Question
Question 3 You will be paying $10,000 a year in tuition expenses at the end of the next two years. Bonds currently yield 4%. In
Question 3 You will be paying $10,000 a year in tuition expenses at the end of the next two years. Bonds currently yield 4%. In order to compute the present value and the duration of the obligation, we conduct the following calculations:
| Period | Time until payment | Payment | Payment discounted at 4% | weight | Time x weight |
|
| (t) | (CFt) | PMT/(1 + y/m)t | (wt = discounted pmt/P) | (t)(wt) |
| 1 | 1.0 | $10,000 | 9615.3846 | 0.5098 | 0.5098 |
| 2 | 2.0 | $10,000 | 9245.5621 | 0.4902 | 0.9804 |
|
| Column Sums |
| $18,860.95 | 1 | 1.4902 |
| (1) What is the present value and duration of your obligation?
(2) What maturity zero-coupon bond would immunize your obligation?
(3) Suppose you buy a zero-coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to 5%. What happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation? What if rates fall to 3%? |
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