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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%?

Answer
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