4 Replies Latest reply on Aug 31, 2012 4:12 AM by 769738

Profit Chart ?

Hi Everyone,

I wanna ask How to calculate profit in profit chart/tab on classification model. On the profit setting there are startup cost,incremental cost,incremental revenue, budget, etc. I know how to calculate lift score but I don't know how to calculate profit/ROI with all those component. Any clue how to calculate profit and ROI ?

Thanks

Edited by: Bayesian on Aug 24, 2012 1:10 AM
• 1. Re: Profit Chart ?
How to compute Profit:

Assume Quantile = 20 (I just pick quantile = 20 for this example)
Targets Cumulative at Quantile 20 = 18 (this value can be found in the lift chart/data)
Non Targets Cumulative at Quantile 20 = 2 (this value can be found in the lift chart/data)
Total Targets = 100 (Targets Cumulative at last Quantile + Non Targets Cumulative at last Quantile)
Startup Cost = 1000 (user input)
Incremental Revenue = 10 (user input)
Incremental Cost = 5 (user input)
Budget = 10000 (user input)
Population = 2000 (user input)

Profit = -1 * Startup Cost + (Incremental Revenue * Targets Cumulative - Incremental Cost * (Targets Cumulative + Non Targets Cumulative)) * Population / Total Targets
Profit = -1 * 1000 + (10 * 18 - 5 * (18 + 2) * 2000 / 100 = 600

How to compute ROI:

ROI = ((profit - cost) / cost) * 100, where profit = Incremental Revenue * Targets Cumulative, cost = Incremental Cost * (Targets Cumulative + Non Targets Cumulative)
ROI = ((180 - 100) / 100) * 100 = 80

Hope this help!
• 2. Re: Profit Chart ?
Thanks a lot dwong, Now I can calculate the profit and ROI.

One more thing, I'm a little bit confuse about definition of variables which is used for this calculation :

1. Startup cost : total startup cost (fixed cost)
2. Incremental revenue : estimated revenue that results from a sale or new customer.
3. Incremental Cost : estimated cost that results from a sale or new customer.
4. Budget : What does budget mean ? since the variable was not using for profit calculation+
5. Population : number of population/cases

is it right ?

What does it mean if we get profit \$600 and ROI 80% in 2000 population (quantile 20). Can you explain a little bit about this ?

Many Thanks
• 3. Re: Profit Chart ?
Hi Bayesian

Your variable definitions seem right. About the Incremental cost, you can think of it as a cost to promote a sale. For example, in a mail order campaign, it could be a cost to mail a catalog to a customer.

The budget is used to calculate how much population it can cover based on user supplied variables.

For example,

Startup Cost = 1000 (user input)
Incremental Revenue = 10 (user input)
Incremental Cost = 5 (user input)
Budget = 10000 (user input)
Population = 2000 (user input)

So each quantile contains 20 cases (total population / number of quantiles = 2000/100)

The cost to promote a sale in each quantile = \$5 * 20 (Incremental Cost * number of cases per quantile) = \$100

The cumulative costs of quantiles are:

Quantile Cost
1 \$1100 (\$100 + start up cost of \$1000)
2 \$1200
: :
20 \$3000
: :
90 \$10000
: :
100 \$11000

The \$10000 budget can covers the first 90 quantiles of population (you should see the budget line drawn in the profit chart on the 90th quantile).

Question: What does it mean if we get profit \$600 and ROI 80% in 2000 population (quantile 20). Can you explain a little bit about this ?
Answer: Use the mail order campaign as an example, it means if you mail catalogs to first 20 quantiles of population (400), it will generate a profit of \$600 (which has ROI of 80%).

If you randomly mail the catalogs to first 20 quantiles of customers (Targets Cumulative = 10, Non Targets Cumulative = 10), the profit you get would be:
Profit = -1 * Startup Cost + (Incremental Revenue * Targets Cumulative - Incremental Cost * (Targets Cumulative + Non Targets Cumulative)) * Population / Total Targets
Profit = -1 * 1000 + (10 * 10 - 5 * (10 + 10)) * 2000 / 100 = -\$1000 (no profit)

Hope this help!