Question

Check my work You will be paying $8,000 a year in tuition cxpenses 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 I years eBook Print Rotarances 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.) Duration Face value 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? (Do not round intermediate calculations. Input the amount as a positive value. Round your answer to 2 decimal places.) Net position in value by

Answer 1

Answer a.

Present Value and Duration are calculated as follows:

Excel Working of the above table is as below:

A F Time till Payment B C Cash Present Weight Weight * Cash Flows Value of Cash Time Flow Present factor@8% Flows Period Value 8000 0.92592593 7407.407 0.519231 0.519231 8000 0.85733882 6858.711 0.480769 0.961538 Total 14266.12 Duration 1.480769 11 21

Time till Payment	Cash Flow	Present Value factor@8%	Cash Flows Present Value	Weight of Cash Flows	Weight * Time Period
1	8000	=1/(1.08)^A2	B2*C2	=D2/D4	E2*A2
2	8000	=1/(1.08)^A3	B3*C3	=D3/D4	E3*A3
		Total	D2+D3	Duration	F2+F3

Therefore,

Present Value	14266.118
Duration	1.4808	years

Answer b.

Immunization means matching assets duration with liabilities duration. Therefore, for immunizing the obligation, the zero coupon bond duration should be equal to tuition expense duration.

Hence, the zero coupon bond maturing in 1.4808 years will immunize the obligation.

Calculating Zero Coupon Bond Face Value:

Face value = Present vaue*(1+rate of interest)^Years to maturity

=$14266.118*(1+8%)^1.4808

=$1589242

Therefore,

Duration	1.4808	years
Face Value	$1589242

Answer c

Computing Present Value of Zero coupon Bond:

Present Value of Bond= Face value/ (1+rate)^duration

= $1589242/(1+0.10)^1.4808

=$1380053

Computing Present Value of Tuition Expense:

Present Value=($8000/(1+10%)^1)+($8000/ (1+10%)^2)

=7272.727+6611.57

=$13884.3

Hence, Change in Net Position =($13884.3 - $ 1380053)

= -$1366169

Therefore,

Net Position

decreased/fell

in value by

1380053