Senate Inc. is considering two alternative methods for producing playing cards. Method 1 involves using a machine with a fixed cost (mainly depreciation) of $17,000 and variable costs of $1.00 per deck of cards. Method 2 would use a less expensive machine with a fixed cost of only $5,000, but it would require a variable cost of $1.50 per deck. The sales price per deck would be the same under each method. At what unit output level would the two methods provide the same operating income (EBIT)?

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jafransp jafransp · Answer 1 · 2019-12-15T12:13:59+01:00

Answer:

24,000 units

Explanation:

We know,

According to the contribution margin approach,

Operating Income (EBIT) = Sales - Variable cost - Fixed cost

or, EBIT = (Price x Quantity) - (Quantity x VC per unit) - Fixed cost

As there are two methods,

Method 1, Variable cost = $1.00/unit, Fixed cost = $17,000

Method 2, Variable cost = $1.50/unit, Fixed cost = $5,000

According to the Question, as both methods will yield same EBIT at the same output levels,

Method 1 EBIT = Method 2 EBIT

or, (Price x Quantity) - (Quantity x $1.00) - 17,000 = (Price x Quantity) - (Quantity x $1.50) - $5,000

or, (Quantity x $1.50) - (Quantity x $1.00) = $(17,000 - 5,000) [Deducted (price x quantity from both the sides]

or, $0.50 x Quantity = $12,000

or, Quantity = $12,000/$0.50

Hence, Quantity = 24,000 units

At 24,000 output level, the EBIT of both methods will be same.