I'm stumped at how to approach this problem and was hoping someone could enlighten me. If I had sold $100 of a product and made a 20% profit up until a specific day. The next day, made three sales; A) $20 making a $5 profit B) $50 making a $30 profit C) $30 making a $15 profit. So now, in total, I've sold $200 worth making a total profit $70 or a margin of 35%. The margin delta of 1500 bps, is there a way to show what each sale contributed to that. E.g. A) -300bps B)1000 bps and C) 800bps. I've tried isolating each sale but I don't want order to be a factor.
"The margin delta of 1500 bps" -- what does this mean? I have no idea where the 1500 comes from, and I don't know what bps stands for.
Sorry, Mark, thanks for your reply. Margin delta meant the change in the margin. Moving from having a 20% profit margin before the day to a 35% profit margin at the end of the day, the change is 15% or 1500 basis points (bps). Hope this makes it clearer.
IF I understand "basis points", then you have "$100 of a product and made a 20% profit", "$20 making a $5 profit" which is 25%, "$50 making a $30 profit" which is 60%, and " $30 making a $15 profit" which is 50%. That is, as you say, a total of $200 dollars sales so a weighted average of the percentage profits, weighted by share of sales, would be [itex]\frac{100}{200}(20)+ \frac{20}{200}(25)+ \frac{50}{200}(60)+ \frac{30}{200}(50)= 10+ 2.5+ 15+ 7.5= 35[/itex]. In terms of "percent" that is 10%+ 2.5%+ 15%+ 7.5%= 35%. In terms of "basis points", it is 1000+ 250+ 1500+ 75= 3500. The four sales would be allocated as 1000, 250, 1500, and 75 bps.
That's great, thank you. The point I'm trying to get to is one step further though I'm afraid. From the first sale, we had a 20% margin. After the fourth, we had a 35% profit. The delta here, 15%, how do I work out the make up of that? If I was to do weighting a of 20/100*25 , 50/100 *60 and 30/100 * 50 then I get 50% which follows. However, I want to know what amount of the 15% increase is attributable to each sale so I could say for example! sale 2 contributed 2.5% of the increase, sale 3 contributed 7.5% and sale 4 contributed 5% effectively showing the make up of the 15% increase. My hunch is that I'd need to find a weighted average of each sales percentage difference from our starting block e.g. Sale2 made 10% more than the first and was 1/5th of the increase but I know I'm missing something. Any help is greatly appreciated.
I've actually worked this out now, my question was quite far from the solution. The increase from 20% to 35% is a 75% increase. The breakdown of the 75% is made up as follows. For sale 2, it made a 25% profit which is 5% more than the original 20% or a 25% increase. ((.25-.2)/2). The weighting of that sale to the total is 20/200 which is equal to .1. Multiply the .1 by .25 to get .025 which is the contribution to the .75 increase. Repeat for sale 3 and 4 to get .5 and .225 respectively and check by adding them all to get .75 Thank you both for looking at my question and giving it a go, apologies I wasn't clear initially, I hadn't really thought through how I was going to present the data.