Firm A vs. Firm B: Break-Even Point Comparison

Break-Even Point Comparison

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Question

Firms A and B have the same fixed costs in producing widgets. However, firm A charges 15% more than firm B for a widget while its variable costs per widget are

12% lower than those of B. If firm A sells a widget for 35% above its variable costs, the break-even point for B is ________ times higher than that for A.

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Explanations

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A. B. C. D.

B

The break-even quantity, Q, is given by Q = FC/(P - V), where FC = total fixed costs, P = average sale price per unit and V = average variable cost per unit.

You're given that FCA = FCB, PA = 1.35VA, PA = 1.15PB and VA = 0.88VB. Therefore, PB = (1.35/1.15)VA = 1.174VA and VB = (1/0.88)VA = 1.136V

A.

This gives QA/QB = FC(PA-VA)/FC(PB-VB) = (PB - VB)/(PA - VA) = (1.174 - 1.136)/(1.35 - 1) = 0.109.

Thus, the break-even point for B is (1/0.109) = 9.21 times that for A.

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