Question

You will be paying $9,200 a year in tuition expenses at the end of the next two years. Bonds currently yield 6%.

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?

b. What maturity zero-coupon bond would immunize your obligation? (Do not round intermediate calculations. Round "Duration" to 4 decimal places and "Face value" to 2 decimal places.)

c. Suppose you buy a zero-coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to 8%. What happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation? (Do not round intermediate calculations. Input the amount as a positive value. Round your answer to 2 decimal places.)

Net value increases or decreases?

By what value?

d. What if rates fall immediately to 4%? (Do not round intermediate calculations. Input the amount as a positive value. Round your answer to 2 decimal places.)

Net value increases or decreases?

By what value?

duration? face value?

Answer 1

a.

1	2	3	4	5
Time until Payment (years) (n)	Time until Payment (FV) (years)	PV of CF (Discount rate, r = 6%)	Weight	Column (1) × Column (4)
1	9200.00	8679.25	0.51	0.51
2	9200.00	8187.97	0.49	0.97
Column Sums	16867.21	1.00	1.4854
Formula for PV = FV/(1+r)^n
Present Value is	$16,867.21
Duration	1.4854 years

b. A zero-coupon bond maturing in 1.4854 years would immunize the obligation. Since the present value of the zero-coupon bond must be $16,867.21, the face value (i.e., the future redemption value) must be: $16,867.21 × 1.06^1.4854 = $18,392.20

c. If the interest rate increases to 8%, the zero-coupon bond would decrease in value to:

$18,392.20/1.08^1.4854 = $16,405.37

The present value will decrease to: $16,405.56

The net position decreases in value by: $0.19

d. If the interest rate decreases to 4%, the zero-coupon bond would increase in value to:

$18,392.20/1.04^1.4854 =$17,351.31

The present value of the tuition obligation would increase to: $17,351.50

The net position decreases in value by: $0.19 The reason the net position changes at all is that, as the interest rate changes, so does the duration of the stream of tuition payments