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 Question from Debbie: What formula or formulas do I use if I want to ultimately charge a customer $300 for a service, but need to factor in a 15% commission for a sales rep,$20 to cover the cost of our overhead, the cost of a $25 coupon that we will be sending to the customer to apply to future services. In other words, what amount do I initially quote the customer to be able to cover these costs? Debbie, I am uncertain about the order of things here. Interpretation A The final bill the customer must pay is$300. From the $300 you collect, you give some of it to the sales people, some of it covers overhead and some covers the coupon. You are looking for the initial base price that things build up from. If this is the case, quote the customer$300. That's the price you will charge, that's the price you should quote.

You can break down your costs as follows. Assuming that the commission is a percentage of the base cost (B) alone (no commission for "selling" a coupon or the overhead), then

B + (15%)B + $20 +$25 = $300 B = ($300 - $20 -$25) / 1.15

B = $221.74 You can then quote and collect$300 and allocate your costs as follows:

base price: $221.74 sales commission:$33.26
coupon value: $25 overhead:$20
total: $300 Interpretation B: If you want to have$300 at the end after paying for your sales, overhead and coupon, then you have $300 as the base price. The total price (T) is: T = B + (15%)B +$20 + $25 T =$300 + (15%)($300) +$20 + $25 T =$390.

So you quote to the customer a final bill of $390. Then you can record in your books the costs as follows: base price:$300
sales commission: $45 coupon value:$25
overhead: $20 total:$390

I think it is interpretation B that you want, but only you know for sure. The important thing is that your initial quote should be the price the customer must pay, not the amount you get paid after covering your internal costs.

Stephen La Rocque>

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.