Question

You will be paying $10,800 a year in tuition expenses at the end of the next two years. Bonds currently yield 9%.

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	$
Duration		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		years
Future redemption value	$

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

c-1. Now suppose that rates immediately increase to 10%. 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 8%? (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-1. PV of Obligation = Yearly payment * PVAF (0.09,2)

PV of Obligation = 10800 * 1.7591

PV of Obligation = $18998.40

a-2.Duration of Obligation

b-1. A ZCB with Duration of 1.4785 Years will immunize the obligation as the duration of a ZCB will be equal to its term.

b-2. Future Redemption Value = PV of Cash Flow * (1 + r)n

Future Redemption Value = 18998.40 * (1 + 0.09)1.4785

Future Redemption Value = 18998.40 * 1.13588

Future Redemption Value = $21580.03

c-1. ZCB after increase in interest rate to 10% = Face Value / (1 + r)^1.4785

ZCB after increase in interest rate to 10% = 21580.03 / (1 + 0.10)^1.4785

ZCB after increase in interest rate to 10% = $18743.60

PV of Obligation = 10800 * 1.74 = $18743.80

Net Position Increases by $0.20

ZCB after increase in interest rate to 8% = Face Value / (1 + r)^1.4785

ZCB after increase in interest rate to 8% = 21580.03 / (1 + 0.08)^1.4785

ZCB after increase in interest rate to 8% = $19259.06

PV of Obligation = 10800 * 1.78 = $19259.26

Net Position decreases by $0.20