Question

Corrigan Enterprises 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 no. 6754:
	Variable costs, $19.00 per unit
	Annual fixed costs, $986,500

Model no. 4399:
	Variable costs, $11.80 per unit
	Annual fixed costs, $1,114,300

Corrigan’s selling price is $63 per unit for the universal gismo, which is subject to a 10 percent sales commission. (In the following requirements, ignore income taxes.)

Required:

1. How many units must the company sell to break even if Model 6754 is selected?

2. Calculate the net income of the two systems if sales and production are expected to average 49,000 units per year.

3. Assume Model 4399 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 Corrigan sell to earn $967,000 of income if Model 4399 is selected? As in requirement (2), sales and production are expected to average 49,000 units per year.

4. Ignoring the information presented in part (3), at what volume level will the annual total cost of each system be equal?

Answer 1

(a) Break even point in units ( Model 6754 )

Breakeven point = Fixed costs / Contribution margin per unit

Contribution margin per unit = selling price - variable cost per unit

Contribution margin per unit = 63 - ( 19 + 6.3 )

Contribution margin per unit = 63 - 25.3 = 37.7

Breakeven point = 986500 / 37.7

Break even point = 26167 units

(b) The net income of the two systems

Particular	model 6754	Model 4399
Sales revenue ( 49000 * 63 )	3087000	3087000
less variable cost
Sales commission ( 10% )	-308700	-308700
System variable expenses
(49000 * 19 )	-931000
( 49000*11.8 )		-578200
Contribution margin	1847300	2200100
Less : fixed costs	-986500	-1114300
Net operating Income	860800	1085800

Model no. 4399 is more profitable when sales and production average is 49000 units .

(c) Annual Fixed costs will increase by $ 90000 ( 450000 / 5 ) because of straight line depreciation

Total fixed costs = 1114300 + 90000 = $ 1204300

Unit contribution margin = 2200100 / 49000 = 44.9

Required sales = (Fixed costs + required profit ) / Contribution margin per unit

Required sales = ( 1204300 + 967000 ) / 44.9

Required sales = 48358.5 units

(d) Let X be the volume level at which annual total costs are equal

so ,

19X + 986500 = 11.8X +1114300

7.2 X = 127800

X= 17750

The volume level at which annual total costs are equal = 17750 units