Question

Suppose your company needs to raise $52 million and you want to issue 30-year bonds for this purpose. Assume the required return on your bond issue will be 4.4 percent, and you’re evaluating two issue alternatives: A semiannual coupon bond with a coupon rate of 4.4 percent and a zero coupon bond. Your company’s tax rate is 23 percent. Both bonds will have a par value of $1,000. a-1. How many of the coupon bonds would you need to issue to raise the $52 million? a-2. How many of the zeroes would you need to issue? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b-1. In 30 years, what will your company’s repayment be if you issue the coupon bonds? (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, e.g., 1,234,567.) b-2. What if you issue the zeroes? (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, e.g., 1,234,567.) c. Calculate the aftertax cash flows for the first year for each bond. (Do not round intermediate calculations and enter your answers in dollars, not millions of dollars, e.g., 1,234,567.)

Answer 1

1. The Coupon for each semi-annual payment will be 2% on the par value.

To decide how many coupon bonds to be raised we need to find the market value of a single bond of par value $1000

The Market value of a bond can be calculated as the present value of its cash flows

The coupon bond has tow cash flow components - semiannual coupons and the maturity (par value).

MarketValue = n/(1+y/2)T* +P/(1+y/2) 60 n=1

C(n) = Value of nth coupon = (Annual coupon/2)* Par value =  (4.4%/2)*1000 = $22

T(n) = Time of nth coupon = n

y = yield to maturity (annualized)= required return on bond = 4.4%

P = Par Value = $1000

Substituting we get Market Value = 1000 ( Since coupon rate and required return are same we get Market Value = Par Value).

We will have to issue = Value of bonds / Market value of single bond = $52000000/$1000 = 52000

Company will have to issue 52000 worth of coupon bonds to raise $52 mn.

2. If the company was issuing zero coupon bonds

Then C(N) = 0 as coupon is paid only at the end

Hence we get Market Value of a bond = 270.9856

Substituting we get Market Value = 270.9856 ( Since coupon rate and required return are same we get Market Value = Par Value).

We will have to issue = Value of bonds / Market value of single bond = $52000000/$270.9856= 191892.1

Company will have to issue 191892.1 worth of zero coupon bonds to raise $52 mn.

3. If company issued the coupon bonds then company would have done 60 semi-annual coupons and par value of repayment at end of 30 years

Hence Repayment = Number of Bonds (60*Coupon + Par Value) = 52000* (60*22+1000) = 120640000

4. Companies pay tax only on profits calculated after interest payments are there. So company tax rate will in no way affect after tax cash flows.

Net cash flow = Cash Inflow - Cash Outflow

= Money raised - Coupon or principal payments made during 1st year

After tax cash flow for zero coupon bond = 52000000 (Only cash inflow from raising money no outgo as no coupons are paid in 1st year)

After tax cash flow for coupon bond = 52000000 - 5200000*4.4% (2 semi annual coupons paid in 1st year) = 49712000