778  Flexibility
Data Availability: Traded vs. Untraded Assets  The results of any contingent 
valuation critically depend on well-grounded estimates for the value and the 
variance of cash flows from the underlying asset.
If the estimate for the underlying asset value is inaccurate, the flexibility 
value also will be inaccurate. Returning to our first example, if we estimate 
incorrectly the future cash flows generated by a highly effective drug, the 
value of the option to defer will be inaccurate. In practice, you would have to 
estimate the value with a full-fledged DCF model projecting sales growth, op-
erating margins, capital turnovers, and so on. All ROV (and DTA) approaches 
build on this valuation of the underlying asset.
A similar argument holds for estimates of the variance of the underlying as-
set’s cash flows (called volatility in the option-pricing literature). Volatility can 
have a great impact on value, because real options typically have long lifetimes 
and are often at-the-money or close to it,17 meaning the decision of whether to 
undertake the project is a close call.18 Still, for many managers and practitioners, 
volatility remains an abstract concept: how do you reasonably estimate the range 
of cash flow outcomes from the sale of a product that has yet to be released?19
Sometimes the underlying asset value and variance can be derived from 
traded assets. Examples include options to shut down gas-fueled power gener-
ation, abandon a copper mine, or defer production of an oil field. In such cases, 
because you can estimate the key inputs with reasonable accuracy, ROV should 
be more accurate than DTA. When estimates for the underlying asset valuation 
and variance (volatility) cannot be derived from traded assets and are largely 
judgmental, a DTA approach is more appropriate. It is more straightforward 
and transparent to decision makers than the ROV approach. Transparency is 
especially important when critical valuation assumptions require the decision 
maker’s judgment. DTA captures the essence of flexibility value, and the theo-
retical advantage of ROV is less important if required inputs are unavailable.
Four Steps to Valuing Flexibility
To value flexibility, use the four-step process illustrated in Exhibit 39.10. In 
step 1, conduct a valuation of the investment project without flexibility, using 
a traditional discounted-cash-flow model. In step 2, expand the DCF model 
into an event tree, mapping how the value of the project evolves over time, 
using (unadjusted) probabilities and the weighted average cost of capital. At 
this stage, the model does not include flexibility, so the present value of the 
17 It follows from option-pricing theory that the sensitivity of option value to changes in variance (re-
ferred to as vega) increases as the option’s lifetime increases and as the option is closer to the money. 
An option is at-the-money if its exercise price equals the value of the underlying asset.
18 If the investment decision were a clear go or no-go, there would be little value in flexibility in the first 
place, and no need to consider the option value.
19 The range needs to include the associated probabilities to provide a variance estimate.