Question

On December 31, 2020, Buffalo Company signed a $1,278,400 note to Carla Bank. The market interest rate at that time was 10%. The stated interest rate on the note was 8%, payable annually. The note matures in 5 years. Unfortunately, because of lower sales, Buffalo’s financial situation worsened. On December 31, 2022, Carla Bank determined that it was probable that the company would pay back only $767,040 of the principal at maturity. However, it was considered likely that interest would continue to be paid, based on the $1,278,400 loan.

Determine the amount of cash Buffalo received from the loan on December 31, 2020. (Round present value factors to 5 decimal places, e.g. 0.52513 and final answer to 0 decimal places, e.g. 5,275.)

Answer 1

The amount of cash Buffalo Company received from the loan on December 31, 2020, is $1,153,607.62.

Step-by-step explanation:

To determine the amount of cash Buffalo Company received from the loan on December 31, 2020, we need to calculate the present value of the future cash flows. The note pays interest of $1,278,400 x 8% = $102,272 per year for 5 years, and the principal of $1,278,400 at maturity. The market interest rate at the time was 10%, so we need to discount the future cash flows using this rate.

Using the present value formula, the cash flow for the first 4 years would be:

$102,272 / (1 + 10%)^1 + $102,272 / (1 + 10%)^2 + $102,272 / (1 + 10%)^3 + $102,272 / (1 + 10%)^4 = $98,429.43.

The cash flow at maturity would be the principal of $1,278,400 / (1 + 10%)^5 = $767,391.90.

Adding up all the discounted cash flows, the amount of cash Buffalo Company received from the loan on December 31, 2020, is $98,429.43 x 4 + $767,391.90 = $1,153,607.62.