Question

Glade, Inc. is trying to decide whether to increase the commission-based pay of its salespeople. Currently, each of its five salespeople earns a 6% commission on the units they sell for $100 each, plus a fixed salary of $41,200 per person. Glade hopes that by increasing commissions to 11% and decreasing each salesperson’s salary to $21,200, sales will increase because salespeople will be more motivated. Currently, sales are 20,000 units. Glade’s other fixed costs, NOT including the salespeople’s salaries, total $580,000. Glade’s other variable costs, NOT including commissions, total $18 per unit.  

a. What is the current profit?

b. What is the current break-even point in units? (Round your answer to the nearest whole number.)

c. What would the break-even point in units be if commissions are increased and salaries decreased? (Round your answer to the nearest whole number.)

d. If sales increase by 14,000 units, what will profit be under the new plan?

e. At what sales level would Glade be indifferent between the lower-commission plan and the higher-commission plan?

Answer 1

a. Calculation of current profits

particulars	$
sales [ 20,000 units * $100 ]	$2,000,000
(-) variable cost excluding salespeople's commission [ 20,000 units * $18 ]	( $360,000 )
(-) salespeople's commission [ 6% * $2,000,000 ]	( 120,000 )
Contribution	$1,520,000
(-) Fixed costs excluding sales people's salaries	( $580,000 )
(-) salespeople's salaries [ $41,200 per person * 5 salespeople ]	( $206,000 )
PROFIT	$734,000

b. First let us calculate contribution per unit

Contribution per unit = total contribution / total units = $1,520,000 / 20,000 = $76.

Break-even point ( in units ) = Total fixed cost / contribution per unit = ( $580,000 + $206,000 ) / $76 = 10,342 units.

c. For calculating break-even point under new plan we will first require to calculate the contribution per unit and fixed cost under the new plan.

First let us calculate contribution per unit under new plan

particulars	$
selling price	100
(-) varibale cost per unit excluding salespeople's commission	(18)
(-) salespeople's commission [ 11% 0f $100 ]	(11)
contribution per unit	71

Now let us calculate fixed cost under new plan

particulars	$
Fixed cost excluding salespeople's salaries	580,000
(+) salespeople's salaries [ $21,200 per person * 5 salespeoples ]	106,000
total fixed cost	686,000

Break-even point ( in units ) under new plan = total fixed cost under new plan / contribution per unit under new plan = $ 686,000 / $71 = 9,662 units.

d. Calculation of profit under new plan if sales increased by 14,000 units

particulars	$
sales [ (20,000 + 14,000) * $100 ]	3,400,000
(-) variable cost excluding salespeople's commission [ $18 * 34,000 ]	( 612,000 )
(-) salespeople's commission [ 11% * $3,400,000 ]	( 374,000 )
Contribution	2,414,000
(-) Fixed cost excluding salespeople's salaries	( 580,000 )
(-) salespeople's salaries [ $21,200 per person * 5 salespeoples ]	( 106,000 )
Profit	1,728,000

e. Indifferent will be the point where profits from both the plans will be same

Let X be the number of units at which the Glade will be indifferent between lower-commission plan and higher commission plan.

contribution - fixed cost = profit

To find out the level of indifferent, we are required to solve the following equation :

profit of lower commission plan = profit of higher commission plan

contribution - fixed cost = contribution - fixed cost

( $76 * X ) - ( $580,000 + $206,000 ) = ( $71 * X ) - ( $580,000 + $106,000 )

$76X - $786,000 = $71X - $686,000

$76X - $71X = $786,000 - $686,000

$5X = $100,000

X = $100,000 / $5

X = 20,000 units

At sales level of 20,000 units ( $2,000,000 ) Glade will be indifferent between the lower-commission plan and the higher-commission plan