Question

Suppose your company needs to raise $41 million and you want to issue 20-year bonds for this purpose. Assume the required return on your bond issue will be 6.1 percent, and you’re evaluating two issue alternatives: a 6.1 percent semiannual coupon bond and a zero coupon bond. Your company’s tax rate is 25 percent. a. How many of the coupon bonds would you need to issue to raise the $41 million? How many of the zeroes would you need to issue? (Do not round intermediate calculations. Round your coupon bond answer to the nearest whole number, e.g., 32 and your zero coupon bond answer to 2 decimals, e.g., 32.16.) b. In 20 years, what will your company’s repayment be if you issue the coupon bonds? What if you issue the zeroes? (Do not round intermediate calculations and enter your answers in dollars, not millions, rounded to the nearest whole number, e.g., 1,234,567.) c. Assume that the IRS amortization rules apply for the zero coupon bonds. Calculate the firm’s aftertax cash outflows for the first year under the two different scenarios. (Input a cash outflow as a negative value and a cash inflow as a positive value. Do not round intermediate calculations and enter your answers in dollars, not millions, rounded to 2 decimal places, e.g., 1,234,567.89.)

Answer 1

Workings:

Note:

a. Number of bonds to be issued to raise $41 Million

Required rate of the coupon bond equals the coupon percent. Hence the value will be sold at par now ($1,000).

Zero coupon bonds does not pay periodic coupons but only pays par value at the end of maturity. To compensate not making periodic coupons, these are issued at discount ($305.98).

b. Repayment in twenty years

In twenty years, for coupon bonds, the firm will make 40 coupon repayments (20 years * 2 semi-annuals in a year) and also par value repayment at the end of 20th year or 40th period. Thus, total paid is $91,020,000

In twenty years, for zero coupon bonds, the firm will make only the par value repayment at the end of 20th year. Thus, total paid is $133,995,908.

c. After tax cash-flows in year 1

In Year 1, the after tax cash-flow of coupon bonds will be the 2 semi-annual coupons paid. Since these are tax deductible, net cash outflow is coupons paid * (1-tax rate) which is $1,875,750

Zero coupon bonds does not pay periodic coupons. However, IRS allows the same to be amortised basis the difference of value of the bond in the beginning of the year and of the end of the year. Value on beginning is $305.98. Value of the bond end of the year 1 is $324.64. Thus the difference of $18.66 per bond ($324.64-$305.98) is tax deductible. Since there is no actual cash-outflow involved here as no coupon payment is made, only the tax benefit is taken as cash-outflow for $625,250 (number of coupons * $18.66 * tax rate)