Question

 

A company financed the sale of equipment and recorded a note receivable for the sale. The accountant inappropriately recorded the sale at the coupon rate instead of market rate and fair value.

Cash received	$80,000
Notes receivable	339,000
Sales price	$419,000
Tax rate	30%
Estimated tax payment	$23,000

Note information:

Term of the note	4 years
Coupon rate	1.5%
Market rate	7.7%

The note is due in equal annual payments of principle and interest.

Incorrect income statement, for the year ended December 31

Sales	$739,000
Expenses	591,000
Interest revenue	5,085
Pretax income	153,085
Tax expense	45,926
Net income	107,159

What is the correct amount of sales for 20X1?

Note: You need to back out the incorrect sales amount used (the N/R at face value) and add in the correct sales amount. The correct sales amount is based on fair value of the note. See problem C7-170 as an example.

Answer 1

Since the Note will be repaid in 4 equated installments of principal and interest, first we need to find that installment amount as given by EMI = P × r × (1 + r)ⁿ/((1 + r)ⁿ - 1) = 339,000 x 1.5% x (1+1.5%)⁴ / ((1+1.5%)⁴ - 1) = $87,951.78 (Approx.)

Now we calculate the present value of these 4 equal installments as on the date of note using the market rate for discounting. Thus present value of Note = $87,951.78 * Cummulative PV Factor (4 Years, 7.7%) = $87,951.78 * 3.334365 = $293,263.35 (Approx.)

Note:- The Cummulative Present value factor has been calculated by using the following formula.

Thus the correct value of sale = Cash Received + Present Value of Note = $80,000 + $293,263 = $373,263

Correct Sales amount for 20X1 = $739,000 - $419,000 + $373,263 = $‭693,263‬ (Approx.)