Operating break even

Rodgers, inc. has fixed operating expense of $2 million and will break even with sales of $5 million. For sales of $7 million, an analyst would estimate the firm’s operating income as: A:$800,000 B:$1,200,000 C:$2,000,000

Does anybody know how to solve it? thank you!

I havent done this in a while but isnt this pretty simple?

The fixed costs are $2M. The variable costs are unknown. The break even is $5, so that means the variable cost is $3M.

If the sales is $7M, then you subtract the fixed and variable costs.

= 7 - 2 - 3 = 2?

No, The correct answer is A: $800,000

Then it’s saying the variable cost is linear to sales., which in this question is 60% of sales.

$5M - 2M = 3M.

3m/5m = 60% variable.

So the new operating cost is 7m minus (2m + 0.6*7m) = $800K


Another way to look at it is that $2 million of the $5 million, or 40%, covers the fixed costs, and 60% covers the variable costs.

After the fixed costs are covered, 60% of sales still covers variable costs, but the 40% is now operating income. Forty percent of the extra $2 million ($7 million − $5 million) is $800,000.