[Skooby]

I've tried to do this question, but I'm coming up blank.

I've searched the internet and looked in my textbook but can't find anything relating to this problem.

A company awards an annual bonus to its managers. The bonus this year was $44,000. The bonus agreement says each branch manager gets a bonus of 14% of the branch income after deductions for the bonus and for the income taxes. The income tax rate is 30%.

Determine the income for the branch before the deductions for the bonus and the income taxes.


I would assume you take the bonus amount divided by the bonus percentage.

$44,000/14% = $314,285??

[ArcSine]

Continuing with your approach, your calculation tells you that 314,285 is the "branch income after bonus, and after tax".

We'll continue to work back up the chain. Since tax would be computed after deducting for the bonus, then going backwards the next thing to do is put the tax back in (before putting the bonus back in). At a tax rate of 30%, that 314,285 after-tax net must be 70% of the pre-tax net; hence the pre-tax net is 314,285 / 0.70 = 448,979.

Finally, we put the bonus back in. If the branch net profit after deducting the bonus is 448,979, then the pre-bonus branch profit must be 448,979 + 44,000 = 492,979.

You also could have set it up algebraically, letting b stand for the bonus; t is the tax rate; and P is the branch profit before bonus and tax. You're given b and t; you're trying to find P.

Since the bonus is 14% of the branch profit after bonus, and after tax, it's...

b = (P - b)(1 - t)(0.14)

Substituting in the values you're given, it becomes (amounts in 000s):

44 = (P - 44)(0.70)(0.14)

When you solve that one for P, you'll find you get the same answer as the one we derived earlier.

Before you call it a day, it's always a good move to verify your answer: Branch had a profit (we think) of 492,979. It paid out a bonus of 44K, leaving profit of 448,979. It paid tax on this profit at 30%, or 134,694.

So after paying the bonus, and paying the tax, the branch had a final net profit of 492,979 - 44,000 - 134,694 = 314,285. Now, does the 44K bonus represent 14% of this final amount?

[Skooby]

44K is 14% of $314,285.

Your explanation make total sense.

Thank you.

I'll use the formula in the future.

[ArcSine]

You're very welcome, Skooby, and best of luck.