Question

Problem 4-31 Changes in Cost Structure; Break-Even Analysis; Indifference (L04, LOS, LO6] Patterson Products Inc. is considering an upgrade to its manufacturing equipment. The two upgrade options under consideration are shown below. Direct material cost per unit Direct labour cost per unit Variable overhead per unit Fixed manufacturing costs Option 1 61.2 48 13.2 $ 2,070,000 Option 2 $ 40.8 $ 41 $ 33.8 $ 4,008,000 The selling price of the company's product is $204 per unit with variable selling costs of 10% of sales. Fixed selling and administrative costs are $3,370,000 per year. There would be no change to the selling price, variable selling costs, or fixed selling and administrative costs as the result of the manufacturing equipment upgrade. Required: 1. At what annual number of unit sales would Patterson Products Inc. be indifferent between the two upgrade options? Annual number of unit sales < Prev 7 of 8 Next >

Answer 1

1.let x be the indifferent point.

at this point profit of both the alternatives will be same.

contribution under both the options:

	option 1	option 2
sale price	204	204
less:
direct material	(61.20)	(40.8)
direct labor	(48)	(41)
variable overhead	(13.20)	(33.80)
variable selling cost ($204*10%)	(20.40)	(20.40)
contribution per unit	61.20	68

profit under option 1 = $61.20 *x units - (2,070,000+3,370,000 fixed costs)

=>61.20x - 5,440,000.

profit under option 2 =68x - (4,008,000 + 3,370,000)

=>68x - 7,378,000

at indifference point, both the profits are equal

=>61.20x - 5,440,000 = 68x -7,378,000

=>6.80x = 1,938,000

=>x=285,000 units.

at 285,000 units patterson products inc can be indifferent between the two upgrade options.

required 2:

option 1;

since fixed costs are low under option 1, we need to opt it for demand under indifference point.

required 3:

break even unit sales for option 1	88,889
break even unit sales for option 2	108,500

working:

break even unit sales = fixed costs / contribution per unit

option 1:

=>5,440,000 / 61.20

=>88,889.

option 2:

=>7,378,000/ 68

=>108,500.