Source: p 603, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley

A similar misuse of percentages is committed by businesses and corporations that, for whatever reason, want to make it appear that they have earned less profit than they actually have. The technique consists of expressing profit as a percentage of sales volume instead of as a percentage of investment. [...] To appreciate the fallacy in this procedure, consider the case of the jewelry merchant who buys one piece of jewelry each morning for $9 and sells it in the evening for $10. At the end of the year the total sales volume is $3,650, the total investment $9, and the total profit $365. Profits as a percentage of sales amount to only 10 percent, but as a percentage of investment they exceed 4,000 percent.

Why is the bold true?
I cannot diagnose why, but I somehow believe that because the merchant buys the 1 piece each morning for 365 days, his total investment should be $9 x 365. Please correct my incorrect thinking.


5 Answers 5


Your initial investment in this case is $9 on the first morning. Every other morning you are using part of your profits to buy the new piece of jewelry, so you are actually not investing any new funds.

So each day you are effectively keeping $1 of your profits and re_re-investing $9. But your initial investment of your own funds is only the first $9.

In other words if you only had $9 in the bank at the start of the year you could make $365 profits during the year and finish up with $374 in the the bank at the end of the year.


Not sure if your question is on topic, but the investment is only $9 because that is maximum amount of money the merchant ever needed to start up the business.

He put in $9, started turning a profit, and never looked back.

  • No, I'd agree, not quite on topic, but I see no close votes, so it might stay. Jan 9, 2016 at 13:33

Nothing wrong with the other answers, but here's a "trick" to hopefully make it totally transparent.

Imagine that you're not the one implementing this business plan, but someone else is. Let's call this other person your asset manager. So on the first day, you give your asset manager $9. He takes this and generates $1 profit from it, recovering the $9 which he then reinvests to generate $1 profit every day. From your perspective, you just gave him $9. At the end of the year, he gives you $365 in addition to your original investment of $9 (in real life he'd take the fees of course, or perhaps he's been lending out the money he's been accumulating and taking the interest from that as pay for his services). So your return on investment is 365 / 9 * 100 % > 4000 %, as claimed by your source.


You're confused because the source you cite leaves out one number that isn't relevant to the argument they're making: total costs.

The number you're expecting, $9 x 365 or $3285 is the total cost of buying the jewelry which, when subtracted from the $3650 sales volume gives us the net profit of $365.

The investment is the amount of money original put into a system our company. In this case the merchant bought his first piece of jewelry for $9, sold it for $10, took one dollar in profit and used the other 9 to reinvest by buying a new piece of jewelry.

We can extend the analogy further. After 9 days of selling, the merchant will posses $18, allowing him to now buy 2 pieces of jewelry each morning and sell them for $20. Every day his costs will be $18 and he'll turn a $2 profit, all with the original investment of $9.


Another way to look at this is if we separate the owner's account from the business's account.

At the start of the year, the owner puts $9 into the business account to get the business started. At the end of the first day, the business account has $10, and at the end of the second day, the business account has $11.

The owner doesn't need to add any more of his own money into the business account. At the end of the 365th day, the business will have $374, which is $365 profit + $9 investment.

Assuming the business has no other expenses, the business will calculate profit for the year like this:

$10 x 365 = $3650 total sales
$9  x 365 = $3285 expenses

$3650 - $3285 = $365 profit

The author is making a strange point. The two numbers he is talking about are two different quantities. The business owner's return on investment is $365 / $9 = 4056%.

But the business's profit margin is $365 / $3650 = 10%.

Both are useful numbers when running the business. I disagree with the author's insinuation that a business is doing something tricky when calculating profit margin. Remember that, in addition to the business owner's monetary investment, he worked every day for a year to earn that $365.

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