Question

part a, number of zero coupon bonds

Suppose your company needs to raise $41.7 million and you want to issue 25-year bonds for this purpose. Assume the required return on your bond issue will be 6.7 percent, and you're evaluating two issue alternatives: a 6.7 percent semiannual coupon bond and a zero coupon bond. Your company's tax rate is 22 percent. a. How many of the coupon bonds would you need to issue to raise the $41.7 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 25 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.) Number of coupon bonds Number of zero coupon bonds b. Coupon bond repayment Zero coupon bond repayment C. Coupon bond cash flow Zero coupon bond cash flow

Answer 1

R = 6.7%

C = 6.7%/2 = 3.35%

Price of Zero Coupon bond (per $1) = 1/(1+r)^25 = 0.1976

Price of coupon bond (per $1) = C/(1+R/2)+C/(1+R/2)²+C/(1+R/2)³+...................................................+C/(1+R/2)⁵⁰ + 1/(1+r/2)⁵⁰ = 1

If we assume maturity amount of $1Mn for both bonds

No. of Coupon bonds to be issued = 41.7 /1 = 42 (rounded off)

No. of zero coupon bonds = 41.7/ 0.1976 = 210.98

Repayment

If the Company issues zero coupon bonds then the Company would have to pay 210,982,552 (41.7/0.1976)*1000000 at the end of 25 years

If the Company issues coupon bonds, then the company would pay $1,396,950 (3.35%*1000000*41.7) semi annually as coupon for 25 years and the Company would have to pay another $41,700,000 (41.7Mn/1) at end of 25th year

Cash flow

In case of zero coupon bond the Company's cash flow in 1st year would look like

Money raised from bonds: $41,700,000

In case of coupon bond the Company's cash flow in 1st year would look like

Money raised from bonds: $41,700,000

Interest paid quarterly: - $1,396,950 * 2= -2,793,900