Question

You will be paying $10,000 a year in tuition expenses at the end of the next 2 years. Bonds currently yield 8%.
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%?
please could you please explain in details?

Answer 1

a)

PV of tuition fees=10000/(1+8%)+10000/(1+8%)^2=$17832.65

To find the duration of obligation,

First we find the PV of two annual tuition fees

PV of tuition fee to be paid at the end of year 1=10000/(1+8%)^1=$9259.26

PV of tuition fee to be paid at the end of year 2=10000/(1+8%)^2=$8573.39

Weight of payment 1 =w1=9259.26/(9259.26+8573.39)=0.519231

Weight of payment 2 =w2=8573.39/(9259.26+8573.39)=0.480769

Duration of obligation is given by

b)

Zero coupon bond with maturity 1.480769 years is needed to immunize the obligation.

Present value of zero coupon bond=PV of tuition payments=$17832.65

Maturity amount of zero coupon bond=17832.65*(1+8%)^1.480769=$19985.21

c)

If the interest rate increases to 9%

PV of tuition fees=10000/(1+9%)+10000/(1+9%)^2=$17591.11

PV of bond=19985.21/(1+9%)^1.480769=$17590.92

Change in net position=17591.11-17590.92=$0.19

If the interest rate decreases to 7%

PV of tuition fees=10000/(1+7%)+10000/(1+7%)^2=$18080.18

PV of bond=19985.21/(1+7%)^1.480769=$18079.99

Change in net position=18080.18-18079.99=$0.19

We can see that there is slight change in net position due to interest changes.