The Congress Company has identified two methods for producing playing cards. One method involves using a machine having a fixed cost of $10,000 and variable costs of $1.00 per deck of cards. The other method would use a less expensive machine (fixed cost = $5,000), but it would require greater variable costs ($1.50 per deck of cards). If the selling price per deck of cards will be the same under each method, at what level of output will the two methods produce the same net operating income?
A) 5,000 decks
B) 10,000 decks
C) 15,000 decks
D) 20,000 decks
E) 25,000 decks

Question

Quizplus · Accepted Answer

Let's assume the selling price per deck is $x.

Method 1:
Fixed Cost = $10,000
Variable Cost = $1.00 per deck
Revenue = $x per deck

Contribution Margin per deck = $x - $1.00 = $x - 1
Contribution Margin Ratio = ($x - 1) / $x = 1 - (1 / $x)

Method 2:
Fixed Cost = $5,000
Variable Cost = $1.50 per deck
Revenue = $x per deck

Contribution Margin per deck = $x - $1.50 = $x - 1.5
Contribution Margin Ratio = ($x - 1.5) / $x = 1 - (1.5 / $x)

To find the level of output where the net operating income is the same under both methods, we can set the contribution margin of one method equal to the contribution margin of the other method and solve for the level of output.

($x - 1) / $x = ($x - 1.5) / $x - $5,000 / $x
$x - $5,000 = $3,333.33
$x = $8,333.33

So the two methods will produce the same net operating income when the selling price per deck is $8,333.33.

Let's check our answer by calculating the net operating income at different levels of output:

At 5,000 decks:
Method 1: 
Revenue = $41,666.65 ($8.33 x 5,000)
Variable Costs = $5,000 ($1.00 x 5,000)
Fixed Costs = $10,000
Net Operating Income = $26,666.65

Method 2:
Revenue = $41,666.65
Variable Costs = $7,500 ($1.50 x 5,000)
Fixed Costs = $5,000
Net Operating Income = $29,166.65

At 10,000 decks:
Method 1: 
Revenue = $83,333.30 ($8.33 x 10,000)
Variable Costs = $10,000 ($1.00 x 10,000)
Fixed Costs = $10,000
Net Operating Income = $63,333.30

Method 2:
Revenue = $83,333.30
Variable Costs = $15,000 ($1.50 x 10,000)
Fixed Costs = $5,000
Net Operating Income = $63,333.30

At 15,000 decks:
Method 1: 
Revenue = $124,999.95 ($8.33 x 15,000)
Variable Costs = $15,000 ($1.00 x 15,000)
Fixed Costs = $10,000
Net Operating Income = $99,999.95

Method 2:
Revenue = $124,999.95
Variable Costs = $22,500 ($1.50 x 15,000)
Fixed Costs = $5,000
Net Operating Income = $97,499.95

At 20,000 decks:
Method 1: 
Revenue = $166,666.60 ($8.33 x 20,000)
Variable Costs = $20,000 ($1.00 x 20,000)
Fixed Costs = $10,000
Net Operating Income = $136,666.60

Method 2:
Revenue = $166,666.60
Variable Costs = $30,000 ($1.50 x 20,000)
Fixed Costs = $5,000
Net Operating Income = $131,666.60

At 25,000 decks:
Method 1: 
Revenue = $208,333.25 ($8.33 x 25,000)
Variable Costs = $25,000 ($1.00 x 25,000)
Fixed Costs = $10,000
Net Operating Income = $173,333.25

Method 2:
Revenue = $208,333.25
Variable Costs = $37,500 ($1.50 x 25,000)
Fixed Costs = $5,000
Net Operating Income = $165,833.25

At 10,000 decks, the net operating income under both methods is the same at $63,333.30. Therefore, the answer is B) 10,000 decks.

The Congress Company Has Identified Two Methods for Producing Playing