What's The Discount I need to give?

Hi,

I have the following math problem which I'm a hardtime finding the best way to reflect/calculate.

If anyone can help I would really appreciated.

Problem:

I have an agreement with a supplier that he will provide a bottle per case (12 bottles in a case) and I will provide a bottle per case. This deal will be passed on to my customer Which I'm asking them to order in increments of6 case quantities so that full case(s) can be shipped no charge on same order. What's the best way to show this special deal?

* My cost is $ 87.85 per case

* My Sales price is $ 114.00

Note: What makes this problem treaky is that the supplier wants to fund 6free bottles and I will fund the other 6 so ultimately this is passed down to the customer as a free case on every 6 cases ordered.

Re: What's The Discount I need to give?

For the customer it's simple. Either, 7 cases for the price of 6, or 6 cases for the price of 5. I think you mean the first of these two. Just make sure everyone is agreed!

As discounts, that's either a seventh off normal price (because the customer pays only 6 sevenths of normal price for every seven cases), i.e. roughly 14.3%, or else (but we don't think you mean this) a sixth off, i.e. 16.7%.

For you, it's trickier, I agree.

But your cost price is reduced by a fourteenth (7.1%), because the supplier is paying for each fourteenth bottle.

And your profit is reduced by a thirteenth (7.7%) of the old profit, and then by another 7.7%, because...

Let original cost price = C, original selling price = S, original percentage profit = M, and new percentage profit P.

And new cost price = 13 fourteenths of C, and new selling price = 6 sevenths of S.

$\displaystyle S\ =\ (100 + M)\% \times C$

So,

$\displaystyle (100 + P)\%\ =\ \frac{\text{new selling}}{\text{new cost}}\ =\ \frac{\frac{6}{7} \times S}{\frac{13}{14} \times C}$

means

$\displaystyle (100 + P)\%\ =\ \frac{\frac{6}{7} \times (100 + M)\% \times C}{\frac{13}{14} \times C}\ =\ \frac{12}{13} \times (100 + M)\%$

$\displaystyle P\%\ =\ (\frac{12}{13} M - \frac{100}{13})\%$

So, your profit goes from 29.8% down to, theoretically, 19.8%.

And that figures. E.g., check your percentage profit on one case after throwing in a free bottle.

Actually, that shows that I didn't need to mention the supplier's contribution at all. Think of his bottle as going straight to the customer. That'll simplify a bit...

$\displaystyle (100 + P)\%\ =\ \frac{(100 + M)\% \times C}{\frac{13}{12} \times C}\ =\ \frac{12}{13} \times (100 + M)\%$

$\displaystyle P\%\ =\ (\frac{12}{13} M - \frac{100}{13})\%$

Re: What's The Discount I need to give?

I think it's quite simple:

you will collect (for the 7 cases) 6 * $114 = $684

since you're supplying half the 7th case, your "extra cost" is 87.85 / 2 = 43.925 ; make that $44

So you're "netting" 684 - 44 = $640

Really, it's same as you deciding to throw in 6 extra bottles for free.