Question

You will be paying $10,500 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	$
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 9%. 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. Round your answer to 2 decimal places.)

Net position changes by

$

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

Net position changes by

$

Answer 1

a). Present value = $18,724.28

Duration = 1.4808 years

Formula		CF/(1+8%)^n	PV/Total PV	n*W
Year (n)	Cash flow (CF)	Present Value (PV) of CF	Weight (W)	Duration calculation
1	10,500	9,722.22	0.52	0.5192
2	10,500	9,002.06	0.48	0.9615
Total		18,724.28	1.00	1.4808

b). A zero coupon bond would need to have the same duration as the liability to immunize it. Present value of the bond has to be the present value of the obligation which is 18,724.28

Future redemption value (or Face value) = Present value *(1+8%)^duration

= 18,724.28*(1+8%)^1.4808 = $20,984.47

Duration = 1.4808 years

c-1). If rate increases to 9% then present value of the zero coupon bond becomes Face value/(1+9%)^duration

= 20,984.47/(1+9%)^1.4808 = 18,470.47

Present value of the tuition obligations becomes $18,470.67

Formula		CF/(1+9%)^n	PV/Total PV	n*W
Year (n)	Cash flow (CF)	Present Value (PV) of CF	Weight (W)	Duration calculation
1	10,500	9,633.03	0.51	0.5145
2	10,500	8,837.64	0.47	0.9440
Total		18,470.67	0.99	1.4584

Net position = 18,470.47 - 18,470.67 = - 0.20

Net position changes by -0.20

c-2). If rate decreases to 7% then present value of the zero coupon bond becomes Face value/(1+9%)^duration

= 20,984.47/(1+7%)^1.4808 = 18,983.99

Present value of the tuition obligations becomes $18,984.19

Formula		CF/(1+7%)^n	PV/Total PV	n*W
Year (n)	Cash flow (CF)	Present Value (PV) of CF	Weight (W)	Duration calculation
1	10,500	9,813.08	0.52	0.5241
2	10,500	9,171.11	0.49	0.9796
Total		18,984.19	1.01	1.5037

Net position = 18,983.99 - 18,984.19 = - 0.21

Net position changes by -0.21