Breakpoints, Black-Scholes calls and a goal seek: the option pricing model calibrated to the latest round, worked from start to finish.
An OPM backsolve finds the total equity value at which the option pricing model values the newly issued preferred share at exactly the price paid, then reads every other class from the same model. In an illustrative company whose Series B is priced at $5.00, implying a post-money of $75.0 million, the backsolved equity value is $44.01 million and the common stock is worth $2.52 a share before any marketability discount, 50.4 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 company is fictional. It has just closed a Series B and the valuation team must mark both the fund's holding and, for other purposes, the common stock. The round price is the best evidence of value available, but it is a price for a preferred share with rights the common does not have. The backsolve calibrates the model to that price rather than multiplying it by the share count.
| Input | Value |
|---|---|
| Common shares | 10,000,000 |
| Series A preferred, preference $2.00 a share | 3,000,000 |
| Series B preferred, issued at $5.00 a share | 2,000,000 |
| Series B raised | $10.0m |
| Volatility | 60% |
| Time to liquidity event | 3 years |
| Risk-free rate | 4% |
| Post-money (15,000,000 shares × $5.00) | $75.0m |
The OPM treats each class of equity as a strip of call options on the company's total equity value. The strike prices of those calls are the breakpoints: the equity values at which the next class starts to share in each extra dollar.
| Tranche ($m) | Why it ends there | Common | Series A | Series B |
|---|---|---|---|---|
| 0 to 10.0 | Series B preference paid | 0% | 0% | 100% |
| 10.0 to 16.0 | Series A preference paid | 0% | 100% | 0% |
| 16.0 to 36.0 | Common reaches $2.00, Series A converts | 100% | 0% | 0% |
| 36.0 to 75.0 | Common and A reach $5.00, Series B converts | 76.92% | 23.08% | 0% |
| Above 75.0 | All shares as converted | 66.67% | 20.0% | 13.33% |
The third breakpoint is 16.0 plus 10,000,000 common shares times $2.00. The fourth is 36.0 plus 13,000,000 shares times the $3.00 gap between $2.00 and $5.00. Getting these two right is most of the work: a non-participating preferred holder converts when the common value per share reaches its preference per share, not when total equity reaches the post-money.
Each breakpoint is priced as a Black-Scholes call on total equity value S. The value of a tranche is the call at its lower strike less the call at its upper strike, and each class takes its share of each tranche.
Call(S, K) = S × N(d1) − K × e^(−rT) × N(d2), with d1 = [ln(S/K) + (r + σ²/2)T] / (σ√T), d2 = d1 − σ√T
Series B value = tranche 1 + 13.33% × tranche 5
Solve for S such that Series B value / 2,000,000 = $5.00. In Excel, put S in one cell, build the five calls with NORM.S.DIST(d,TRUE), and use Goal Seek on the Series B per-share cell.
The search lands on S = $44.01 million. At that value the calls at the five strikes are 44.01, 35.64, 31.49, 21.75 and 12.2 million, which gives the tranche values below.
| Tranche | Value | Common | Series A | Series B |
|---|---|---|---|---|
| 1 | 8.37 | 0.00 | 0.00 | 8.37 |
| 2 | 4.15 | 0.00 | 4.15 | 0.00 |
| 3 | 9.74 | 9.74 | 0.00 | 0.00 |
| 4 | 9.54 | 7.34 | 2.20 | 0.00 |
| 5 | 12.20 | 8.13 | 2.44 | 1.63 |
| Total | 44.01 | 25.22 | 8.79 | 10.00 |
| Per share | $2.52 | $2.93 | $5.00 |
The Series B is worth exactly its $10.00 million cost, which is the calibration. The equity value that produces that result is $44.01 million, 58.7 per cent of the $75.0 million post-money. The difference is not a write-down. The post-money assumes every share is worth the Series B price; the backsolve recognises that the Series B paid $5.00 partly for a senior preference that pays it more than its as-converted share in every outcome below $75.0 million.
The common stock, at $2.52 a share, is the figure that feeds a common stock valuation once a discount for lack of marketability is applied. The Series A, at $2.93, is worth more than its $2.00 preference because it also holds the upside above the third breakpoint. The scenario-based version of the same idea, with explicit exit outcomes rather than a volatility, is in why common stock is worth less than the preferred round price.
| Volatility / term | Equity value ($m) | Common per share |
|---|---|---|
| 40%, 3 years | 49.81 | $2.99 |
| 60%, 3 years | 44.01 | $2.52 |
| 80%, 3 years | 45.32 | $2.64 |
| 60%, 2 years | 42.02 | $2.36 |
| 60%, 4 years | 46.14 | $2.70 |
The common value ranges from $2.36 to $2.99, a spread of 63 cents, across a plausible range of inputs, and not always in the direction intuition suggests. Raising volatility from 40 to 60 per cent lowers the common value, while raising it again to 80 per cent increases it. Higher volatility makes the senior preference more valuable, so the backsolve needs less total equity to justify the Series B price, but it also adds option value to the common. Which effect wins depends on where the breakpoints sit. The inputs therefore need evidence, typically guideline company volatilities and a term tied to the expected exit, rather than a convention.
The backsolve calibrates to one security. If the round was priced with unusual terms, such as a participating preference, a ratchet or a strategic investor paying for commercial rights, the price is evidence of the preferred's value under those terms and the model must carry them, or the calibration transfers the distortion to every other class.
An OPM backsolve turns a preferred round price into an equity value and a value per class that all reconcile to the same transaction. Build the breakpoints from the terms, price them as calls, solve so the new security is worth what was paid, and disclose the volatility and term, because they move the common more than any other input. Calibration to the entry price runs through the free companion workbooks, and the related hybrid method combines this model with explicit exit scenarios.
Because the post-money prices every share at the preferred price, while the preferred paid partly for its liquidation preference. In the illustrative case the $75.0 million post-money backsolves to $44.01 million of equity value, 58.7 per cent of it. The difference reflects the preference rights of the Series B, not a fall in value.
Usually the volatility of guideline public companies, adjusted for stage and leverage, over a term matching the expected time to exit. The choice matters: in the worked case moving between 40 and 80 per cent volatility, or between 2 and 4 years, moves the common between $2.36 and $2.99 a share, and not in one direction.
No. The backsolve gives a marketable minority value per share for each class, here $2.52 for the common. A discount for lack of marketability is applied afterwards, typically to the common only, using a put option model or another supportable method, before the value is used for option grants or reporting.
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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