Question

On January 1, 2020, a borrower signed a long-term note, face amount, $260,000; time to maturity, three years; stated rate of interest, 8%. The market rate of interest of 10% determined the cash received by the borrower. The note will be paid in three equal annual installments of $100,888 each December 31 (which is also the end of the accounting period for the borrower).Required:1. Compute the cash received by the borrower. $ 231,593 2. Prepare a debt amortization schedule.2. Provide the required entries for the borrower for the issuance of the note on January 1, 2020, and the interest payments in 2020, 2021, and 2022.Date Cash Interest Expense Reduction in NP. Carrying valueJan. 1, 2020 231,593Dec. 31, 2020 93,127 23,159 699,680 161,625Dec. 31, 2021 93,127 16,163 76,964 84,661Dec 31, 2022 93,127 8,466 848,661 0 Total 279,381 47,788 0Date Account Name Cr. Dr.Jan. 1, 2020 Cash 231,590 0 Note Payable 8,410 8,410 Dec. 31, 2020 Interest Expense 23,159 0 Cash 69,968 0Dec. 31, 2021 Interest Expense 0 93,127 Note Payable 16,163 0 Cash 76,964 0Dec 31, 2022 Interest Expense 0 93,127 Note Payable 8,466 0

Answer 1

The present value of a $3,000 bond paying 8% interest annually is calculated using the present value formula, totaling $3,000 at an 8% discount rate. When the discount rate increases to 11%, the bond's present value diminishes, reflecting a lower worth in today's dollars compared to the face amount.

Step-by-step explanation:

Calculating the present value of a bond involves determining what the future payments are worth in today's dollars. The present value (PV) formula is often used to calculate the value when the interest rates fluctuate or when the market rate of interest is different from the bond's rate. In the example of the simple two-year bond issued for $3,000 at an 8% interest rate, the bond pays $240 interest annually. At an 8% discount rate, the present value of the bond, which includes both the interest payments and the principle, is calculated as:

• $240/(1+0.08)1 = $222.20 for the first year's interest
• $3,240/(1+0.08)2 = $2,777.80 for the second year's interest and principal payment

The total present value of the bond at an 8% discount rate is calculated by adding the present value of both payment periods together, which equals $3,000.

If the discount rate increases to 11%, reevaluating the present value requires using the new discount rate in the PV formula. The adjusted present values become:

• $240/(1+0.11)1 = $216.22 for the first year's interest
• $3,240/(1+0.11)2 = $2,630.63 for the second year's interest and principal payment

The total present value of the bond at an 11% discount rate yields a sum less than the face amount, reflecting the bond's reduced worth when the discount rate exceeds the bond's interest rate.