Question

Dillon, Jones, and Kline, Ltd. is studying the acquisition of two electrical component insertion systems for producing its sole product, the universal gismo. Data relevant to the systems follow. Model A: Variable costs, $17.00 per unit Annual fixed costs, $986,400 Model B: Variable costs, $11.80 per unit Annual fixed costs, $1,114,000 The selling price is $68 per unit for the universal gismo, which is subject to a 5 percent sales commission. (In the following requirements, ignore income taxes.)

How many units must the company sell to break even if Model A is selected? Calculate the net income of the two systems if sales and production are expected to average 42,000 units per year and which of the two systems would be more profitable? Assume Model B requires the purchase of additional equipment that is not reflected in the preceding figures. The equipment will cost $450,000 and will be depreciated over a five-year life by the straight-line method. How many units must the company sell to earn $973,000 of income if Model B is selected? As in requirement (2), sales and production are expected to average 42,000 units per year. Ignoring the information presented in part (3), at what volume level will the annual total cost of each system be equal?

Answer 1

1.) Contribution per unit = Sales price less variable cost

Variable cost = 17 + 5% of 68

= 17+3.4

= 20.4

Contribution per unit = 68-20.4

Contribution per unit = $47.6

Breakeven point = Fixed costs / Unit contribution margin

= $986400/ $47.6

20722 units

2.) Net Income = Revenue - Variable costs - Fixed costs

Sales Revenue = 43,000 X 68

= $2,924,000

Sales Commision = $2,924,000 X 5%

= $146,200

Varibale cost for A = 43,000 X 17

= $731,000

Varibale cost for B = 43,000 X 11.80

= $507,400

Model A = Sales revenue less Variable cost less Annual Fixed costs

Model A = 2924000 - 146200 - 731000 - 986400

= $1,060,400

Model B = 2924000 - 146200 - 507400 - 111400

= $ 2,159,000

Therfore, Model B would be more profitable

3.) Let X be the no of units to be sold

Therfore, X * Selling price = X* Variable costs + Fixed costs + targeted Operating Income

Variable costs = X * 11.80 + 68*5%

= 11.80X + 3.4X

= $15.2X

Fixed costs = 1,114,000 + 450,000 / 5 year SLM depreciation

= 1,114,000 + 90,000

= $1,204,000

Selling price = 68X

Therefore, 68X = 15.2X +1,204,000 + 973,000

68X-15.2X = 2,177,000

52.8X = 2,177,000

X = 41231 units

4.) Let X be the Volume level at what annual cost of each system will be equal

Therefore , Variable cost of A * X + Fixed cost of A = Variable cost of B * X + Fixed cost of B

17X + $986,400 = 11.80X + $1,114,000

5.2X = $127,600

X = 24,538 units