Question

You will be paying $10,000 a year in tuition expenses at the end of the next two years. Bonds currently yield 8%.

An a. What is the present value and duration of your obligation?

b. What maturity zero-coupon bond would immunize your obligation?

c. Suppose you buy a zero-coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to 9%. 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 7%?

Short answer

Answer

a. Obligation = $17832.65 and Duration = 1.4808 years

b.$19.985.26

c. $17590.92 and $18,079.99

Step-by-step solution

Step by Step Solution Step 1: Calculation of present value and duration ‘a’

Time (t)	Payment in (CF)	Payment discounted @8% = PV(CF)@8%	Weight (Wt)	D=t x wt
1	10,000	9259.26	0.5192	0.51920
2	10,000	8573.39	0.4808	0.96160
		17832.6500	1.0000	1.4808

Obligation = $17832.65 and

Duration = 1.4808 years

Calculation of maturity of zero-coupon bond ‘b’

The present value of zero coupon bond = $17832.65

Its face value @8% = F/ (1 + r)^t

= $17832.65 x (1.08)^1.4808

F = $19.985.26

Calculation of net position after an increase of rates to 9% and 7% ‘c’

In case of rate increase to 9%, the price of zero coupon value would be:

= . F/ (1 + r)^t

= $19.985.26 / (1.09)^1.4808

= $17590.92

In case of rate increase to 9%, the price of zero coupon value would be:

= . F/ (1 + r)^t

= $19.985.26 / (1.07)^1.4808

= $18,079.99