1
$\begingroup$

Missing something very basic here and cannot pin point it.

We need to charge a client \$100 for a product. Let's say our payment processor charges us 10% on every transaction. We make this transparent to the client and charge them accordingly:

$\$x = \$100 / (1 - (10 / 100)) = $111.11111..$

Now, we want to offer to contribute to transaction fees such that they only have to pay half of what the payment processor charges. But clearly, $(\$100 + ((\$111.11111... - \$100) / 2))$ is not the answer.

The question is, how do we calculate the selling price such that the transaction fee is split half way between us and the client?

UPDATE: Based on the answers, here is the clarification that should have been part of the original question. $\$x=\$100$ is the pre-determined "selling price" to the client. We add whatever the payment processor charges us (10% in this case) and increase the selling price such that we receive $\$x=\$100$. Since we now want to "split" the processing fee with the client, we should lose from $\$100$ exactly how much extra the client is paying above $\$100$.

$\endgroup$
  • $\begingroup$ Erm, wait. Do they charge the customer 110 if you request (and obtain) 100? Or do you obtain 90 if you request 100 (and the customer is charged 100)? $\endgroup$ – Hagen von Eitzen Nov 8 '13 at 18:35
  • $\begingroup$ @HagenvonEitzen: We charge the customer \$111.111... such that the payment processor deducts 11.111... and we receive \$100. Now we are willing to charge \$x even if we receive less than \$100 as long as the processing fee is split equally. $\endgroup$ – Raheel Khan Nov 8 '13 at 18:53
1
$\begingroup$

As I understand it, you will charge the customer $p$ and receive $0.9p$. You want to pay half the processing fee, so $0.95p=100$, $p=\frac {100}{0.95}\approx 105.263$ You receive about $94.737$, so you are paying $5.263$ as are they.

$\endgroup$
  • $\begingroup$ Thank you. That is exactly what I was after but am not sure how to express it generically. The only known factors in the equation are $p=retail price$, $f=fee (10% in our case)$ and $sr=split ratio (50% is our contribution)$. Could you please elaborate $100/0.95$ as a generic expression having p, f & sr? $\endgroup$ – Raheel Khan Nov 8 '13 at 19:02
  • 1
    $\begingroup$ It is $\frac p{1-f\cdot sr}$ if you express $f$ and $sr$ as decimals instead of percents. $\endgroup$ – Ross Millikan Nov 8 '13 at 19:04
  • $\begingroup$ Thanks again. Now I understand why it was bugging me not to have simply multiplied (f & sr) in the standard (p / (1 - f)) equation. And sorry about about the mini-Markdown mistakes in my last comment. Cannot edit them. $\endgroup$ – Raheel Khan Nov 8 '13 at 19:16
0
$\begingroup$

I understand you want to calculate the price $a$ such that your contribution $100-a$ equals the customer's contribution $\left(1+\frac{10}{100}\right)a-100$. (At least this is the case if the payment service adds ten percent to your request and charges an accordingly higher amount from the customer; see below for th eothre way around). That is equivalent to $$\left(2+\frac{10}{100}\right)a=200$$ or $$a=\frac{2000}{21}= 95.\overline{238095} $$ (For $p$ % the answer would be $\frac{20000}{200+p} $)


If the payment service charges the original amount from the customer and subtracts ten percent from the amount and gives the rest to you, there is a slightly different siutuation: Your contribution is $100-\left(1-\frac{10}{100}\right)a$ and the customer's contribution is $a-100$. Again we equate, but this time obtain $$\left(2-\frac{10}{100}\right)a=200 $$ or $$a = \frac{2000}{19}=105.\overline{263157894736842105}$$ (For $p$ % the answer would be $\frac{20000}{200-p}$).

$\endgroup$
  • $\begingroup$ I think the customer contribution is $\frac {10}9a-100$ as then the seller is receiving $a$. If you charge the customer $\frac {11}{10}a$, the seller only gets $0.99a$, not $a$ $\endgroup$ – Ross Millikan Nov 8 '13 at 18:36

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.