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W LTD wishes to attain a before tax-net profit equal to $20\%$ of sales revenue. Variable costs are $60\%$ of sales and fixed costs are $360,000$. Calculate the dollar amount of sales necessary for archiving the profits goal.

My attempt:
$Sales=fixed \ costs+variable \ costs+desired \ profit$
But I failed to get the answer given.

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  • $\begingroup$ Could you expand a bit, and where does that exercise come from? $\endgroup$ Jun 16, 2016 at 7:32
  • $\begingroup$ This is an algebra question tangentially related to the field of economics, so I'll have to vote to close. To solve your equation, substitute in $\text{variable costs}$ for $\text{sales} \cdot 0.6$ and $\text{profit}$ for $\text{sales} \cdot 0.2$ and substitute in the fixed cost. Then solve for sales. $\endgroup$
    – Kitsune Cavalry
    Jun 19, 2016 at 21:42

1 Answer 1

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Let profits be $P$, total revenue or sales be $TR$, total variable cost $V$ and fixed cost $F$. So total cost, $TC = V + F$ and
$P = TR - TC = TR - (V + F)$.
We have $P = 0.2 \times TR$, $V = 0.6 \times TR$ and $F = 360,000$. Substitute $P, V \text{and} \ F$:

$0.2 \times TR = TR - (0.6 \times TR + 360,000)$

Now solve the above equation for $TR$ which turns out to be $1,800,000$.

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