Question

1.) Suppose you will go to graduate school for 2 years beginning in year 4. Tuition is $28,359 per year, due at the end of each school year. What is the Macaulay duration (in years) of your grad school tuitions? Assume a flat yield curve of 0.06. Assume annual compounding. In the above description, if you see a flat yield curve of 0.08 for example, then it means that the yield at all maturities is 8%.

2.) Suppose in the question above, the tuition obligations have a Macaulay duration of 5.06 in years, and that you wish to immunize against the tuition payments by buying a single issue of a zero coupon bond. What maturity zero coupon bond should you buy?

Assume annual compounding. Round your answer to 2 decimal places.

3.) Suppose in question 1, the tuition obligations have a Macaulay duration of 5.96 in years and a present value of 57,321. In order to immunize against the tuition payments by investing in some combination of two bonds with duration 2.83 and 8.61, what is the dollar amount that you should invest in the bond with duration 8.61?

Assume annual compounding. Round your answer to 2 decimal places.

Answer 1

Answer-1

Macaulay duration=

PV of CF is the present value of the cash flow.

	A	B		A*B
year end(t)	Cash Flow	PVF@Yield 6%		Present value of the cash flow(PVCF)	PVCF*t
0	0	1	=1/(1.06)^0	0	0
1	0	0.9433962264	=1/(1.06)^1	0	0
2	0	0.88999644	=1/(1.06)^2	0	0
3	0	0.839619283	=1/(1.06)^3	0	0
4	28,359	0.7920936632	=1/(1.06)^4	22462.9842	89851.93678
5	28,359	0.7472581729	=1/(1.06)^5	21191.49452	105957.4726
			Total	43654.47872	195809.4094

Macaulay duration= 195809.4094/43654.47872=4.485 years

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Answer-2

To immunize the obligation of the Tution , theMacaulay Duration of the Obligation should be equal with the weighted Macaulay duration of the assets used to immunize it.

Here the zero coupon bond is used to immunize the Obligation.

Macaulay duration of the Zerocoupon bond is Its maturity period only.

As the Macaulay duration of obligation is 5.06 years , henceMacaulay duration of the Zerocoupon bond should be 5.06 years to immunize it.

Macaulay duration of Zerocoupon bond = maturity of zero coupon bond

hence you should buy Zero coupon bond of maturity 5.06 years.

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Answer-3

To immunize the obligation of the Tution , theMacaulay Duration of the Obligation should be equal with the weighted Macaulay duration of the assets used to immunize it.

let the total weight be 1

let the weight of the bond with duration 8.61year is W and hence the weight of bond with 2.83 Duration =1-W

Hence

5.96=8.61*W +(1-W)*2.83

=> W or weight of Bond with 8.61 duration = 0.542

dollar amount that you should invest in the bond with duration 8.61 = Present value of obligation * Weight

=>57,321 * 0.542 = $31040.61

Note-Intermediate calculations are not rounded off. But the final answer has been round off to 2 decimal point.