The annual discount buys retention and early cash. Price both, and two months free turns out to be a giveaway.
Offer an annual plan discount no larger than the share of a year's revenue that monthly customers would not have paid anyway, after churn and the cost of money. On an illustrative 50 a month plan with 3 per cent monthly churn and a 10 per cent cost of capital, the break-even is 18.33 per cent on revenue but only 15.51 per cent on contribution, so the familiar "two months free", 16.67 per cent, already gives away 6.95 of contribution per customer before you ask who takes it.
Worked in full in Pricing Strategy by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The annual discount is a price for two things: twelve months of cash collected on day one, and twelve months of revenue from customers some of whom would have cancelled. Both have a value you can calculate. The discount is worth giving up to the point where it pays for them, and not a point further.
| Input | Value |
|---|---|
| Monthly list price | 50.00 |
| Annual plan at list (12 months) | 600.00 |
| Monthly churn of monthly-plan customers | 3% |
| Cost of capital, annual | 10% |
| Equivalent monthly discount rate | 0.797% |
| Gross margin (cost to serve is the other 20%) | 80% |
Monthly customers pay at the start of each month they are still subscribed. Annual customers pay once, up front, and are served for the full twelve months whether they use the product or not. The comparison covers the first year, which is what the discount buys; from the first renewal both customers face the same decision again.
PV factor = Σ (1 − churn)m ÷ (1 + r)m, for m = 0 to 11
Break-even discount (revenue) = 1 − PV factor ÷ 12
Here r is the monthly rate, (1 + 10%)1/12 − 1. In Excel, with churn in B2 and the monthly rate in B3: =1-SUMPRODUCT((1-B2)^(ROW(A1:A12)-1)/(1+B3)^(ROW(A1:A12)-1))/12.
At 3 per cent churn, 71.5 per cent of the starting customers are still paying in month twelve and 69.4 per cent reach the renewal date. Undiscounted, the average customer pays for 10.2053 months; discounted at 0.797 per cent a month, the twelve payments are worth 9.8008 months of price, or 490.04 today against the 600.00 list price of an annual plan.
So an annual plan sold at any price above 490.04 brings in more present value of revenue than the monthly customer would have. That is a discount of 18.33 per cent. About fifteen points of that is churn the annual plan locks out; the rest is the time value of cash received up front.
Revenue overstates the room. An annual customer who would have left in month five is still served, at the 20 per cent cost to serve, in months six to twelve. A monthly customer who leaves costs nothing after leaving.
Monthly customer contribution = margin × price × PV factor = 0.80 × 50 × 9.8008 = 392.03
Annual customer contribution = 600 × (1 − d) − 0.20 × 50 × 11.4914
11.4914 is the present value of twelve months of service with no churn. The cost to serve an annual customer is therefore 114.91, and the break-even discount solves 600 × (1 − d) = 392.03 + 114.91.
That gives 15.51 per cent. The gap to the revenue figure, almost three points, is the cost of serving customers the annual plan keeps who would otherwise have gone.
| Annual discount | Annual price | Gain on revenue | Gain on contribution |
|---|---|---|---|
| 10.00% | 540.00 | 49.96 | 33.05 |
| 15.00% | 510.00 | 19.96 | 3.05 |
| 16.67% (two months free) | 500.00 | 9.96 | -6.95 |
| 20.00% | 480.00 | -10.04 | -26.95 |
Two months free looks fine on a revenue dashboard and loses money on contribution. The usual answer, 15 per cent, is close to the line; 10 per cent leaves a clear margin.
Churn sets the answer almost on its own. The cost of capital moves it by a point or two: at 3 per cent churn, the revenue break-even is 16.7 per cent at a 5 per cent cost of capital, 19.8 per cent at 15 and 21.2 per cent at 20.
| Monthly churn | Reach renewal | Break-even, revenue | Break-even, contribution |
|---|---|---|---|
| 1% | 88.6% | 9.2% | 8.2% |
| 2% | 78.5% | 13.9% | 12.0% |
| 3% | 69.4% | 18.3% | 15.5% |
| 5% | 54.0% | 26.3% | 21.9% |
| 8% | 36.8% | 36.4% | 30.0% |
A product with high churn can afford a deep annual discount, because the discount is mostly buying retention. A product customers rarely leave can afford very little, because the discount is mostly a gift.
The 3 per cent churn is the average of the monthly base. The customers who choose the annual plan are not average: they are the ones already confident they will stay. If the people who take the offer would have churned at 1 per cent a month, their twelve monthly payments were worth 544.52 in present value. Selling them a year for 500.00 loses 44.52 of revenue each, and 50.53 of contribution (435.61 against 385.09).
Across 1,000 such customers, two months free costs 44,516 of revenue in the first year alone. The discount should be set on the churn of the customers who are likely to accept it, which in practice means looking at the cohort that already pays annually, or at monthly customers who have stayed past their first year, not at the whole base.
The other recurring error is to count the annual discount as a price cut on the 600.00 list and stop there. The value of an annual plan lives in the churn it removes and the cash it pulls forward; a discount set without those two numbers is a guess, and it is often the same mistake as an unpriced volume rebate. The real cost of a retroactive volume rebate works the same kind of hidden giveaway, and converting monthly churn to annual churn shows where the 69.4 per cent comes from.
Compute the present value of twelve monthly payments at your churn and cost of capital, subtract the cost of serving the customers who would have left, and the discount that remains is the most an annual plan can give: 15.51 per cent here, not the 16.67 per cent of two months free. Then rerun it at the churn of the customers who actually take the offer. Pricing Strategy treats every discount as a deduction on the way from list to pocket price, and the free workbooks for the book put a number on each one.
Only if monthly churn is high enough. Two months free is 16.67 per cent. On an illustrative 50 a month plan with a 10 per cent cost of capital and 80 per cent gross margin, it breaks even on contribution at about 3.3 per cent monthly churn; at 3 per cent it loses 6.95 per customer in the first year, and at 1 per cent churn the break-even is only 8.2 per cent.
Partly because the plan stops them leaving for twelve months, and partly because the customers who choose it already intended to stay. Only the first effect is bought by the discount. If the customers taking the offer would have churned at 1 per cent a month, their monthly payments were worth 544.52, so selling them a year at 500.00 loses 44.52 each.
On contribution. An annual customer who would have cancelled is still served for the rest of the year. With a 20 per cent cost to serve, the illustrative break-even falls from 18.33 per cent on revenue to 15.51 per cent on contribution, and two months free moves from a 9.96 gain to a 6.95 loss per customer.
This article is one calculation from Pricing Strategy. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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