The probability-weighted expected return method is simple arithmetic; what makes it defensible is forcing it to reproduce the price investors just paid.
A PWERM values a share by running the capital structure's waterfall in each exit scenario, weighting each payoff by its probability and discounting it to today. The rate is then calibrated so that the latest preferred round is worth what investors paid for it. On an illustrative venture-backed company with a 5.00 Series B, that calibration gives a rate of 19.5 per cent and a common share worth 3.95, or 79.0 per cent of the round price.
Worked in full in The Private Markets Valuation Specialist by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The probability-weighted expected return method is the natural choice when a company's exit routes are visible: a credible IPO, a likely trade sale, a downside sale and a failure. The arithmetic takes a page. The difficulty is that every probability and every exit value is a judgment, and an uncalibrated PWERM can produce almost any number. Calibration is what turns it into evidence.
| Class | Shares | Liquidation preference | Per share |
|---|---|---|---|
| Series B (senior) | 4,000,000 | 20.0m | 5.00 |
| Series A | 5,000,000 | 10.0m | 2.00 |
| Common | 10,000,000 | ||
| Total | 19,000,000 | 30.0m |
| Scenario | Equity value | Probability | Years to exit |
|---|---|---|---|
| IPO | 400.0m | 20% | 3 |
| Strategic sale | 120.0m | 40% | 3 |
| Downside sale | 30.0m | 30% | 2 |
| Dissolution | 0.0m | 10% | 1 |
Value per share = Σ probabilitys × payoff per shares / (1 + r)ts
In Excel, one row per scenario: =Prob*Payoff/(1+Rate)^Years, summed with =SUMPRODUCT. Then Goal Seek the rate so that the Series B value equals its issue price.
Step 1, the waterfall in each scenario. Each preferred series takes the better of its preference or conversion. At the IPO, 400.0m over 19,000,000 shares is 21.05 a share, so both series convert. In the strategic sale 120.0m is 6.32 a share, above the Series B's 5.00 preference, so everyone converts again. In the downside sale the Series B takes its 20.0m, the Series A its 10.0m, at 2.00 a share, and common receives nothing. In dissolution nobody receives anything.
Step 2, weight and discount at an assumed rate. At 25 per cent the Series B is worth 4.41 and the common 3.45.
Step 3, calibrate. Investors paid 5.00 for the Series B in an arm's length round. A model that says it is worth 4.41 is telling you its scenarios or its rate do not match what the market priced. Holding the scenarios, the rate that values the Series B at exactly 5.00 is 19.5 per cent.
| Scenario | Probability | Discount factor | Series B payoff | Series B weighted PV | Common payoff | Common weighted PV |
|---|---|---|---|---|---|---|
| IPO | 20% | 0.5862 | 21.05 | 2.47 | 21.05 | 2.47 |
| Strategic sale | 40% | 0.5862 | 6.32 | 1.48 | 6.32 | 1.48 |
| Downside sale | 30% | 0.7005 | 5.00 | 1.05 | 0.00 | 0.00 |
| Dissolution | 10% | 0.8369 | 0.00 | 0.00 | 0.00 | 0.00 |
| Value per share | 5.00 | 3.95 |
The common is worth 3.95 a share, a 21.0 per cent discount to the Series B, before any discount for lack of marketability the valuation policy applies to common.The whole of the gap comes from one row: in the downside sale the Series B collects 1.05 of present value per share and the common nothing. In the two good outcomes the classes are identical, because both preferred series convert.
Here calibration earns its keep. Change the scenario probabilities and an uncalibrated model swings widely; recalibrate each time and the answer is far more stable, because the round price keeps anchoring it.
| IPO / sale / dissolution | At 25%, uncalibrated | Calibrated rate | Common, calibrated | Share of round price |
|---|---|---|---|---|
| 10% / 40% / 20% | 2.37 | 7.7% | 3.71 | 74.1% |
| 10% / 50% / 10% | 2.69 | 11.5% | 3.79 | 75.9% |
| 20% / 30% / 20% | 3.13 | 16.2% | 3.89 | 77.8% |
| 20% / 40% / 10% (base) | 3.45 | 19.5% | 3.95 | 79.0% |
| 30% / 30% / 10% | 4.20 | 26.4% | 4.06 | 81.2% |
Uncalibrated, the common ranges from 2.37 to 4.20. Calibrated, from 3.71 to 4.06. But read the rate column too: a calibrated rate of 7.7 per cent for a venture-stage company is not credible, which says the pessimistic scenario set is inconsistent with the price investors paid. Calibration tests the scenarios as much as it sets the rate.
Check before you sign off: the calibrated rate should sit within the range of venture returns the valuation policy documents. If it does not, revisit the exit values and probabilities rather than accepting the rate.
The common mistake is to value the common at the round price, 5.00, as if every class were the same security; here that overstates it by 1.05 a share. The second is to choose probabilities and a discount rate independently and never test them against the transaction, which at 25 per cent would have put the common at 3.45 while implying the Series B investors overpaid by 13.4 per cent. A model that cannot reproduce the last price is not yet a valuation.
Waterfall each scenario, weight, discount, then calibrate to the latest round: here 19.5 per cent and 3.95 a share for common. The book's companion files run a full equity waterfall through participating and non-participating preferred in the free valuation workbooks, and the other way to calibrate the same kind of scenario model, holding the timing aside and solving for the upside exit value instead of the rate, is worked in why common stock is worth less than the preferred round price.
PWERM values each share class in a handful of discrete exit scenarios and weights them by probability; the option pricing method models equity as a continuous distribution and values each class as a call option. PWERM suits a company with visible exit routes. On the illustrative company PWERM gives common 3.95 a share against a 5.00 Series B.
The one that makes the model reproduce the most recent arm's length round. On the illustrative company an assumed 25 per cent values the Series B at 4.41, 11.8 per cent below the 5.00 investors paid, so the model is miscalibrated. The rate that returns 5.00 is 19.5 per cent, and the same rate is then applied to the common.
Because in the downside scenarios the liquidation preferences absorb the exit value. In a 30.0m sale the Series B takes 20.0m and the Series A 10.0m, so common receives nothing. Common only participates in the IPO and the strategic sale, which is why it is worth 79.0 per cent of the round price here.
This article is one calculation from The Private Markets Valuation Specialist. 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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