Future Valuation formula for customer base projections

Question

In order to estimate customer growth, I think the right track is to use the formula FV (future value) = n(1+r)^t

 

I'm trying to project how many customers I will have in 4 cycles from now, so I think 4 would be "t"

 

In this scenario, I have 90 customers which I think would be "n"

 

Assuming that every cycle, each customer refers 3 friends who become customers, which may be "r" ?

 

If I solve it that way it comes to 22,784. HOWEVER,

 

aside from customer growth via referrals, at the beginning of each cycle we'll also be adding 50 new customers to "n." I'm not sure how to properly measure that and then combine these two customer inputs into one formula. 

 

Thanks for the help!

Answer 1

To estimate the number of customers after 4 cycles while accounting for both referrals and new customer additions, we need to consider both exponential growth from referrals and a linear increase from new customers. The customer base starts at 90, and each customer refers 3 new customers per cycle, meaning the total number of customers grows by a factor of 4 each cycle. If we only considered referrals, the formula would be:

Future Customers from Referrals = Initial Customers × (1 + Referral Rate) ^ Number of Cycles

= 90 × 4⁴

= 90 × 256

= 23,040

However, an additional 50 customers are manually added at the beginning of each cycle, and they also experience the same referral growth in subsequent cycles. To account for their impact, we calculate the cumulative effect of these new customers. Each batch of 50 new customers grows based on how many cycles they have left to experience referrals. The total additional customers from these batches can be calculated using a sum of growing contributions:

Additional Customers from New Additions = 50 × (4³ + 4² + 4¹ + 4⁰)

= 50 × (64 + 16 + 4 + 1)

= 50 × 85

= 4,250

Adding both components together gives the total number of customers after 4 cycles:

Total Customers After 4 Cycles = 23,040 + 4,250 = 27,290.