Question

Patterson Products Inc. is considering an upgrade to its manufacturing equipment. The two upgrade options under consideration are shown below.

 

	Option 1	Option 2
Direct materials cost per unit	$18	$15
Direct labour cost per unit	$34	$27
Variable overhead per unit	$26	$32
Fixed manufacturing costs	$2,000,000	$3,000,000

 

The selling price of the company's product is $120 per unit with variable selling costs of 5% of sales. Fixed selling and administrative costs are $3,300,000 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

At what annual number of unit sales would Patterson Products Inc. be indifferent between the two upgrade options?

Answer 1

Patterson Products Inc. will be indifferent between the two manufacturing methods at the volume (X) where annual operating income is equal.

 

Option 1 CM – total fixed costs = Option 2 CM – total fixed costs.

 

Option 1 CM: $120 – ($18 + $34 +$26 + $6*) = $36

Option 1 total fixed costs: $2,000,000 + $3,300,000 = $5,300,000

 

Option 2 CM: $120 – ($15 + $27 +$32 + $6*) = $40

Option 2 total fixed costs: $3,000,000 + $3,300,000 = $6,300,000

 

*$120 × 5%

 

$36Q - $5,300,000 = $40Q - $6,300,000

Where Q = indifference point in unit sales

 

Solving for Q= 250,000 units

 

Alternatively, the solution can be obtained by using the following simplification of the above formula:

 

Q = Change in Fixed costs / Change in Contribution Margin

    $1,000,000 / $4 = 250,000 units

 

Finally, in this case the sales price, variable selling costs, and fixed selling and administrative expenses do not differ between the two options. So, the following equality based on total costs using only the costs that differ between the options can be used to solve for Q:

 

$78Q + $2,000,000 = $74Q + $3,000,000

  Q = 250,000 units

Patterson Products Inc. will be indifferent between the two manufacturing methods at 250,000 units where annual operating income is equal.