Question

Problem 9-7a (algo) prepare a bond amortization schedule and record transactions for the bond issuer (lo9-5) skip to question [the following information applies to the questions displayed below.] on january 1, 2024, universe of fun issues $840,000, 8% bonds that mature in 15 years. the market interest rate for bonds of similar risk and maturity is 9%, and the bonds issue for $771,587. interest is paid semiannually on june 30 and december 31. problem 9-7a (algo) part 1 required: 1. complete the first three rows of an amortization schedule. (do not round intermediate calculations. round your final answers to the nearest whole dollar.)

Answer 1

The value of bonds is calculated using present value (PV) formulas that consider future cash flows discounted at the current market interest rate. A two-year bond with an 8% coupon is worth $3060.24 when discounted at 8% and worth $2932.28 at an 11% discount rate. A local water company's $10,000 bond at 6% would be worth $9678.90 a year before maturity if the market rate is 9%.

Step-by-step explanation:

To calculate the value of a bond when the market interest rate is higher than the bond's coupon rate, you use the present value formula for each cash flow and then sum them up. The present value (PV) formula is PV = FV / (1 + r)n, where FV represents the future value of the cash flow, r is the market interest rate, and n is the number of periods until the cash flow is received.

Example of 2-Year Bond Valuation at a 8% Discount Rate:

The bond with a face value of $3,000 and an interest rate of 8% will pay $240 in interest each year. Using a discount rate of 8%, the present value of the first interest payment is $240 / (1 + 0.08)1 = $222.22, and the present value of the second interest payment and the principal repayment is ($240 + $3,000) / (1 + 0.08)2 = $2838.02. Adding these up gives the bond value of $222.22 + $2838.02 = $3060.24.

Example of 2-Year Bond Valuation at a 11% Discount Rate:

If the discount rate rises to 11%, the present value of the first interest payment is $240 / (1 + 0.11)1 = $216.22, and the present value of the second interest payment and the principal repayment is ($240 + $3,000) / (1 + 0.11)2 = $2716.06. Summing these up results in a bond value of $216.22 + $2716.06 = $2932.28.

Valuation of a Local Water Company Bond with Changing Interest Rates:

For the $10,000 ten-year bond at 6%, if you were to buy it a year before maturity when the market rate is 9%, you would expect to pay less than $10,000 due to the higher current interest rates. Specifically, the present value of the bond would be ($600 + $10,000) / (1 + 0.09)1 = $9678.90.