Simply put it, breakeven analysis concerns the most straightforward question in
ID: 2667563 • Letter: S
Question
Simply put it, breakeven analysis concerns the most straightforward question inbusiness: How many sales are needed to get revenues exceed costs? This exercise
provides an overview of this method. To fix idea, let’s consider some particular
numbers: A firm, called A, has purchased a $250,000 machine to produce certain
products. The machine will be fully depreciated by the straight-line method over
its five-year useful life. Each product sells for $25. The variable cost per product
is $6, and the firm incurs fixed costs of $360,000 each year. The corporate tax rate for the company is 34%. The discount rate is 12%
(b) Let n denote the number of sales each year, p denote the selling price per
unit, c denote the variable cost per unit, FC denote the fixed costs each year
and D denote the depreciation each year. Note that FC does not depend
on n, while in each year the total revenue is n x p and total variable cost is
n x c. Now, in a given year, the EBT , or earnings before taxes are
EBT= n(p-c)-FC-D
We call a sales level n to be the accounting profit break-even point if at this
sales level a firm’s accounting profit is zero. (Observer that for a sales level
greater than n, the accounting profit must be positive.) Then, what is n
of firm A? Hint: If the EBT is zero, then the income tax is zero, and the
accounting profit is zero as well. As a result, to find out n, one only needs to
solve the equation where EBT = 0.
EBT D n.p ?? c/ ?? FC ?? D:
Explanation / Answer
When EBT = 0, 0 = n(p-c) - FC - D. Add FC and D to both sides of the equation: FC + D = n(p-c) Dividing both sides by (p-c): (FC+D)/(p-c) = n So n = (360,000 + 50,000)/(25 - 6) = 21578.95