Question using retention rate... Can you confirm that I did this right?

[sammysrefuge]

I need help making sure I am doing this right...

I am trying to solve for the total Lifetime Value of a member where I deduct their initial order from the total.

Variables:

A = # of members
B = 42% retention rate
C = $750 lifetime spend
D = $48 initial order

Total Lifetime Value = ABC - ABD (I know I can reduce this to AB(C-D) but I want to keep it easy for now.)

The "ABC" portion calculates the Lifetime Value portion.
The "ABD" portion is supposed to calculate the Initial Order amount that I need to deduct from the Lifetime Value.

Here is the part that has me questioning myself. Since the retention rate is only 42%, I would want to calculate the value of the initial order, which I am deducting in the second part of the equation, by taking the number of members * the initial order * .42. Correct? I am just questioning whether the second part of the equation should be "ABD" or just "AD"...

Can anyone help? If it is "ABD", can you help me understand why?

I really appreciate your help!

 

[stapel]

You've been busy? :
http://www.sosmath.com/CBB/viewtopic.php?f=1&t=68313

Here, too.

I am trying to solve for the total Lifetime Value of a member where I deduct their initial order from the total.

What is the precise mathematical definition of "lifetime value"? (We can help you with the math, but you'll need to make explicit all underlying assumptions, rules, formulas, etc.)

Variables:

A = # of members

In what manner does the value of one particular member depend upon the total number of members?

B = 42% retention rate
C = $750 lifetime spend

On what basis are you saying (when the member first joins) that the "lifetime spend" (which I'm guessing means "the amount paid by the member over the lifetime of the membership) will be $750?

D = $48 initial order

Total Lifetime Value = ABC - ABD (I know I can reduce this to AB(C-D) but I want to keep it easy for now.)

The "ABC" portion calculates the Lifetime Value portion.
The "ABD" portion is supposed to calculate the Initial Order amount that I need to deduct from the Lifetime Value.

Here is the part that has me questioning myself. Since the retention rate is only 42%, I would want to calculate the value of the initial order, which I am deducting in the second part of the equation, by taking the number of members * the initial order * .42. Correct?

We have no idea. You'll need to explain what you're doing, what you're intending, and what assumptions are going into this.

Can anyone help? If it is "ABD", can you help me understand why?

It would be very helpful to us if you'd please post the full and exact text of the exercise, along with the complete instructions. Once we know, precisely, what this homework exercise is asking, we may be better able to advise you. Thank you!