Crakow Machine Company wishes to borrow $10 million for 10 years. It can issue either a noncallable bond at 11.40 percent interest or a bond callable at the end of 5 years for 12 percent. For simplicity, we assume that the bond will be called only at the end of year 5. The interest rate that is likely to prevail 5 years hence for a 5-year straight bond can be described by the following probability distribution:
Issuing and other costs involved in selling a bond issue 5 years hence will total $200,000. The call price is assumed to be par.
a. What is the total absolute amount of interest payments for the noncallable issue over the 10 years? (Do not discount.) What is the expected value of total interest payments and other costs if the company issues callable bonds? (Assume that the company calls the bonds and issues new ones only if there is a savings in interest costs after issuing expenses.) On the basis of total costs, should the company issue noncallable or callable bonds?
b. What would be the outcome if the probability distribution of interest rates 5 years hence were the following?
SOLUTION
a. Total interest payments for the noncallable bonds =
$10 million × 11.40% × 10 = $11.4 million.
Interest payments for callable bonds the first five years =
$10 million × 12% × 5 = $6 million.
Interest payments for the next five years:
| (a) | (b) | (c) | (d) | (e) | (f) |
|---|---|---|---|---|---|
| Interest Rate | 5-year Cost (millions) | Issuing Expenses (millions) | (b) + (c) (millions) | Probability | (d) x (e) (millions) |
| 9% | $4.5 | $0.2 | $4.7 | 0.1 | $0.47 |
| 10 | 5.0 | 0.2 | 5.2 | 0.2 | 1.04 |
| 11 | 5.5 | 0.2 | 5.7 | 0.4 | 2.28 |
| 12* | 6.0 | 0.0 | 6.0 | 0.2 | 1.20 |
| 13* | 6.0 | 0.0 | 6.0 | 0.1 | 0.60 |
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