The Backsolve Method Explained Step-by-Step (with Worked Example)
The Backsolve Method uses a recent funding round price to work backward to a company's total equity value, then allocates that value across share classes. Here is exactly how it works, when to use it, and a full numerical example.
Key Takeaways
- check_circleThe Backsolve Method uses the price paid in a recent funding round to solve backward for the company's total implied equity value.
- check_circleIt relies on the Option Pricing Model (OPM) to allocate that total equity value across preferred shares, common shares, and options.
- check_circleThe method is accepted by the AICPA Practice Aid, the IRS, and the SEC for 409A valuations when a recent arm's-length transaction exists.
- check_circlePreferred liquidation preferences must be modeled accurately; ignoring them can materially understate the implied equity value.
- check_circleWhen the latest round is senior to earlier classes, or market conditions have shifted, analysts should consider adjustments or supplemental methods.
- check_circleThe common stock value per share is typically lower than the preferred price per share because common stock lacks liquidation preference and other protective rights.
You closed a Series A at $8.00 per preferred share. Your board wants to grant options to new engineers. Before you can set a strike price, you need the fair market value (FMV) of your common stock, and that number is not $8.00. Preferred shares carry liquidation preferences, anti-dilution rights, and other protections that common stock does not. The Backsolve Method is the standard technique for translating a known preferred share price into a defensible common stock FMV. This guide walks through the method step-by-step, explains the Option Pricing Model (OPM) mechanics underneath it, and closes with a worked numerical example you can follow in a spreadsheet.
What the Backsolve Method Actually Does
The Backsolve Method, formally called the subject company transaction method, starts from an observed fact: the price per share paid by investors in a recent, arm's-length financing round. It then asks a specific question: what total equity value for the company would cause the OPM to allocate exactly that price to the most recently issued preferred share class?
The answer, the implied total equity value, is the backsolve output. Once you have it, you run the OPM forward to allocate that total value across all share classes and arrive at a per-share FMV for common stock. The AICPA Practice Aid, the IRS, and the SEC all accept this approach for IRC Section 409A (the federal tax code section governing deferred compensation) purposes when a recent transaction exists.
The OPM Foundation: Breakpoints and Call Options
The OPM treats each share class as a call option on the company's total equity value. The key insight is that common stock has value only when the total proceeds available at a liquidity event exceed the liquidation preferences of all senior share classes. Below that threshold, preferred shareholders absorb the entire exit value.
In practice, the OPM commonly uses the Black-Scholes option pricing model to price these call options. The model requires five inputs for each breakpoint in the capital structure:
- Total equity value (the variable being solved for in the backsolve step)
- Breakpoint (the liquidation preference or conversion threshold for each share class)
- Expected time to a liquidity event (in years)
- Equity volatility (typically benchmarked against comparable public companies)
- Risk-free rate of interest
The OPM calculates the value of a call option at each breakpoint, then subtracts adjacent call option values to determine how much of the total equity value falls within each share class's range. The result is a dollar allocation to each class, which you divide by shares outstanding to get a per-share value.
Step-by-Step: Running the Backsolve
- Map the full cap table. List every share class (common, Series A preferred, Series B preferred, options, warrants), the number of shares, liquidation preferences, and conversion ratios. Errors here propagate directly into the output.
- Identify the reference transaction. Confirm the most recent round was arm's-length and closed near the valuation date. If the round was a distressed financing or involved a strategic investor paying a premium, the price may not represent FMV and adjustments may be needed.
- Set the OPM assumptions. Choose expected time to liquidity, equity volatility, and risk-free rate. Volatility is often derived from the historical trading volatility of comparable public companies.
- Solve for implied total equity value. Using a goal-seek or iterative solver, find the total equity value that causes the OPM to allocate exactly the observed preferred price per share to the most recently issued preferred class. This is the backsolve step.
- Allocate value to common stock. With the implied total equity value fixed, run the OPM forward. The model distributes value across all share classes based on their breakpoints and option values.
- Apply a DLOM if appropriate. Common stock in a private company is illiquid. A Discount for Lack of Marketability (DLOM) is typically applied to the common stock value. The appropriate range depends on facts and circumstances.
- Conclude on common stock FMV. Divide the post-DLOM common stock value by common shares outstanding to arrive at the per-share FMV used for option strike prices.
Worked Example: Series A Backsolve
Here is what typically happens in a straightforward Series A scenario. The numbers below are illustrative.
Cap Table and Round Terms
| Share Class | Shares Outstanding | Liquidation Preference per Share | Total Liquidation Preference |
|---|---|---|---|
| Series A Preferred | 1,000,000 | $8.00 | $8,000,000 |
| Common Stock | 5,000,000 | None | N/A |
| Options (unexercised) | 500,000 | None | N/A |
| Total (fully diluted) | 6,500,000 |
The Series A closed at $8.00 per preferred share, implying a post-money headline value of $52,000,000 (6,500,000 fully diluted shares × $8.00). The backsolve will produce a different, typically lower, implied equity value because it accounts for the preferred stock's seniority.
OPM Assumptions
| Assumption | Value | Notes |
|---|---|---|
| Expected time to liquidity | 4.0 years | Management estimate |
| Equity volatility | 55% | Benchmarked to comparable public companies |
| Risk-free rate | 4.5% | Approximate current rate; use the rate at valuation date |
| Series A liquidation preference | $8,000,000 | 1,000,000 shares × $8.00 |
The Backsolve Calculation
The OPM has one breakpoint in this simplified example: the Series A liquidation preference of $8,000,000. Below that threshold, all exit proceeds go to Series A preferred. Above it, common stock participates.
Goal: find Total Equity Value (TEV) such that:
OPM allocation to Series A preferred / Series A shares = $8.00
Breakpoint B1 = $8,000,000 (Series A liquidation preference)
Value of call option at B1 = Black-Scholes(TEV, B1, t=4, σ=55%, r=4.5%)
Value of call option at B2 = Black-Scholes(TEV, ∞, ...) = TEV (trivially)
Allocation to preferred = TEV - Call(TEV, B1)
Allocation to common = Call(TEV, B1)
Solve iteratively until:
(TEV - Call(TEV, B1)) / 1,000,000 = $8.00Running a goal-seek on this system (for example, in Excel using Data > What-If Analysis > Goal Seek) produces an implied total equity value of approximately $35,000,000 in a scenario with these assumptions. The preferred stock absorbs $8,000,000 of that value (its liquidation preference), and the remaining $27,000,000 is allocated to common stock and options.
Allocating to Common Stock
| Share Class | Allocated Value | Shares | Value per Share (pre-DLOM) |
|---|---|---|---|
| Series A Preferred | $8,000,000 | 1,000,000 | $8.00 |
| Common Stock + Options | $27,000,000 | 5,500,000 | $4.91 |
| Total | $35,000,000 | 6,500,000 |
After applying a DLOM of, say, 20% (subject to facts and circumstances), the concluded common stock FMV would be approximately $3.93 per share. That is the strike price for options granted at this valuation date, not $8.00. The gap illustrates exactly why the backsolve exists: the headline preferred price overstates common stock value when preferred shares carry meaningful liquidation preferences.
When to Use the Backsolve Method (and When Not To)
The method works best when a recent, arm's-length transaction exists and the round is representative of fair market value. The IPEV Guidelines note that when a recent transaction exists, it should be considered, but when the transaction price is not representative of FMV, analysts should consider adjustments or other methods.
| Situation | Backsolve Appropriate? | Notes |
|---|---|---|
| Recent priced round, arm's-length | Yes | Primary method for 409A; accepted by IRS, AICPA, SEC |
| Round closed more than 12 months ago | With caution | Staleness may require supplemental methods or adjustments |
| Latest round is senior to all prior classes | With caution | IPEV flags this as a specific risk; consider adjustments |
| Strategic investor paid a control premium | Adjust or supplement | Transaction price may exceed FMV for minority common shares |
| Pre-revenue, no priced round | No | Use income approach, asset approach, or GPC method instead |
| Multiple plausible exit scenarios | Hybrid | Combine with PWERM; backsolve provides equity value in one scenario |
Advantages and Limitations
| Advantages | Limitations |
|---|---|
| Grounded in an actual investor transaction | Requires a recent, arm's-length priced round |
| Accepted by IRS, AICPA Practice Aid, and SEC | Staleness: value drifts as time passes since the round |
| Accounts for preferred share seniority and liquidation preferences | Sensitive to volatility and time-to-exit assumptions |
| Produces a defensible, auditable common stock FMV | Latest round being senior can distort the implied value |
| Straightforward to implement with goal-seek tools | Does not capture company-specific developments post-round |
How the Backsolve Fits Into a Full 409A
The Backsolve Method is one of three standard approaches accepted for 409A purposes. The other two are the income approach (typically a Discounted Cash Flow analysis) and the asset approach. For a deeper look at how these methods compare and when each is appropriate, see our guide on startup valuation methods explained. For background on the 409A process itself, including safe harbor rules and when a refresh is required, see what is a 409A valuation.
In practice, most 409A reports for post-seed and Series A companies weight the Backsolve result heavily, sometimes exclusively, when the round is recent and arm's-length. Later-stage companies with meaningful revenue may blend the Backsolve with a Guideline Public Company (GPC) analysis. For a comparison of income-based and market-based approaches, see our post on DCF vs. GPC valuation approaches.
Key Inputs Checklist Before You Start
- Fully diluted cap table with all share classes, liquidation preferences, and conversion ratios
- Closing documents for the most recent round (price per share, date, investor identity)
- Confirmation that the round was arm's-length (not a related-party or distressed transaction)
- List of comparable public companies for volatility benchmarking
- Management's estimate of time to a liquidity event
- Current risk-free rate (typically the yield on a U.S. Treasury note matching the expected holding period)
- DLOM analysis (quantitative model or qualitative factors, depending on the report standard)
The Backsolve Method is not complicated in concept, but it is sensitive to inputs that require real judgment. Getting the cap table wrong, skipping the preferred-share seniority, or anchoring volatility to an irrelevant peer set can each move the concluded common stock FMV by a meaningful amount. The key is treating each assumption as a documented, defensible choice rather than a default.
Frequently Asked Questions
What is the Backsolve Method in valuation?expand_more
The Backsolve Method, also called the subject company transaction method, uses the price paid by investors in a recent funding round to calculate the implied total equity value of a company. It works backward through an Option Pricing Model (OPM) to determine what enterprise value would produce the observed per-share price for the most recently issued share class.
Why is the Backsolve Method used for 409A valuations?expand_more
When a startup has recently closed a priced funding round, that transaction is treated as an arm's-length indicator of fair market value. The AICPA Practice Aid, the IRS, and the SEC all accept the subject company transaction (Backsolve) method for 409A purposes. It provides a defensible, auditable starting point that is grounded in an actual investor price rather than projections.
How is the Backsolve Method different from the post-money valuation?expand_more
The post-money valuation is simply the round price multiplied by fully diluted shares. The Backsolve Method goes further: it uses the OPM to account for the seniority, liquidation preferences, and economic rights of each share class. The resulting common stock FMV is typically lower than the headline post-money figure because common shares lack the downside protection that preferred shares carry.
What inputs does the OPM Backsolve require?expand_more
The key inputs are: the price per share paid in the most recent round, the full cap table (all share classes, liquidation preferences, and conversion ratios), expected time to a liquidity event, equity volatility (often benchmarked against comparable public companies), and the risk-free rate. Volatility and time-to-exit are the assumptions that most affect the common stock allocation.
When should analysts consider adjusting or replacing the Backsolve Method?expand_more
Adjustments are warranted when the most recent round is not representative of fair market value, for example if it was a distressed financing, a strategic investor paid a premium, or significant time has passed since the round. The IPEV Guidelines note that when a transaction is not representative of FMV, analysts should consider adjustments to the transaction price or use supplemental methods.
Can the Backsolve Method be used alongside other valuation methods?expand_more
Yes. In practice, analysts often weight the Backsolve result alongside a Guideline Public Company (GPC) method or a Discounted Cash Flow (DCF) analysis. A hybrid approach, sometimes called a PWERM-OPM hybrid, is also used when multiple exit scenarios are plausible, with the Backsolve providing the equity value under one of those scenarios.
