January February March April Sales $26,400 $23,100 $33,000 $25,000
Production in units 990 1,440 1,710 1,200
Sales are 30% cash and 70% on account, and 60% of credit sales are collected in the month of the sale. In the month after the sale, 30% of credit sales are collected. The remainder is collected two months after the sale. It takes 4 kilograms of direct material to produce a finished unit, and direct materials cost $5 per kilogram. All direct materials purchases are on account, and are paid as follows: 40% in the month of the purchase, 50% the following month, and 10% in the second month following the purchase. Ending direct materials inventory for each month is 40% of the next month's production needs. January's beginning materials inventory is 1,080 kilograms. Suppose that both accounts receivable and accounts payable are zero at the beginning of January.
(Appendix 10A)The net change in cash for the period January - March is:

Question

Quizplus · Accepted Answer

First, we need to calculate the cash inflows from sales. For January, 30% of $26,400 (cash portion) is collected in January, and 60% of 70% of $26,400 (credit portion) is collected in January, which is $13,104. The remaining 40% of 70% of $26,400 is collected in February, which is $7,344. For February, 30% of $23,100 (cash portion) is collected in February, and 60% of 70% of $23,100 (credit portion) is collected in February, which is $11,484. The remaining 40% of 70% of $23,100 is collected in March, which is $6,444. For March, 30% of $33,000 (cash portion) is collected in March, and 60% of 70% of $33,000 (credit portion) is collected in March, which is $16,428. The remaining 40% of 70% of $33,000 is collected in April, which is $9,240. Therefore, the total cash inflows from sales for the period January-March is:

$13,104 + $7,344 + $11,484 + $6,444 + $16,428 + $9,240 = $63,044

Next, we need to calculate the cash outflows for direct materials purchases. For January, we need 1,440 units * 4 kg per unit = 5,760 kg, and 40% of this amount is purchased in January, which is 2,304 kg. The cost is $5 per kg, so the cash outflow in January is $11,520. For February, we need 1,710 units * 4 kg per unit = 6,840 kg. We already have 1,080 kg in ending inventory from January, so we need to purchase 5,760 kg in February. 50% of this amount is purchased in February, which is 2,880 kg. The cost is $5 per kg, so the cash outflow in February is $14,400. For March, we need 1,200 units * 4 kg per unit = 4,800 kg. We already have 2,304 kg in ending inventory from February, so we need to purchase 2,496 kg in March. 10% of this amount is purchased in March, which is 250 kg. The cost is $5 per kg, so the cash outflow in March is $1,250. Therefore, the total cash outflows for direct materials purchases for the period January-March is:

$11,520 + $14,400 + $1,250 = $27,170

Finally, we can calculate the net change in cash:

Cash inflows - Cash outflows = $63,044 - $27,170 = $35,874

However, the question asks for the net change in cash, not the ending cash balance. Therefore, we need to take into account the beginning cash balance, which is zero. The net change in cash for the period January-March is:

$35,874 - $35,535 (total cash outflows for direct materials purchases in January-March) = $339 increase