Question

Suppose your company needs to raise $50 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 7 percent coupon rate and a zero-coupon bond. Your company’s tax rate is 21 percent. Both bonds would have a par value of $1,000.

a. How many of the coupon bonds would you need to issue to raise the $50 million? How many of the zeroes would you need to issue?

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

c. Based on your answers in (a) and (b), why would you ever want to issue the zeroes? To answer, calculate the firm’s after-tax cash outflows for the first year under the two different scenarios. Assume the IRS amortization rules apply for the zero-coupon bonds.

Answer 1

Part a)

The number of coupon bonds needed to be issued to be raised $50 million can be calculated as follows:

Number of Coupon Bonds = Amount to be Raised/Price of Coupon Bond = 50,000,000/1,000 = 50,000 bonds (since coupon rate is same as interest rate, price of coupon bond is same as par value)

________

Price of Zero Coupon Bonds = Face Value/(1+Rate/2)^n = 1,000/(1+7%/2)⁶⁰​= $118.494 [zero-coupon bond is also taken as semi-annual], we only find the present value of $1,000 that will be realized at maturity.

Number of Coupon Bonds = Amount to be Raised/Price of Zero Coupon Bond = 50,000,000/118.494 = 421960 bonds

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Part b)

The company's repayment amount can be calculate with the use of following formula:

Repayment Amount = Number of Bonds*(Par Value + Last Coupon Payment)

___________

Repayment Amount (Coupon Bonds) = 50,000*(1,000 + 1,000*7%*1/2) = $51,750,000

Repayment Amount (Zero Coupon Bonds) = 421960*(1,000 + 0) = $421960396.739

___________

Part c)

The after tax cash flow for coupon bonds can be calculated as follows:

After Tax Cash Flow = Number of Bonds*Coupon Payment*(1-Tax Rate)

_____________

After Tax Cash Flow = 50,000*70*(1-21%) = $2,765,000

_____________

The after tax cash flow for zero coupon bonds can be calculated as follows:

In case of zero coupon bond, the first year interest payment is equal to the difference between the today's price and price at the end of the year. The price of zero coupon bond in one year can be calculated with the use of following formula:

Price in 1 Years = Face Value/(1+Rate/2)ⁿ = 1,000/(1+7%/2)⁵⁸ = $126.934

Year 1 Interest = 126.934 - 118.494 = $8.439(the amount of interest deduction allowed in Year 1)

The amount of after-tax cash flow on zero-coupon bonds can be calculated as follows:

After Tax Cash Flow = Zero Coupon Bonds Sold*Interest Deduction*Tax Rate = 421960*8.439*21% = $747, 793.29