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This answer results from assuming that more salespeople will be required to sell more product. I.e., it is assumed that since 17 salespeople were required in August to sell 20,000 units, then 20.4 salespeople will be required in September to sell 24,000 units (17 ÷ 20,000 × 24,000). At a step cost of $5,000 per salesperson ($85,000 August expense divided by 17 salespeople), this would mean the step costs for September would be $5,000 × 20.4 salespeople, or $102,000. However, the problem tells us that two salespeople will be leaving at the end of August and will not be replaced, so the number of salespeople in September will be only 15 at $5,000 each, for a total cost of $75,000. Furthermore, the nature of step costs is that they stay at one level for a while and then make a large increase to the next level. In this case, each time a salesperson is added, the total cost increases by $5,000; and each time a salesperson leaves, the total cost decreases by $5,000. The company does not hire part-time salespeople, so it could not possibly have 20.4 salespeople.
First, we need to find the August selling price per unit, so we can calculate what the price will be after the price cut. To find the August selling price per unit, we begin by calculating the total sales revenue for the month of August. The variable costs are the sales commissions, which are 6.2% of sales revenue. Therefore, sales revenue for August was $372,000 ÷ .062, or $6,000,000. Since that revenue was for 20,000 units, the price per unit in August was $6,000,000 ÷ 20,000, or $300 per unit. The price will be cut by 10%, to $270 per unit ($300 × .90). Number of units sold will increase to 24,000. Therefore, sales revenue for September will be $270 × 24,000, or $6,480,000. The variable cost is sales commissions at 6.2%, so the variable cost will be $6,480,000 × .062, or $401,760. Step costs are based on the number of salespeople. In August, when there were 17 salespeople, the total step costs were $85,000. In September, there will be only 15 salespeople. So step costs will be $85,000 ÷ 17 × 15, or $75,000. Fixed costs will not change, because the fixed costs will stay the same until volume exceeds 30,000, and volume will not exceed 30,000 in September. Therefore, fixed costs are $176,000. The sum of all of these costs is $401,760 + $75,000 + $176,000 = $652,760.
This is the total per unit cost at a sales level of 20,000 multiplied by 24,000 units. This fails to take into consideration the facts that the step costs are based on the number of salespeople, not the number of units sold, and that fixed costs in total will not change because the anticipated sales volume is within the relevant range.
This answer results from two incorrect calculations: (1) the assumption is made that more salespeople will be required to sell more product. I.e., it is assumed that since 17 salespeople were required in August to sell 20,000 units, then 20.4 salespeople will be required in September to sell 24,000 units (17 ÷ 20,000 × 24,000). At a step cost of $5,000 per salesperson ($85,000 August expense divided by 17 salespeople), this would mean the step costs for September would be $5,000 × 20.4 salespeople, or $102,000. And (2) the fixed costs are assumed to increase with the increased production, to $8.80 × 24,000, or to $211,200. However, the problem tells us that two salespeople will be leaving at the end of August and will not be replaced, so the number of salespeople in September will be only 15 at $5,000 each, for a total cost of $75,000. Furthermore, the fixed cost does not change with the increased sales, because the sales volume is still within the relevant range.