# Customer Lifetime Value Concept Card: [Course, business or customer base] > A concept card on customer lifetime value (CLV) for MBA marketing and marketing analytics courses: the > retention-based CLV formula, customer acquisition cost (CAC) and payback, cohort retention curves, and RFM > segmentation. It is for MBA students preparing a core marketing exam or case, and for managers who must decide how > much a customer is worth acquiring and keeping. It follows the learning design of the library: the idea in plain > language, formulas with a notation table, Worked example A (fully solved), Worked example B (half solved), Exercise C > (unsolved), common mistakes, a self-test and a separate answer key. > Source basis: Berger and Nasr (1998), Gupta, Lehmann and Stuart (2004), Fader and Hardie (2007), Fader, Hardie and > Lee (2005), written up in original words with fictional Northfield Outdoor Co. data. > Replace every [bracketed] value and every row marked *Example* with your own course or company data. ## Document control | Field | Value | |---|---| | Course or project | [Marketing management / marketing analytics / client project] | | Learner or analyst | [Your name] | | Data set | [Northfield Outdoor Co. loyalty data (fictional) / your data and source] | | Timing convention | [First margin one period after acquisition / first margin at acquisition] | | Discount rate used | [10% a year / course value] | | Reviewed by | [Study partner, tutor or mentor] | | Date | YYYY-MM-DD | | Version | [0.1] | ## When to use it Use customer lifetime value when a decision depends on what a customer is worth over the whole relationship rather than on one transaction: - **Acquisition budgets.** How much can the firm spend to win a customer in each channel? CLV sets the ceiling for customer acquisition cost. - **Retention programmes.** Is a loyalty scheme, a service upgrade or a win-back offer worth its cost? CLV shows how much a few points of retention are worth. - **Segment and channel choice.** Which segments and channels bring customers who stay and buy again (see `mba/mba-stp-positioning-card`)? - **Valuing a customer base.** Gupta, Lehmann and Stuart (2004) showed that the value of the customer base can be used to estimate the value of a firm, including a fast-growing one with negative earnings. - **Subscription and repeat-purchase businesses**, where investors and boards ask for LTV/CAC and payback months. | Use when | Be careful when | |---|---| | Customers buy repeatedly or pay a recurring fee | Purchases are one-off (a house, a wedding dress): use contribution per sale | | You can estimate retention from cohort data | The business is new and no cohort has lived long enough | | Margins per customer are reasonably stable | Margins depend heavily on future price changes or cross-selling you have not tested | | You compare channels, segments or programmes | You need a precise forecast for one individual customer | ## The idea in plain language A customer is an asset. Like any asset, it is worth the present value of the cash it will produce. CLV is that present value: the margin a customer brings each period, multiplied by the probability the customer is still active in that period, discounted back to today. Three levers drive it: **margin** (how much the customer is worth per period), **retention** (how long the customer stays) and the **discount rate** (how much the firm values money later versus now). Acquisition cost is then compared with CLV: a customer is worth acquiring if the expected CLV exceeds the cost of winning that customer. The intuition MBA courses stress is that retention is a powerful lever. With a 10% discount rate, raising annual retention from 75% to 80% raises CLV by about a quarter in the Northfield example below, while a 1% rise in margin raises CLV by exactly 1%. Gupta, Lehmann and Stuart (2004) reported a similar asymmetry across the five firms they studied: a 1% improvement in retention improved firm value far more than a 1% improvement in margin or in acquisition cost. The ideas come from direct and database marketing. Berger and Nasr (1998) set out a family of CLV models with explicit assumptions about purchase timing, retention and promotion costs. Gupta, Lehmann and Stuart (2004) linked the customer view to firm valuation. Fader and colleagues showed how to project retention properly (Fader and Hardie 2007) and how to link RFM data to lifetime value (Fader, Hardie and Lee 2005). ## Formulas and notation **General form.** For a customer acquired today, with margin $m_t$ in period $t$, probability $S_t$ of still being active in period $t$ and discount rate $i$: $$CLV = \sum_{t=1}^{T} \frac{m_t \, S_t}{(1+i)^t}$$ **Constant margin and constant retention, infinite horizon (end-of-period convention).** If the customer must survive each period (including the first) to pay a margin at its end, $S_t = r^t$ and the sum is a geometric series: $$CLV = m \sum_{t=1}^{\infty} \frac{r^t}{(1+i)^t} = m \cdot \frac{r}{1+i-r}$$ The fraction $r/(1+i-r)$ is the **margin multiple**, the form used by Gupta and Lehmann in their work on managing customers as investments. **First margin at acquisition (start-of-period convention).** If the first margin is collected when the customer is acquired (a subscription billed in advance, a first order that comes with sign-up), add that margin and shift the series by one period: $$CLV_{start} = m \sum_{t=0}^{\infty} \frac{r^t}{(1+i)^t} = m \cdot \frac{1+i}{1+i-r}$$ The two versions differ by exactly one undiscounted margin: $CLV_{start} = m + CLV$. **Finite horizon.** Many firms cap the horizon at three to five years because forecasts further out are unreliable: $$CLV_T = \sum_{t=1}^{T} \frac{m \, r^t}{(1+i)^t}$$ **Net value of an acquired customer and LTV/CAC.** $$\text{Net CLV} = CLV - CAC, \qquad \text{LTV/CAC} = \frac{CLV}{CAC}$$ **Expected lifetime.** With constant retention, the expected number of periods a customer is active, counting the period of acquisition, is $1/(1-r)$. **Simple payback.** The number of periods of margin needed to recover acquisition cost, ignoring churn and discounting: $CAC/m$. A retention-adjusted, discounted payback adds expected margins $m S_t/(1+i)^t$ until the running total reaches CAC. | Symbol | Meaning | Unit | Northfield example A | |---|---|---|---| | $m$ | Margin per period per active customer (revenue minus cost of goods, minus variable cost to serve and retention spend) | USD per period | 60 | | $r$ | Retention rate: share of active customers still active next period | proportion | 0.75 | | $i$ | Discount rate per period | proportion | 0.10 | | $S_t$ | Survival: probability a newly acquired customer is still active in period $t$ | proportion | $0.75^t$ | | $T$ | Horizon in periods | periods | infinite, or 5 | | $CAC$ | Customer acquisition cost: acquisition spend divided by customers acquired | USD | 45 | | $CLV$ | Customer lifetime value at the moment of acquisition | USD | 128.57 | **Excel.** Margin multiple and CLV: `=r/(1+i-r)` and `=m*r/(1+i-r)`. Start convention: `=m*(1+i)/(1+i-r)`. Finite horizon with periods 1 to 5 in `A2:A6`: `=SUMPRODUCT(m*r^A2:A6/(1+i)^A2:A6)`, or put the expected margins $m r^t$ in a row and use `=NPV(i, B2:F2)` (Excel's `NPV` discounts the first value by one period, which matches the end-of-period convention). ## Assumptions and limits | Assumption | When it holds | When it fails, and what to do | |---|---|---| | Constant retention $r$ | Contractual settings with stable churn | Real cohorts usually show retention that rises with tenure, because the least loyal customers leave first. Use cohort survival curves or a shifted-beta-geometric model (Fader and Hardie 2007) | | Constant margin $m$ | Mature, stable product and price | Margins grow with cross-selling or fall with discounting: model $m_t$ per period | | Retention is observable | Subscriptions, contracts, memberships | Non-contractual retail (most of Northfield's business): nobody "cancels", they just stop buying. Define "active" (for example, a purchase in the last 12 months) or use probability models such as Pareto/NBD | | One discount rate for all customers | Similar risk across segments | Riskier segments or young businesses may need a higher rate | | Customers are independent | No network or referral effects | Referrals and word of mouth add value not captured in $m$ (see diffusion in `mba/mba-marketing-guide`) | | Average CLV describes the segment | Homogeneous customers | Averages hide a skewed distribution: a small share of customers often brings most of the value. Segment first (RFM below) | CLV is a model estimate, not an accounting number. Report it with the inputs, the convention and a sensitivity table, and never compare CLVs computed with different conventions or horizons. ## How managers use it - **Setting a maximum CAC by channel.** If own e-commerce customers are worth USD 185.72 and marketplace customers USD 17.65 (see the mini-case in `mba/mba-marketing-guide`), the acquisition budget per customer should differ by channel. Many growth-stage firms target LTV/CAC of about 3 as a rule of thumb; treat that as a heuristic, not a law, and check the payback period and cash needs too. - **Valuing retention programmes.** Compute CLV at the current and the target retention rate, multiply the difference by the number of customers affected, and compare with the programme cost. - **Prioritising service.** Customers with high RFM scores and high predicted CLV get proactive service; at-risk high-value customers get win-back offers. - **Budget discussions with finance.** Framing marketing spend as an investment in customer assets, with a CLV per cohort, makes marketing proposals comparable with capital projects (see `mba/mba-npv-irr-card`). - **Investor metrics.** Subscription businesses report net revenue retention, gross churn, CAC payback and LTV/CAC. Check how each is defined before you compare two firms: definitions vary. ```mermaid flowchart TD A["Define the customer and 'active'"] --> B{"Contractual setting?"} B -- "Yes (subscription, contract)" --> C["Measure churn from cancellations"] B -- "No (retail, e-commerce)" --> D["Define activity window or fit a probability model"] C --> E["Build cohort survival curves"] D --> E E --> F{"Retention roughly constant over tenure?"} F -- Yes --> G["Use m times r over (1 + i - r)"] F -- No --> H["Sum margin times survival per period, or fit sBG"] G --> I["Compare CLV with CAC by channel and segment"] H --> I I --> J["Check payback period and cash needs"] J --> K["Decide: acquisition budget, retention spend, segment focus"] ``` ## Worked example A (fully solved): Northfield Outdoor Club members **Situation (fictional).** Northfield Outdoor Co., a mid-size outdoor-gear retailer with stores and e-commerce, runs a free loyalty programme, the Northfield Outdoor Club. Analysis of past cohorts gives: | Input | Value | Source | |---|---|---| | Annual margin per active member, after cost of goods, cost to serve and loyalty rewards | USD 60 | Finance, *Example* | | Annual retention (member buys again in the next 12 months) | 75% | Cohort data, *Example* | | Discount rate | 10% a year | Finance policy, *Example* | | Acquisition cost per member (in-store sign-up incentive plus paid media) | USD 45 | Marketing, *Example* | Convention: a member acquired today pays the first margin at the end of year 1 only if still active (end-of-period convention). **Step 1: margin multiple.** $r/(1+i-r) = 0.75/(1.10 - 0.75) = 0.75/0.35 = 2.1429$. Excel: `=0.75/(1+0.1-0.75)`. **Step 2: CLV.** $CLV = 60 \times 2.1429 = 128.57$, so USD 128.57. Excel: `=60*0.75/(1+0.1-0.75)`. **Step 3: net value.** $128.57 - 45 = 83.57$, so each new member is worth USD 83.57 after acquisition cost; LTV/CAC $= 128.57/45 = 2.86$. **Step 4: the first five years, period by period.** | Year $t$ | Survival $0.75^t$ | Expected margin $60 \times 0.75^t$ | Discount factor $1/1.1^t$ | Present value | Cumulative PV | |---|---|---|---|---|---| | 1 | 0.7500 | 45.00 | 0.9091 | 40.91 | 40.91 | | 2 | 0.5625 | 33.75 | 0.8264 | 27.89 | 68.80 | | 3 | 0.4219 | 25.31 | 0.7513 | 19.02 | 87.82 | | 4 | 0.3164 | 18.98 | 0.6830 | 12.97 | 100.79 | | 5 | 0.2373 | 14.24 | 0.6209 | 8.84 | 109.63 | Excel for the five-year CLV, with years 1 to 5 in `A2:A6`: `=SUMPRODUCT(60*0.75^A2:A6/1.1^A2:A6)` returns 109.63. The ten-year value is 125.78, close to the infinite-horizon 128.57: most of the value is earned in the first five years. **Step 5: payback.** Cumulative PV passes the USD 45 acquisition cost in year 2 (40.91 after year 1, 68.80 after year 2), so the retention-adjusted, discounted payback is two years. **Step 6: sensitivity to retention.** | Retention $r$ | CLV (USD) | Net CLV after CAC of 45 (USD) | |---|---|---| | 0.70 | 105.00 | 60.00 | | 0.75 | 128.57 | 83.57 | | 0.80 | 160.00 | 115.00 | | 0.85 | 204.00 | 159.00 | A one-point rise in retention (0.75 to 0.76) raises CLV to 134.12, plus 4.31%; a 1% rise in margin (60 to 60.60) raises CLV to 129.86, plus 1.00%. **Step 7: the other convention.** If Northfield counted the sign-up purchase as the first margin, the start-of-period formula gives $60 \times 1.10/0.35 = 188.57$ (`=60*(1+0.1)/(1+0.1-0.75)`), exactly one margin of USD 60 more. Both are correct under their own assumptions; mixing them is the error. **Interpretation.** An Outdoor Club member is worth about USD 129 at acquisition, so the current USD 45 acquisition cost is justified, with a two-year payback. Each extra point of retention is worth about USD 5.55 per member (134.12 minus 128.57), which gives the ceiling for what a retention programme may cost per member per point gained. ## Worked example B (half solved): Trail Club rental subscription **Situation (fictional).** Northfield tests the Trail Club, a monthly gear-rental subscription billed at the start of each month. Data from the pilot: | Input | Value | |---|---| | Monthly fee | USD 19 | | Gross margin on the fee after cleaning, repair and logistics | 55% | | Monthly retention | 92% | | Monthly discount rate | 0.8% | | CAC (paid social plus first-month promotion) | USD 66 | 1. Monthly margin $m = 19 \times 0.55 =$ [ ]. Excel: `=19*0.55`. 2. Because the first fee is billed at sign-up, use the start-of-period formula. Multiple $(1+i)/(1+i-r) = 1.008/(1.008-0.92) =$ [ ] (to four decimals). 3. $CLV_{start} = $ [ ] (USD). Excel: `=19*0.55*(1+0.008)/(1+0.008-0.92)`. 4. Net CLV $= CLV_{start} - 66 =$ [ ]; LTV/CAC $=$ [ ]. 5. Simple payback $= CAC/m = 66/10.45 = 6.32$ months. Retention-adjusted, discounted payback: the cumulative expected margin $\sum_{t=0}^{k} 10.45 \times 0.92^t/1.008^t$ reaches 66 at billing month [ ] (count the sign-up bill as month 1). Partial results: after 6 bills, 50.51; after 7 bills, 56.55; after 8 bills, 62.06. 6. Expected number of billed months $1/(1-r) =$ [ ]. 7. In one sentence: is the Trail Club worth scaling at this CAC, and which lever would you work on first? ## Exercise C (unsolved): Northfield business accounts Northfield sells uniforms and gear to outdoor-education centres. Each account brings an annual margin of USD 140 (end-of-period convention), annual retention is 60%, the discount rate is 12% and the acquisition cost (sales visits and samples) is USD 120 per account. 1. Compute CLV and net CLV, with the Excel formula. 2. What is the break-even retention rate at which CLV equals CAC? Solve $m\,r/(1+i-r) = CAC$ for $r$ and check it in Excel with Goal Seek. 3. A key-account programme would raise retention to 70% for an extra cost of USD 25 per account per year (reducing $m$ to 115). Is it worth it? Show both CLVs. 4. Name two reasons why a constant 60% retention rate may be wrong for these accounts. ## Cohort retention curves A cohort is the group of customers acquired in the same period. Plot the share still active by periods since acquisition. Two patterns matter: 1. **Retention usually rises with tenure.** Customers differ in their propensity to churn. The least loyal leave early, so the survivors are increasingly loyal, and the period-to-period retention rate rises even though no individual customer changes. Fader and Hardie (2007) model this with the shifted-beta-geometric (sBG) model, in which each customer has a constant churn probability drawn from a beta distribution. Projecting the first-period retention rate forward as a constant understates long-run survival. 2. **Newer cohorts can behave differently.** A change in acquisition channel, product or price shows up as a shift between cohorts. Compare cohorts at the same age, not at the same calendar date. The chart shows three quarterly cohorts of Northfield Trail Club members (fictional, generated from sBG parameters) and, dashed, a constant-rate projection that applies the 2025-Q1 cohort's first-quarter retention (73.2%) to every later quarter. After eight quarters the 2025-Q1 cohort still has 24.2% active, while the constant-rate projection predicts 8.2%. The period retention of the 2025-Q1 cohort rises from 73.2% in quarter 1 to 90.1% in quarter 8. ```vega-lite { "$schema": "https://vega.github.io/schema/vega-lite/v5.json", "description": "Northfield Trail Club cohort retention by quarter since acquisition (fictional data)", "width": 420, "height": 240, "data": {"values": [ {"cohort": "2025-Q1", "quarter": 0, "active_pct": 100.0}, {"cohort": "2025-Q1", "quarter": 1, "active_pct": 73.2}, {"cohort": "2025-Q1", "quarter": 2, "active_pct": 57.4}, {"cohort": "2025-Q1", "quarter": 3, "active_pct": 47.0}, {"cohort": "2025-Q1", "quarter": 4, "active_pct": 39.8}, {"cohort": "2025-Q1", "quarter": 5, "active_pct": 34.4}, {"cohort": "2025-Q1", "quarter": 6, "active_pct": 30.2}, {"cohort": "2025-Q1", "quarter": 7, "active_pct": 26.9}, {"cohort": "2025-Q1", "quarter": 8, "active_pct": 24.2}, {"cohort": "2025-Q3", "quarter": 0, "active_pct": 100.0}, {"cohort": "2025-Q3", "quarter": 1, "active_pct": 78.3}, {"cohort": "2025-Q3", "quarter": 2, "active_pct": 64.3}, {"cohort": "2025-Q3", "quarter": 3, "active_pct": 54.5}, {"cohort": "2025-Q3", "quarter": 4, "active_pct": 47.4}, {"cohort": "2025-Q3", "quarter": 5, "active_pct": 41.9}, {"cohort": "2025-Q3", "quarter": 6, "active_pct": 37.5}, {"cohort": "2025-Q3", "quarter": 7, "active_pct": 34.0}, {"cohort": "2025-Q3", "quarter": 8, "active_pct": 31.0}, {"cohort": "2026-Q1", "quarter": 0, "active_pct": 100.0}, {"cohort": "2026-Q1", "quarter": 1, "active_pct": 82.4}, {"cohort": "2026-Q1", "quarter": 2, "active_pct": 70.2}, {"cohort": "2026-Q1", "quarter": 3, "active_pct": 61.3}, {"cohort": "2026-Q1", "quarter": 4, "active_pct": 54.5}, {"cohort": "2026-Q1", "quarter": 5, "active_pct": 49.1}, {"cohort": "2026-Q1", "quarter": 6, "active_pct": 44.7}, {"cohort": "2026-Q1", "quarter": 7, "active_pct": 41.1}, {"cohort": "2026-Q1", "quarter": 8, "active_pct": 38.0}, {"cohort": "Constant-rate projection", "quarter": 0, "active_pct": 100.0}, {"cohort": "Constant-rate projection", "quarter": 1, "active_pct": 73.2}, {"cohort": "Constant-rate projection", "quarter": 2, "active_pct": 53.5}, {"cohort": "Constant-rate projection", "quarter": 3, "active_pct": 39.2}, {"cohort": "Constant-rate projection", "quarter": 4, "active_pct": 28.7}, {"cohort": "Constant-rate projection", "quarter": 5, "active_pct": 21.0}, {"cohort": "Constant-rate projection", "quarter": 6, "active_pct": 15.3}, {"cohort": "Constant-rate projection", "quarter": 7, "active_pct": 11.2}, {"cohort": "Constant-rate projection", "quarter": 8, "active_pct": 8.2} ]}, "mark": {"type": "line", "point": true}, "encoding": { "x": {"field": "quarter", "type": "quantitative", "title": "Quarters since acquisition"}, "y": {"field": "active_pct", "type": "quantitative", "title": "Share of cohort still active (%)", "scale": {"domain": [0, 100]}}, "color": {"field": "cohort", "type": "nominal", "title": "Cohort"}, "strokeDash": { "condition": {"test": "datum.cohort === 'Constant-rate projection'", "value": [6, 4]}, "value": [1, 0] } } } ``` **Excel.** With the active counts of a cohort in `B2:J2` (quarter 0 to 8): share active `=B2/$B2`; period retention `=C2/B2`. Compare each cohort's period retention at the same quarter of age. ## RFM: recency, frequency, monetary value RFM is a long-standing direct-marketing method. Each customer is scored on how recently they bought (R), how often (F) and how much they spent (M), usually in quintiles from 1 (worst) to 5 (best). Fader, Hardie and Lee (2005) showed that these three summaries carry most of the information needed to project a customer's future value in a non-contractual setting, and linked RFM formally to CLV. **Worked RFM example (fictional, ten Northfield e-commerce customers).** Quintile scores, with ties given the same score. Excel, with the column of values in `B2:B11`: for frequency and monetary value `=CEILING.MATH(RANK.EQ(B2,$B$2:$B$11,1)/COUNT($B$2:$B$11)*5)`; for recency (fewer days is better) use descending order, `=CEILING.MATH(RANK.EQ(B2,$B$2:$B$11,0)/COUNT($B$2:$B$11)*5)`. | Customer | Days since last order | Orders, last 12 months | Spend, last 12 months (USD) | R | F | M | RFM code | Suggested action | |---|---|---|---|---|---|---|---|---| | NC-001 *(Example)* | 12 | 9 | 1,180 | 5 | 5 | 5 | 555 | Recognise, early access, referral ask | | NC-002 *(Example)* | 200 | 1 | 95 | 2 | 1 | 1 | 211 | Low-cost reminder only | | NC-003 *(Example)* | 45 | 4 | 410 | 4 | 3 | 3 | 433 | Cross-sell a second category | | NC-004 *(Example)* | 8 | 12 | 1,650 | 5 | 5 | 5 | 555 | Recognise, early access, referral ask | | NC-005 *(Example)* | 400 | 1 | 60 | 1 | 1 | 1 | 111 | Suppress from paid campaigns | | NC-006 *(Example)* | 95 | 3 | 520 | 3 | 2 | 4 | 324 | Premium product content | | NC-007 *(Example)* | 30 | 7 | 760 | 4 | 4 | 4 | 444 | Loyalty tier upgrade | | NC-008 *(Example)* | 150 | 2 | 140 | 2 | 2 | 2 | 222 | Seasonal reminder | | NC-009 *(Example)* | 60 | 5 | 300 | 3 | 3 | 3 | 333 | Bundle offer | | NC-010 *(Example)* | 310 | 6 | 230 | 1 | 4 | 2 | 142 | Win-back: was a regular, has lapsed | NC-010 shows why RFM codes beat score sums: the sum (7) is close to NC-008's (6), but NC-010 was a frequent buyer who has stopped, a classic "at risk" profile that deserves a personal win-back offer, while NC-008 has always been an occasional buyer. ## Connections to other cards - **NPV and discounting** (`mba/mba-npv-irr-card`): CLV is an NPV of expected customer cash flows; Excel's `NPV` convention is the end-of-period convention. - **Segmentation and targeting** (`mba/mba-stp-positioning-card`): segment attractiveness should include expected CLV, not only size and growth. - **Marketing mix and budget allocation** (`mba/mba-marketing-mix-card`): CLV sets how much each channel may spend per customer; marginal response sets where the next dollar goes. - **Pricing** (`mba/mba-pricing-card`): a price cut that raises acquisition may lower $m$; check CLV, not only volume. - **Unit economics** (`finance/unit-economics-analysis`): LTV/CAC and payback in a start-up or subscription context. - **Statistics** (`academic/stats-probability-basics`, `academic/stats-logistic-regression`): survival probabilities and churn prediction models. ## Common mistakes and misconceptions - **Mixing timing conventions.** $m\,r/(1+i-r)$ and $m(1+i)/(1+i-r)$ differ by one full margin. State the convention and stay with it. - **Using revenue instead of margin.** CLV built on revenue overstates value, sometimes by a factor of three or more. Use contribution after cost of goods, variable cost to serve and retention spend. - **Deducting acquisition cost twice.** CAC is subtracted once, at acquisition, to get net CLV. Do not also put it in $m$. - **Treating churn as constant when cohort curves flatten.** A constant first-period rate understates the value of survivors (24.2% versus 8.2% after eight quarters in the chart above). - **Comparing cohorts at different ages.** A young cohort's twelve-month retention is not yet observed; compare cohorts at equal age. - **Averages hiding skew.** A few heavy customers can carry the average. Segment (RFM, predicted CLV deciles) before setting budgets. - **Ignoring the discount rate.** Undiscounted lifetime value ($m/(1-r)$ in the start convention) is larger and is not a present value. - **Treating LTV/CAC of 3 as a rule.** It is a heuristic. A business with long payback can have a good ratio and still run out of cash. - **Counting margins that the customer would have generated anyway.** For a retention programme, value only the incremental retention it causes, ideally measured with a control group (`academic/stats-experiment-design`). ## Self-test questions 1. In one sentence, what is CLV? 2. With $m = 80$, $r = 0.8$ and $i = 0.1$ (end-of-period convention), compute CLV and write the Excel formula. 3. For the same customer, what is CLV under the start-of-period convention, and why does it differ? 4. Why does period-to-period retention in a cohort often rise with tenure even if no individual customer changes? 5. A start-up reports LTV/CAC of 5. Name two questions you would ask before you accept that this is good. 6. In a non-contractual retail setting, why is "retention rate" harder to define than for a subscription? 7. Two customers have RFM codes 155 and 515. Which do you contact first with a win-back offer, and why? 8. Northfield can raise retention from 75% to 78% for USD 6 per member per year, reducing $m$ from 60 to 54 ($i = 10\%$). Is it worth it? 9. Why does Excel's `NPV` function match the end-of-period convention? 10. What did Gupta, Lehmann and Stuart (2004) show about the link between customer value and firm value? ## My notes and next steps | Item | My entry | |---|---| | Confidence with CLV (1 = lost, 5 = could teach it) | [ ] | | Convention my course uses | [ ] | | One decision in my firm or case where CLV changes the answer | [ ] | | Mistakes logged in `mba/mba-error-log` | [Date and short description] | | Next review date (spacing: +2 days, +1 week, +1 month) | YYYY-MM-DD | | Next card to study | [mba/mba-marketing-mix-card / mba/mba-stp-positioning-card] | ## Sources and further reading - Berger, P. D., and Nasr, N. I. (1998). Customer lifetime value: marketing models and applications. *Journal of Interactive Marketing*, 12(1), 17-30. - Gupta, S., Lehmann, D. R., and Stuart, J. A. (2004). Valuing customers. *Journal of Marketing Research*, 41(1), 7-18. - Fader, P. S., and Hardie, B. G. S. (2007). How to project customer retention. *Journal of Interactive Marketing*, 21(1), 76-90. - Fader, P. S., Hardie, B. G. S., and Lee, K. L. (2005). RFM and CLV: using iso-value curves for customer base analysis. *Journal of Marketing Research*, 42(4), 415-430. - Reichheld, F. F., and Sasser, W. E. (1990). Zero defections: quality comes to services. *Harvard Business Review*, 68(5), 105-111. - Further reading (by name only): Gupta, S., and Lehmann, D. R., *Managing Customers as Investments* (Wharton School Publishing); Farris, Bendle, Pfeifer and Reibstein, *Marketing Metrics*; Kumar and Reinartz, *Customer Relationship Management*; Kotler and Keller, *Marketing Management*; OpenStax, *Principles of Marketing* (free, CC BY-NC-SA 4.0, openstax.org). ## Answer key **Worked example B.** (1) $m = 10.45$. (2) $1.008/0.088 = 11.4545$. (3) $CLV_{start} = 10.45 \times 11.4545 = 119.70$, so USD 119.70. (4) Net CLV $= 119.70 - 66 = 53.70$; LTV/CAC $= 119.70/66 = 1.81$. (5) After 9 bills the cumulative expected discounted margin is 67.09, which first exceeds 66: payback at billing month 9, about three months later than the simple payback of 6.32 months. (6) $1/(1-0.92) = 12.5$ months. (7) Positive but thin: LTV/CAC of 1.81 and a nine-month payback leave little room for error. Work on retention first (one point from 92% to 93% lifts the multiple from 11.45 to $1.008/0.078 = 12.92$) or on CAC through cheaper channels, before scaling paid acquisition. (End-of-period comparison, for reference: $10.45 \times 0.92/0.088 = 109.25$.) **Exercise C.** (1) $CLV = 140 \times 0.6/(1.12 - 0.6) = 161.54$ (`=140*0.6/(1+0.12-0.6)`); net CLV $= 161.54 - 120 = 41.54$. (2) $m\,r = CAC(1+i-r)$ gives $r = CAC(1+i)/(m + CAC) = 120 \times 1.12/260 = 0.5169$, so 51.7%. (3) With the programme: $115 \times 0.7/0.42 = 191.67$ versus 161.54 without, so yes, by USD 30.13 per account (for reference, at $m = 140$ and $r = 0.70$ CLV would be 233.33). (4) Accounts that survive the first years are more loyal, so retention rises with tenure; contracts or budget cycles create renewal dates where churn clusters; large and small centres may churn at different rates (heterogeneity). **Self-test.** 1. The present value of the margins a customer is expected to generate over the relationship, allowing for the probability that the customer leaves. 2. $80 \times 0.8/0.3 = 213.33$; `=80*0.8/(1+0.1-0.8)`. 3. $80 \times 1.1/0.3 = 293.33$. It adds the first margin, collected at acquisition and not discounted; the difference is exactly $m = 80$. 4. Customers are heterogeneous. The most churn-prone leave first, so the surviving group is increasingly loyal and its average retention rises (the effect the sBG model captures). 5. How is LTV computed (revenue or margin, horizon, discount rate, retention assumption, cohort age)? What is the CAC payback and does the firm have the cash to fund it? Is CAC fully loaded (sales salaries, promotions) and blended or paid-only? 6. Customers do not announce that they have left. "Active" must be defined by an activity window or estimated with a probability model, and the choice changes the rate. 7. 155: a customer who bought often and spent a lot but has not bought recently, the classic at-risk high-value customer. 515 bought recently, so no win-back is needed. 8. Current $60 \times 0.75/0.35 = 128.57$; with the programme $54 \times 0.78/0.32 = 131.63$. Gain USD 3.05 per member: marginally worth it, and sensitive to whether the 78% is really achieved (test it first). 9. `NPV(rate, values)` discounts the first value in the range by one full period, the same as a first margin received at the end of period 1. 10. Customer value, estimated from public data on customers, margins, retention and acquisition costs, can approximate firm value, including for fast-growing firms with negative earnings, and retention is a far stronger value lever than margin, acquisition cost or the discount rate. ## Revision history | Version | Date | Author | Change summary | |---|---|---|---| | 0.1 | YYYY-MM-DD | [Your name] | First draft from the template | | 0.2 | YYYY-MM-DD | [Your name] | *Example:* Replaced Northfield data with course case data, switched to start-of-period convention | ## Standard and licence note Based on the published customer lifetime value literature (Berger and Nasr 1998; Gupta, Lehmann and Stuart 2004; Fader and Hardie 2007; Fader, Hardie and Lee 2005) as taught in MBA marketing courses; no single standard governs CLV. The explanations, worked examples, data and layout are original and fictional; no textbook text, published case or exam question is reproduced. The template is not affiliated with or endorsed by any business school or publisher. Check your own course materials for the notation and conventions they require. Template licence: MIT.