Question

As of 12/31/03, an insurance company has a known obligation to pay 3,300,000 on 12/31/2007. To fund this liability, the company immediately purchases 4-year 7% annual coupon bonds totaling 2,517,554 of par value. The maturity value of the bond equals the par value. The company anticipates reinvestment interest rates to remain constant at 7% through 12/31/07. Under the following reinvestment interest rate movement scenarios effective 1/1/2004, what best describes the insurance company's profit or (loss) as of 12/31/2007 after the liability is paid? The answers are in the form Interest Rates Drop by 1/2 %, Interest Rates Increase by 1/2 %. 5,822 o O Breakeven (5,761) Breakeven (5,775) (5,791) (5,790) 5,812 o 5,796 5,802

Answer 1

The insurance company has an obligation to pay 3,300,000 in 4 years. For this purpose, it issues 4-year coupon bonds carrying coupon rate of 7%. Initially the reinvestment rate is 7%. Insurance company profit or loss needs to be calculated if the reinvestment rate drops by 12% and if it increases by 1%. Firstly, calculate the annual coupon payment that will be received on the bond as follows: Coupon payment=Par valuex Coupon rate =2,517,554x7% =176,228.78 Thus, the annual coupon payment on the bond is 176,228.78. Now, if the reinvestment rate decreases by 12%, the revised rate will be 0.065 (7% -12%). Calculate the future value of annual coupon payments on the revised rate of 0.065 and initial reinvestment rate of 7% using the following inputs on the spreadsheet: B. 176228.78 0.07 0.065 1 DECREASE IN INTEREST RATE 2 Annual coupon payments 3 Initial reinvestment rate 4 Revised reinvestment rate 5 Number of years 6 Calculate the future value as follows: 7 Future value with initial rate 8 Future value with revised rate 9 Now, calculate the difference in future value 10 Difference in future value =FV(B3,B5,-B2) =FV(B4,B5,-B2,0,0) =B8-B7

The results obtained are as follows: 176228.78 0.07 0.065 1 DECREASE IN INTEREST RATE 2 Annual coupon payments 3 Initial reinvestment rate 4 Revised reinvestment rate 5 Number of years 6 Calculate the future value as follows: 7 Future value with initial rate 8 Future value with revised rate 9 Now, calculate the difference in future value 10 Difference in future value $782,445.74 776671.007 -5774.731 Thus, when the interest rate drops by 12% the insurance company will lose 5,775. Now, if the reinvestment rate increases by 12%, the revised rate will be 0.075 (7% + 1/2%). Calculate the future value of annual coupon payments on the revised rate of 0.075 using the following inputs on the spreadsheet:

176228.78 0.07 0.075 1 INCREASE IN INTEREST RATE 2 Annual coupon payments 3 Initial reinvestment rate 4. Revised reinvestment rate 5 Number of years 6 Calculate the future value as follows: 7 Future value with initial rate 8 Future value with revised rate 9 Now, calculate the difference in future value 10 Difference in future value =FV(B3,B5,-B2) =FV(B4,B5,-B2,0,0) =B8-B7 The results obtained are as follows: B 176228.78 0.07 0.075 А 1 INCREASE IN INTEREST RATE 2 Annual coupon payments 3 Initial reinvestment rate 4 Revised reinvestment rate 5 Number of years 6 Calculate the future value as follows: 7 Future value with initial rate 8 Future value with revised rate 9 Now, calculate the difference in future value 10 Difference in future value 782445.7382 788257.565 5811.827 Thus, when the interest rate increases by 12% the insurance company will gain 5,812. Hence, from the given options the correct answer is option 3rd.