Backsolve Method
As discussed in the overview of the Option Pricing Model (OPM), one of the key inputs to the OPM is the Total Equity Value of the company. If the valuator has the Total Equity Value of an enterprise, then he/she can input that (along with the other parameters) into the OPM to derive the fair market value of common stock; i.e., the strike price at which future options should be issued.
There are an assortment of methods used to determine the Total Equity Value of a firm, one of which is the backsolve method.
Backsolve Overview
In an OPM framework, the backsolve method is used to answer the singular question:
What would the total value of the enterprise need to be, in order for a thirdparty investor to invest at the given pershare price, accounting for all liquidation preferences and seniorities for all share classes in the enterprise?
In other words, given that an investment occurred, the backsolve method outputs the implied total value of the enterprise if the valuation accounts for all share class rights and preferences, as of the date of the latest financing.
Backsolve Requirements
According to the AICPA, the backsolve is the most reliable indicator of enterprise value for earlystage customers, provided the following:
 transactions in the enterprise's shares have occurred at arm's length*
*Arm's length transaction: A transaction that was entered into by informed but unrelated market participants, simultaneously seeking the best terms possible.
Note: In many situations, the transactions are not done at arm's length. It is still possible to perform the valuation in these cases, but additional considerations need to be made.
Backsolve Considerations
Similar to the OPM, the backsolve considers the various terms of an enterprise's stockholder agreements that would affect the distributions to each class of equity upon a liquidity event as of the future liquidation date, including:
 the level of seniority among securities,
 dividend policy,
 conversion ratios,
 and cash allocations.
Backsolve Inputs
Similar to the OPM, the backsolve relies on these inputs:
 expected time to exit
 the riskfree interest rate as of the valuation date
 the volatility derived from similar publicly traded companies
However, while the total equity value is an input into the OPM, it is precisely the output of the backsolve.
Backsolve Example
eShares is engaged to value ABC, Inc., a small earlystage company that expects to exit in 5 years (t=5). Using a basket of similar public companies, eShares estimates the volatility to be 50%. Additionally, the riskfree rate from the valuation date until the exit date is 1.08% as of the valuation date.
ABC, Inc. Capitalization Table (as of valuation date):
Series Seed Preferred  Common  Common Options  
Number of shares:  1,000,000  500,000  125,000 
Purchase (or exercise) Price:  $1.00    $0.20 
Liquidation Multiplier  1.0x     
Liquidation Preference  $1,000,000     
First, eShares computes the equity breakpoints to determine which share class(es) will have value at various liquidation amounts for the company:
From  To  Description 
$0.00  $1,000,000.00  Series Seed Preferred only. 
$1,000,000.00  $1,100,000.00  Common shares only. 
$1,100,000.00  $1,600,000.00  Common options exercised 
$1,600,000.00  Infinity  Series Seed Preferred converts to common. 
Next, compute the implied calloption value of each of these breakpoints, using the BlackScholesMerton model:
$???  Total equity value
1.08%  Riskfree rate
50.00%  Volatility
5 years  Time to exit
Problem:
What's the right total equity value?
Solution:
By trialanderror, 'guess' total equity values until the pershare price of the Series Seed Preferred equals the price paid in the most recent transaction ($1.00)
Iteration 1: Try a value of $1,000,000.
$1,000,000  Total equity value
1.08%  Riskfree rate
50.00%  Volatility
5 years  Time to exit
From  To  Option Value  Incremental Option Value 
$0.00  $1,000,000.00  $439,426.46  $560,573.54 
$1,000,000.00  $1,100,000.00  $411,966.06  $27,460.40 
$1,100,000.00  $1,600,000.00  $307,497.12  $104,468.94 
$1,600,000.00  Infinity    $307,497.12 
    Total:  $1,000,000.00 
The above implies a pershare value of:
From  To  Series Seed Preferred 
Common Shares 
Common Options 
$0.00  $1,000,000.00  $560,573.54  $0.00  $0.00 
$1,000,000.00  $1,100,000.00  $0.00  $27,460.40  $0.00 
$1,100,000.00  $1,600,000.00  $0.00  $83,575.15  $20,893.79 
$1,600,000.00  Infinity  $189,229.00  $94,614.50  $23,653.62 

Total:  $749,802.54  $205,650.05  $44,547.41 

Value per share:  $0.75  $0.41  $0.36 
Problem:
The implied value per Series Seed Preferred share is too low (it should be $1.00 instead of $0.74).
Iteration 2: Try a value of $2,000,000.
$2,000,000  Total equity value
1.08%  Riskfree rate
50.00%  Volatility
5 years  Time to exit
From  To  Option Value  Incremental Option Value 
$0.00  $1,000,000.00  $1,265,356.77 
$734,643.23 
$1,000,000.00  $1,100,000.00  $1,215,494.98  $49,861.79 
$1,100,000.00  $1,600,000.00  $1,007,497.28  $207,997.70 
$1,600,000.00  Infinity    $1,007,497.28 
    Total:  $2,000,000.00 
The above implies a pershare value of:
From  To  Series Seed Preferred 
Common Shares 
Common Options 
$0.00  $1,000,000.00  $734,643.23  $0.00  $0.00 
$1,000,000.00  $1,100,000.00  $0.00  $49,861.79  $0.00 
$1,100,000.00  $1,600,000.00  $0.00  $166,398.16  $41,599.54 
$1,600,000.00  Infinity  $619,998.33  $309,999.16  $77,499.79 

Total:  $1,354,641.56  $526,259.11  $119,099.33 

Value per share:  $1.35  $1.05  $0.95 
Problem:
The implied value per Series Seed Preferred share is too high (it should be $1.00 instead of $1.35).
Iteration 3: Try a value of $1,407,116.15.
$1,407,116.15  Total equity value
1.08%  Riskfree rate
50.00%  Volatility
5 years  Time to exit
From  To  Option Value  Incremental Option Value 
$0.00  $1,000,000.00  $756,202.27 
$650,913.88 
$1,000,000.00  $1,100,000.00  $718,125.95  $38,076.31 
$1,100,000.00  $1,600,000.00  $566,306.00  $151,819.95 
$1,600,000.00  Infinity    $566,306.00 
    Total:  $1,407,116.15 
The above implies a pershare value of:
From  To  Series Seed Preferred 
Common Shares 
Common Options 
$0.00  $1,000,000.00  $650,913.88  $0.00  $0.00 
$1,000,000.00  $1,100,000.00  $0.00  $38,076.31  $0.00 
$1,100,000.00  $1,600,000.00  $0.00  $121,455.96  $30,363.99 
$1,600,000.00  Infinity  $348,496.00  $174,248.00  $43,562.00 

Total:  $999,409.88  $333,780.28  $73,925.99 

Value per share:  $1.00  $0.67  $0.59 
Success:
The implied value per Series Seed Preferred equals the price that was paid in the most recent investment ($1.00).
Thus, the Total Equity Value that would be used as input into the OPM would be $1,407,116.15.
For a refresher on how pershare values are calculated using the OPM, see the Option Pricing Model article.