Contribution to margin movement

[Analyze]

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.

 

[Mark44]

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.

 

[Analyze]

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.

 

[HallsofIvy]

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
$\frac{100}{200}(20)+ \frac{20}{200}(25)+ \frac{50}{200}(60)+ \frac{30}{200}(50)= 10+ 2.5+ 15+ 7.5= 35$. 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.

 

[Analyze]

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.

 

[Analyze]

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.