Question

You will be paying $12,200 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.)

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.)

c. Suppose you buy a zero-coupon bond with value and duration equal to your obligation. 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.)

d. 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.)

Answer 1

Part 1)

Present Value

The present value of the obligation is calculated as below:

Present Value of Obligation = Value of Tuition Expenses Paid at the End of Year 1/(1+Current Yield)^1 + Value of Tuition Expenses Paid at the End of Year 2/(1+Current Yield)^2  = 12,200/(1+9%)^1 + 12,200/(1+9%)^2 = $21,461.16

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Duration

The duration of the obligation is arrived as follows:

Year (1)	Payment (2)	Present Value of Payment (3)	Weight of Payment (4)	(1*4)
1	12,200	11,192.66 [12,200/(1+9%)^1]	0.5215 (11,192.66/21,461.16)	0.5215
2	12,200	10,268.50 [12,200/(1+9%)^2]	0.4785 (10,268.50/21,461.16)	0.9569
		$21,461.16	1.0000	1.4785

The duration of the obligation is 1.4785 years.

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Part 2)

The duration of a zero-coupon bond that would immunize your obligation is 1.4785 years.

____

The future redemption value is determined as follows:

Future Redemption Value = Present Value of Obligation*(1+Current Yield)^(Duration) = 21,461.16*(1+9%)^1.4785 = $24,377.38

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Part 3)

The change in net position is arrived as below:

Value of Bond = Future Redemption Value or Face Value as determined in Part 2/(1+Interest Rate)^Duration = 24,377.38/(1+10%)^1.4785 = $21,173.33

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Value of Tuition Obligation = = Value of Tuition Expenses Paid at the End of Year 1/(1+Interest Rate)^1 + Value of Tuition Expenses Paid at the End of Year 2/(1+Interest Rate)^2  = 12,200/(1+10%)^1 + 12,200/(1+10%)^2 = $21,173.55

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Change in Net Position = Value of Tuition Obligation - Value of Bond = 21,173.55 - 21,173.33 = $0.22

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Part 4)

The change in net position is arrived as below:

Value of Bond = Future Redemption Value or Face Value as determined in Part 2/(1+Interest Rate)^Duration = 24,377.38/(1+8%)^1.4785 = $21,755.60

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Value of Tuition Obligation = = Value of Tuition Expenses Paid at the End of Year 1/(1+Interest Rate)^1 + Value of Tuition Expenses Paid at the End of Year 2/(1+Interest Rate)^2  = 12,200/(1+8%)^1 + 12,200/(1+8%)^2 = $21,755.83

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Change in Net Position = Value of Tuition Obligation - Value of Bond = 21,755.83 - 21,755.60 = $0.23 (it can be $0.22 as well)

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Notes:

There can be a slight difference in final answers on account of rounding off values.