You will be paying $12,400 a year in tuition expenses at the end of the next two
ID: 2745014 • Letter: Y
Question
You will be paying $12,400 a year in tuition expenses at the end of the next two years. Bonds currently yield 8%.
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.)
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.)
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.)
What if rates fall to 7%? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
You will be paying $12,400 a year in tuition expenses at the end of the next two years. Bonds currently yield 8%.
Explanation / Answer
1) Calculation of Present value and Duration of Tuition fee Obligation :
Present value = (12400 * PVAF@8%,1Year) + (12400*PVAF@8%,2ndyear)
= 12400 * 0.9260 + 12400 * 0.85734
= 11482.4 + 10631
= $22113
Duration of obligation = 22113 / 12400
= 1.783 years
2) Calculation of Duration and Future redemption value of Zero coupon bonds :
Since Zero coupon bond will be issued at discount and will be redeemable at face value meanwhile the issuer dont pay any coupon payment.
Duration will be 2 years and Future redemption will would be $24800 ( 12400 + 12400)
3) Calculation of Net change if interest rate rises to 9% :
If the interest rate changes to 9% then present value of obligation would be
= (12400 * PVAF@9%,1st year) + (12400 * PVAF@9%,2nd year)
= 12400 * 0.91743 + 12400 * 0.84168
= 11376.132 + 10436.832
= $21813
Change in Net position = 22113 - 21813
= $300 ( Positive change)
4)Calculation of Net change if interest rate falls to 7% :
If the interest rate changes to 7% then present value of obligation would be
= (12400 * PVAF@7%,1st year) + (12400 * PVAF@7%,2nd year)
= 12400 * 0.93458 + 12400 * 0.87344
= 11588.792 + 10830.656
= $22420
Change in Net position = 22113 - 22420
= $307 (Negative change)
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