If you knew with absolute certainty that you could put one dollar into investment and get two in return, what would you do? Chances are, you would pour as much money as you could into that investment as quickly as possible and smile all the way to the bank. This simple scenario is an example of an arbitrage opportunity, in which you can buy something at a low price and sell it again at a higher price with minimal risk.

Arbitrage opportunities are essentially precursors to growth, especially in a startup. They signal when and where you should spend your money in order to produce the largest return on an investment. The challenge is knowing definitively that every product you sell and dollar you spend is going to contribute to a positive bottom line.

There are many complex and creative ways companies can find and leverage arbitrage opportunities, but a classic example is seen through customer acquisition. Essentially, the goal is to create a gap in which the lifetime value of a customer is greater than the cost to acquire that customer.

Customer lifetime value (CLTV) > Customer acquisition cost (CAC)

The wider a company is able to stretch the gap, the more net profit it will be able to take home from each customer. Take, for example, a company that sells online subscriptions to users. To calculate if there is an arbitrage opportunity, the company would first start by determining its customer lifetime value (CLTV). This value is important because it provides a baseline understanding of how much money a company can expect to receive from a given customer. Below is a simplified equation for finding CLTV:

(Average \$ amount of a sale) X (Average number of repeated transactions) X (Average retention time for a customer) = Customer lifetime value

In the case of the example, if the company knows that its typical subscriber spends \$15 a month for one year, then the value of that customer would be:

\$15 x 12 months x 1 year = \$180 in total revenue per year

This means that if the company spends under \$180 to acquire a customer, it will make a short-term profit. The next step is to compare that value with how much the company is spending to convert someone into a paying customer, or its customer acquisition cost (CAC). A basic CAC equation looks like this:

(Marketing spend per year) / (Number of customers) = Cost to acquire a customer

In the case of the example, if the company had spent \$10,000 on a particular marketing campaign that resulted in 500 paying customers, then:

\$10,000 / 500 customers = \$20 per customer per year

By comparing the CLTV and CAC, we can see that the lifetime value of the customers is greater than the costs to acquire them. The company has managed to find an arbitrage opportunity.

The next logical strategy for this company is to dedicate as many resources as possible to expand that specific customer acquisition channel, now that the company has proven that it will see a positive return. In addition, the company should look to optimize the channel by tweaking both sides of the equation to widen the profit gap as much as possible. Improving cost efficiency, removing buying friction, and improving the retention rate of customers are all ways companies capitalize on an arbitrage opportunity.

Every business wants a profitable model that it can scale aggressively. Interestingly enough, scaling becomes mechanical once you have found at least one channel of investment with proven returns. The fastest-growing companies are the ones that have proven the math behind their growth and maximized their returns through optimization. Put the odds in your favor by clearly understanding the math behind your business and investing deeply where it means the most.