Question

You will be paying $12,400 a year in tuition expenses at the end of the next two years. Bonds currently yield 8%.

a. What is the present value and duration of your obligation? (Do not round intermediate calculations. Round "Present value" to 2 decimal places and "Duration" to 4 decimal places.)

Present value $ 22113

Duration 1.4808 years

b. What is the duration of a zero-coupon bond that would immunize your obligation and its future redemption value? (Do not round intermediate calculations. Round "Duration" to 4 decimal places and "Future redemption value" to 2 decimal places.)

Duration 1.4808 years

Future redemption value $ 24,781.71

You buy a zero-coupon bond with value and duration equal to your obligation.

c-1. 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? (Enter your answer as a positive value. Do not round intermediate calculations. Round your answer to 2 decimal places.)

Net position changes by $

c-2. What if rates fall to 7%? (Enter your answer as a positive value. Do not round intermediate calculations. Round your answer to 2 decimal places.)

Net position changes by $

Answer 1

a) Present value = 12400/1.08 + 12400/1.082

=22112.48

Duration

year	Amount	Present value	Weight Of payment	Year x weight
1	12400	11481.48	0.51923	0.51923
2	12400	10631.00	0.48077	0.96154

	Total	22112.48	1.48077
		Duration	1.4808

b)

Duration of the expenses is 1.4808 years.

Investing in zero coupon bonds with a 1.4808 year maturity would immunize the

obligation Proof 22112.48 x( 1.08) 1.4808= 24781.71

c) If interest rate increase to 9 % the value bond will be

24781.71 / (1.09)1.4808 = 21812.73

Tution obligation will be 12400/(1.09) + 12400/ (1.09)2 = 21812.98

So difference is 21812.98 - 21812.73 = 0.25

d) If rate decline to 7 % value of bon

24781.71 / (1.07)1.4808 = 22419.18

Tution obligation would be

12400/ (1.07) +12400/(1.07)2 = 22419.43

difference is 22419.43-22419.18 = 0.25