Wednesday, July 27, 2011

Business Model Analysis, Part 6: LTV and CAC

This post is part of a series on business model analysis for entrepreneurs. The first post in the series presents a comprehensive list of issues (available as a downloadable PDF) entrepreneurs should consider when designing a business model. Others delve into specific issues; this one provides an overview of customer lifetime value (LTV) and customer acquisition cost (CAC) calculations, and how they are used in startups.
As they decide whether to race for scale, startups face a function that relates their long-term payoff—the net present value of future cash flows earned as a result of acquiring new customers during the current period—to their level of current-period investment in customer acquisition. Entrepreneurs cannot observe this function directly; they must estimate its shape based on customer and competitor responses to the firm’s initial marketing efforts and historical information for similar products. Early in a product’s life cycle, with limited data available, these estimates will be imprecise, so entrepreneurs should be wary of overconfidence biases that may lead them to overinvest in growth.

The function relating long-term returns to current-period investments in customer acquisition will have an inverted “U” shape. Up to some point—I* in the figure below—increasing investments should boost a firm’s net present value (NPV), but at a diminishing rate as the cost of acquiring each additional customer rises. Beyond the value-maximizing point, I*, it costs more to acquire additional customers than they are worth. Put another way, if you race too hard, or not hard enough, you will hurt your long-term returns.

Net present value per new customer—that is, customer lifetime value (LTV) minus customer acquisition cost (CAC)—may decline with investment levels for four reasons:

  • Broadening Beyond the Firm’s Natural Market Segments. Most products have attributes — features, service quality, brand image, etc. — that match the needs of some customer segments better than others. When racing for scale, a firm may target prospects outside of the customer segments that find its product most appealing. Large price reductions or promotional expenditures may be required to convert these prospects into buyers.
  • Prematurely Soliciting Mainstream Customers. Mainstream customers often defer purchases until early adopters have “tested the water” and can verify that a product has an attractive value proposition. If mainstream prospects are solicited prematurely, conversion rates may be low unless inducements are offered.
  • Pricing and Promotional Battles. Aggressive moves to capture share may precipitate pricing and promotional battles with competitors.
  • Scalability Constraints. The operational strains of rapid growth may degrade product or service quality. This can hurt solicitation conversion rates and raise acquisition costs per new customer. The resulting damage to the firm’s reputation can also put downward pressure on pricing and customer retention rates, further reducing the payoff from racing.

NPV Impact of Customer Acquisition Investments

The ratio of customer lifetime value (LTV) to customer acquisition cost (CAC) is a useful measure of the productivity of customer acquisition efforts. LTV equals the discounted present value of variable contribution—revenues minus variable costs—earned over the life of a typical customer’s relationship with a company. LTV does not deduct customer acquisition costs (CAC). Unless a firm exhibits viral growth or increasing returns to scale (scenarios discussed below), CAC = LTV is the most that a company can profitably afford to invest to acquire a new customer.

Calculating LTV and CAC

Calculating a firm’s maximum customer acquisition cost (CAC) based on the average lifetime value (LTV) of a customer involves four steps:

Step 1: Determine contribution per customer. Variable contribution equals revenue earned less all variable costs incurred in serving a customer in a given year, excluding marketing costs related to customer acquisition. A back-of-the-envelope approach for calculating the average contribution per customer—usually sufficient for providing a rough “reality check” on a business model—simply subtracts a company’s total variable cost from its revenue for the most recent period, then divides the remainder by the average number of customers served during that period.

A more sophisticated approach recognizes that 1) contribution per customer may vary substantially for different customer segments, and 2) the annual contribution per customer is likely to change over the life of a customer relationship. With respect to the latter point, a company may be able to increase its prices over time. Also, the company should be able to collect information about the customer’s preferences and may be able to use that information to cross-sell related products. Finally, over time, variable costs incurred in serving a customer tend to decline as a percentage of revenues for two reasons. First, experienced customers tend to generate fewer customer service inquiries because they “know the ropes.” Second, as a company grows, it typically can improve its operational efficiency and realize volume discounts in procurement.

Step 2: Determine customer life. To calculate the average length of a customer relationship, one can employ the formula 1/x, where “x” is the annual customer churn rate, that is, the percentage of customers that terminate their relationship with a company from year to year. So, if a company retains 70% of its customers each year, then the average customer life is 1/0.3 = 3.33 years. Of course, the average length of a customer relationship may vary widely for different customer segments.

Step 3: Calculate LTV. The annual cash flows per customer calculated in Step 1 are discounted to their present value, using the number of years for the duration of a customer relationship calculated in Step 2.

Step 4: Calculate CAC. A back-of-the-envelope approach for calculating the average cost of acquiring a new customer takes total sales and marketing expense incurred during a period, then 1) subtracts any costs related to retention and usage stimulation efforts targeted at existing customers (e.g., time spent by sales reps calling on existing accounts, rather than prospecting for new customers); and 2) divides by the total number of new customers acquired during the period.

As with the other inputs described above, average customer acquisition costs will vary considerably by customer segment. Likewise, different acquisition methods may have very different costs. Each method will be subject to decreasing returns during a given period as available prospects in the most attractive segments are converted into purchasers and the company is then forced to target prospects for whom the product is less compelling. For this reason, companies employ cohort analysis: they measure the productivity of their marketing efforts—and optimize their efforts accordingly—by tracking, over time, the LTV and CAC of “vintages” of new customers acquired during a given period through different marketing methods.

Step 5: Compare LTV and CAC. In theory, for any given new customer, a company can afford to increase CAC up to the point that CAC = LTV for that customer. Of course, if CAC = LTV for every new customer that a company acquired, it would not generate enough contribution to cover its fixed costs. For this reason, many companies employ a target LTV/CAC ratio. For many software-as-a-service businesses, for example, the target ratio is 3:1.

Calculating LTV and CAC with Virality and Network Effects

When calculating LTV and CAC for businesses that exhibit virality and/or strong network effects, complications may arise:

  • Virality. The maximum amount that a firm can afford spend to acquire a customer through paid marketing methods should take viral growth opportunities into account. In theory, in calculating the value of a “seed” customer, one should reflect the LTV of every additional customer who will be subsequently acquired due to free, viral mechanisms that are put in motion by the seed. This could conceivably involve a chain of viral acquisitions that stretches for many years into the future. In practice, it is more conservative to credit the seed customer with only one year’s worth of viral acquisitions. A straightforward way to do this is to multiple the LTV directly generated by the seed customer by the 1.0 + V, where V is the viral coefficient for a new customer of that cohort type.
  • Network Effects Generate Value for Other Customers. When a business exhibits increasing returns to scale due to network effects or scale economies in production, acquiring a customer in the current period increases future cash flows from other customers. In calculating LTV, this incremental value should be added to the present value of future cash flows derived directly from a new customer, as illustrated in the technical appendix to Part 2 of this series.
  • Variable Costs Depend on Network Density. When networks have a spatial component, the physical proximity of customers may be an important factor in determining variable costs. For example, an online grocery service can achieve much lower delivery costs per customer when a driver’s stops are just a few minutes apart. Hence, to calculate contribution margins accurately, managers need a reliable forecast for network density.
  • Two-Sided Networks. Two-sided networks have two distinct user groups whose respective members consistently play the same role in transactions, for example, cardholders and merchants in American Express’s credit card network; job seekers and recruiters in’s online recruitment network. To mobilize a two-sided network, platform providers must attract users to both sides—typically simultaneously.
    • In this context, LTV calculations can become very complicated; explaining their mechanics is beyond the scope of this post. In fact, marketing scholars have only recently begun to develop statistical models that can be used to estimate LTV in two-sided networks; my colleague Sunil Gupta has done some pioneering work on this front. Consistent with the previous point, these models factor the impact on future cash flows from Side B users in estimating the value of additional Side A users, and vice versa.
    • In most companies serving two-sided networks, distinct organizational units will be charged with marketing to the separate sides; these units must coordinate their plans to ensure that overall marketing spending is optimized. In particular, it is important to avoid double counting the profit increase attributable to network effects when separate organizational units each calculate LTV for their respective sides. Complicating matters further, certain marketing programs will impact user acquisition rates on both sides (for example,’s Olympic sponsorships, which built awareness among both recruiters and job seekers). Managers must determine how to allocate these expenses across the two sides when calculating CAC.

For more on LTV and CAC analysis, see F. Reichheld, The Loyalty Effect; Blattberg et al., Customer Equity: Building and Managing Relationships as Valuable Assets; Blattberg & Deighton, “Manage Marketing by the Customer Equity Test”; and posts by David Skok of Matrix Partners.