Question

2. Company X has to decide the sales force to maximize its profit contribution. From the past experience, the company considers only the following range: 21 to 26 persons. As more salespersons are hired, the sales will continue to increase but at a decreasing rate. The table below is the best total sales estimates corresponding to the number of persons hired. Furthermore, the following information is provided: Contribution ratio: 30% Each sales person is paid a basic salary of $25,000 per year + 5% commission on sales Travel expense $800 per month Size of ' 21 22 23 24 25 26 salesforce Total $6,300,000 $6,820,000 $7,360,000 $7,560,000 $7,685,000 $7,787,000 yearly Gross sales Given the information above, how many sales persons should be hired to maximize the profit contribution? (10 points, show all your works)

Answer 1

Let us first understand some common points.

• Profit Contribution = Sales - Variable Costs
• Variable costs can be of 2 types. Here, in this question there one variable cost which varies depending on the number of Sales Force; and one Variable Cost which is independent of the Sales force
• Contribution Ratio= Contribution/Sales. Here in this formula Contribution includes only that Variable Cost which is dependent on the number of units sold( not dependent on the number sales person)

Please refer to the excel workings attached, where entire analysis statement is prepared, as per which we reach to answer of 24 Sales person, where our Profit Contribution is the Highest.

We know the following: 1 Profit Contribution = Sales - ( VC 1 + VC 2) * VC 1 means varaible cost which is not dependent on Sales Force * VC 2 means varaible cost which is dependent on Sales Force 2 Contribution Ratio = Contribution* Sales * In this contribution VC 1 is already deducted 3 The following formula are used below to arrive at the figures Contribution = Basic Salary = Commission = Travel Exoense = Profit Contribution = Contribution ratio(%)* Sales 25000 * number of Sales person 5% * total sales 800 per month * 12 months * number of Sales person Contribution - total of VC2 Statement showing Analysis Size of Sales Force 21 22 6300000 6820000 23 24 25 7360000 7560000 7685000 26 7787000 Yearly Sales Contribution(%) Contribution($) 30% 30% 30% 30% 30% 30% 1890000 2046000 2208000 2268000 2305500 2336100 (-) VC2 - Basic Salary - Commission - Travel Expense -525000 -315000 -201600 -550000 -341000 -211200 -575000 -368000 -220800 -600000 -378000 -230400 -625000 -384250 -240000 -650000 -389350 -249600 Profit Contribution 848400943800 1044200 1059600 1056250 1047150 Hence our answer is 24 Sales person, where our profit contribution is maximised Scanned with CamScanner