Pleasant View Nursing Home estimates that its building will last another ten years and then it will need to be replaced. The home estimates that the capital cost of a new building in ten years will be $10 million. The home plans to set aside a portion of an endowment fund in government bonds to ensure it has sufficient funds to pay for replacement of the building. If we assume that the yield curve is horizontal, the current interest rate on all Treasury securities is 9 percent, and the type of security used for the building fund is Treasury bonds, then the present value of $10 million discounted back ten years at 9 percent is $4,224,108. Suppose interest rates change from the current 9 percent rate immediately after the nursing home has bought the Treasury bonds. What would be the value of the bonds at the end of ten years under each of the following situations? (For simplicity, assume annual coupons).
a. The home buys $4,224,108 of 9 percent, ten-year maturity bonds; rates fall to 7 percent immediately after the purchase and remain at that level; rates rise to 12 percent."
b. The home buys $4,224,108 of 9 percent, 40-year maturity bonds; rates fall to 7 percent immediately after the purchase and remain at that level; rates rise to 12 percent.