Question

Mary Products, Inc. has decided to introduce a new product, which can be manufactured by either a computer-assisted manufacturing system or a labor-intensive production system. The manufacturing method will not affect the quality of the product. The estimated manufacturing costs by the two methods are as follows:
	Computer-Assisted Manufacturing System				Labor-Intensive Production System
Direct Material			$6.00				$8.00
Direct Labor (DLH denotes direct-labor hours)	0.7DLH@$20		$14.00		1.3DLH@$15.6		$20.28
Variable mfg. overhead (applied based on DLH)	0.7DLH@$15		$10.50		1.3DLH@$15		$19.50
Fixed mfg. overhead*	$4,250,000				$375,000
* These costs are directly traceable to the new product line and they would not be incurred if the new product were not produced.
The company's market research department has recommended an introductory unit sales price of $80.00. Selling expenses are estimated as $400,000 annually plus $2.00 for each unit sold.
Required: (Round up all numbers to the next higher digit in case of breakeven volumes and round up to the nearest integer in other cases.)
a) Calculate the estimated break-even point (in annual sales volume in units) of the new product if the compnay uses the (i) Computer-Assisted Manufacturing System; (ii) Labor-Intensive Production System.
b)Estimate the number of units that Mary Products should sell to earn an after-tax profit of $4.20 million under (i) Computer-Assisted Manufacturing System (ii) Labor-Intensive Production System. Assume an income-tax rate of 30%
c) Determine the annual sales volume (in units) at which the firm would be indifferent (if profit maximization is the objective) between choosing between the two manufacturing methods. Justify your answer with appropriate calculations.

Answer 1

	Computer-assisted manufacturing system	Labor-intensive production system
Sale price per unit	$80	$80
Less: Variable cost per unit:
Direct material	6	8
Direct labor	14	20.28
Variable manufacturing overhead	10.50	19.50
Variable selling expense	2	2
Total variable cost per unit	32.5	49.78
Contribution margin per unit	$47.5	$30.22

a. Break-even point in annual sales volume in units = Total fixed costs / Contribution margin per unit

Computer-assisted manufacturing system = $4,250,000+400,000 / $47.5 = 97,895 units

Labor-intensive production system = $375,000+400,000 / $30.22 = 25,645 units

b. Desired sales units = Fixed costs + Target before tax profit / Contribution margin per unit

Computer-assisted manufacturing system = $4,650,000+(4,200,000/70%) / $47.5

Computer-assisted manufacturing system = $4,650,000+6,000,000 / $47.5 = 224,211 units

Labor-intensive production system = $775,000+6,000,000 / $30.22 = 224,189 units

c. Let sales volume (in units) at which firm would be indifferent be X

$47.5X - $4,650,000 = $30.22X - $775,000

$47.5X - $30.22X = $4,650,000 - $775,000

$17.28X = $3,875,000

X = $3,875,000 / $17.28 = 224,248 Units

Sales volume (in units) at which firm would be indifferent is 224,248 units