Determining the first year turnover of a business

clementyeung

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Jan 30, 2013
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Hi everyone,

I'm drafting a proposal for investment and I have a math question which asks: what is the first year turnover of a business taking into account customer acquisition and attrition.

The details are as follows:

- New business—no customers from business start date
- $47 per month fee, per customer
- 10 new accounts, per month, from business start date
- 20% customer attrition rate after 2 months of their business (so, 20% of the 10 additional customers per month, will stop paying the monthly fee after 2 months of paying it)

Do you know what would be the first year turnover? I have tried many times to navigate math equations online to come up with a solution but failed. My friend has given me the following equation which I really don't understand either (I really suck at math): f(t)=(470+470t)*0.8^t

I don't think that equation is correct, either.

Please help—it is much appreciated :)
 
Hi everyone,

I'm drafting a proposal for investment and I have a math question which asks: what is the first year turnover of a business taking into account customer acquisition and attrition.

The details are as follows:

- New business—no customers from business start date
- $47 per month fee, per customer
- 10 new accounts, per month, from business start date
- 20% customer attrition rate after 2 months of their business (so, 20% of the 10 additional customers per month, will stop paying the monthly fee after 2 months of paying it)

Do you know what would be the first year turnover? I have tried many times to navigate math equations online to come up with a solution but failed. My friend has given me the following equation which I really don't understand either (I really suck at math): f(t)=(470+470t)*0.8^t

I don't think that equation is correct, either.

Please help—it is much appreciated :)
"Turnover" is a word that has several related but not identical meanings in financial analysis. Unless you can specify the definition that you need to use, any answer is going to be a shot largely in the dark. One reason is that your presumed growth rate is constantly declining, but never reaches saturation. An informal way to explain this is that a turnover rate derived from constant attrition rate on a base that is constantly changing cannot be constant. So as your friend's equation implies, turnover is going to be a function of time. Furthermore, if I were analyzing your proposal, I would be highly dubious that every customer who lasts two months will then last forever. People move, die, change their habits, etc.

This is all negative and so is not constructive. Rather than a formula, I might build a model.

Month 1: beginning customer base = 0; new customers = 10; attrition new customers = 0; attrition old customers = 0;
final customer base = 0 + 10 - 0 - 0 = 10; fee revenue = 10 final customers * monthly fee per customer.

Month 2: beginning customer base = 10; new customers = 10; attrition new customers = 0; attrition old customers = 0;
final customer base = 10 + 10 - 0 - 0 = 20; fee revenue = final customers * monthly fee per customer.

Month 3: beginning customer base = 20; new customers = 10; attrition new customers = 2; attrition old customers = 0;
final customer base = 20 + 10 - 2 - 0 = 28; fee revenue = final customers * monthly fee per customer.

Then in month 13 you can begin to insert a number (or rate) for attrition of old customers. Do this for several years, and you can compute average attrition rates per year, etc.

There are a number of advantages to such an approach. The model can be made as realistic as you want. You can see what the effect of changed assumptions is. A model can be updated as you get experience. And most important, you can adjust for unanticiapted concerns or answer unanticiapated questions from potential investors. Finally, if you know how to build an excel spreadsheet, you can do this yourself and understand what the whole thing means.

Hope this helps.
 
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