A monthly total sales level of $1,500,000 would result in total commissions paid of $90,000 if J J Motors continues paying commissions at the rate of 6% of sales (1,500,000 × .06). If J J Motors adopts the new commission formula of $2,000 per month per salesperson plus 2% of sales, the total commissions paid would be $120,000 ($2,000 × 45) + (.02 × $1,500,000). At a sales level of $1,500,000, J J Motors would prefer the existing commission formula because the commission payout would be lower.
There is more than one correct way to calculate the answer to this problem. One solution is to calculate the sales volume where J J Motors will indifferent as to which plan is selected. Remember that the total sales volume will be the sales made per salesperson multiplied by the number of sales personnel. The solution can be calculated algebraically as follows: Let X be the monthly sales per salesperson. Create two equations, each containing one of the possible commission payment methods. The two equations are: C = .06X and C = $2,000 × .06X, where X = the monthly car sales. Next, set the right sides of the two commission payment methods equal to one another, since we are looking for the total monthly sales at which the same commission amounts would be paid under both methods. Solve for X, and then multiply the value you get for X by 45 to get the total sales for all salespeople per month. .06X = $2,000 + .02X Simplify by subtracting .02X from both sides of the equation: .04X = $2,000 Solve for X by dividing both sides of the equation by .04: X = $50,000, which is the sales per salesperson at which the payment under both plans will be equal. Multiply $50,000 by 45 salespeople to get the total sales per month at which both payment plans will result in the same payments to salespeople: $50,000 × 45 = $2,250,000 To check: At a sales volume of $2,250,000, a straight commission of 6% will result in a total payment of $2,250,000 × .06, or $135,000. At a sales volume of $2,250,000, a salary of $2,000 per month paid to each salesperson plus a commission of 2% will result in a total payment of: ($2,000 × 45) + (.02 × $2,250,000) = $135,000 If you calculated the answer a different way but got the same answer, then your method is also correct.
A monthly total sales level of $3,000,000 would result in total commissions paid of $180,000 if J J Motors continues paying commissions at the rate of 6% of sales ($3,000,000 × .06). If J J Motors adopts the new commission formula of $2,000 per month per salesperson plus 2% of sales, the total commissions paid would be $150,000 ($2,000 × 45) + (.02 × $3,000,000). At a sales level of $3,000,000, J J Motors would prefer the new commission formula because the commission payout would be lower.
A monthly total sales level of $1,250,000 would result in total commissions paid of $75,000 if J J Motors continues paying commissions at the rate of 6% of sales (1,250,000 × .06). If J J Motors adopts the new commission formula of $2,000 per month per salesperson plus 2% of sales, the total commissions paid would be $115,000 ($2,000 × 45) + (.02 × $1,250,000). At the sales level of $1,250,000, J J Motors would prefer the existing commission formula because the commission payout would be lower.
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