You will be paying $10,300 a year in tuition expenses at the end of the next two

ID: 2623493 • Letter: Y

Question

You will be paying $10,300 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 $10,300 a year in tuition expenses at the end of the next two years. Bonds currently yield 8%.

Explanation / Answer

Discounting rate Year 8 Cash flow Dsic. Cash flow 0 1.00 0 0.00 1 0.93 0 0.00 2 0.86 10300 8830.59 Duration = 2 yrs The duration of a zero-coupon bond that would immunize the obligation and its future redemption value is the life of the bond.the reason being no interest is expected.Hence whatever is expected is only at the end of life of bond. Future redemption value will be as per the company policy i.e it may at par or premium or discount.However normally ZCB are issued at discount hence the redemption is done at par i.e at face value. Discounting rate Year 9 Cash flow Dsic. Cash flow 0 1.00 0 0.00 1 0.92 0 0.00 2 0.84 10300 8669.30 Decrease in value of bond = 8830.59-8669.30 = 161.29 Discounting rate Year 7 Cash flow Dsic. Cash flow 0 1.00 0 0.00 1 0.93 0 0.00 2 0.87 10300 8996.42 Increase in value of bond = 8830.59-8996.42 = 165.83

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You will be paying $10,000 a year in tuition expenses at the end of the next two

You will be paying $10,300 a year in tuition expenses at the end of the next two

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You will be paying $10,300 a year in tuition expenses at the end of the next two

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