Hi Brian,

When you state a percentage you should really say percentage of what. For example you say your administration is 20% by which I assume you mean 20% of the direct costs. 20% is $\frac{20}{100}$ so 20% of the direct costs is

\[\frac{20}{100} \times \$100 = \$20.\]

Thus your administration cost is $\$20$ and hence your costs are $\$100 + \$ 20 = \$120.$

Now you want a profit of 15%. Is that 15% of your costs ($\$120$) or do you want your profit to be 15% of what your customer pays? If your profit is to be 15% of your costs then your profit is

\[\frac{15}{100} \times \$120 = \$18\]

and the cost to your customer would be $\$120 + \$18 = \$138.$

If your profit is to be 15% of what your customer pays you have to work a little harder. If your customer pays you $\$C$ and your profit is 15% of these $C$ dollars then your costs are 85% of the $C$ dollars. Thus

\[\frac{85}{100} \times \$C = \$120.\]

If you multiply both sides of this equation by $\frac{100}{15}$ you get

\[\$C = \frac{100}{85} \times \$120 = \$141.18.\]

Thus you would charge your customer $\$141.18$ and your profit would be $\$141.18 - \$120 = \$21.18.$

I hope this helps,
Penny

Brian wrote back

Hi , I have a further question on the same subject , if my direct cost is $\$100$. and my administration costs are 20% and I want to make 15% profit. My accountant told me I can divide 100 by 65, $\$100/65 = \$153.$ Does this make sense or should it be $\$100 * 20\% =120 / 85 = \$141.17$

Thanks,

Brian.

Hi Brian,

WE all use the term percent in a non-precise way and this question really makes that clear. You accountant has yet another valid way o interpret your question. He (or she) sees the cost to the customer, $\$C$ in three distinct parts. 20% of $\$C$ is the administration cost, 15% of $\$C$ is your profit and the remainder is your direct cost. The remainder after removing the 20% plus 15% is 65% and thus your fixed cost is 65$ of $\$C.$ That is

\[0.65 \times \$C = \$100.\]

Dividing both sides of this equation by $0.65$ gives

\[\$C = \frac{\$100}{0.65} = \$153.85\]

All three answers are correct. Which you choose depends on what your interpretation of percentage of what.

Penny