

Repayment of zero bonds = 67,202 * $1000 = $67,202,000

c]

Coupon bonds

After-tax cash outflow = face value per bond * coupon rate * number of bonds * (1 - tax rate)

(Since interest is tax deductible, we multiply with (1 - tax rate))

After-tax cash outflow = $1000 * 5% * 18,000 * (1 - 31%) = $621,000

Zero bonds

Cash inflow = annual amortization of discount * tax rate (the amortization is tax deductible and hence provides a tax shield)

annual amortization of discount = total discount / number of years to maturity

total discount = number of bonds issued * (face value - issue price)

total discount = 67,202 * ($1000 - $267.85) = $49,201,944.30

annual amortization of discount =  $49,201,944.30 / 27 = $1,822,294.23

Cash inflow = $1,822,294.23 * 31% = $564,911.21