Valuation Techniques: Discounted Cash Flow, Earnings Quality, Measures of Value Added, and Real Options

VALUE OF LIQUIDITY

Longstaff’s fundamental insight is that liquidity is properly construed as the option to sell an asset at the time of one’s choosing (i.e., liquidity is a put option). Thus, the value of liquidity can be estimated by using techniques from option-pricing theory. Longstaff’s analysis assumes a hypothetical world where a perfectly liquid asset is continuously traded in a frictionless market with a constant riskless interest rate and where an investor with perfect market timing sells the asset and invests the proceeds in the riskless asset to maximize the value of the investor’s portfolio. If the investor is restricted from selling the asset for a period of time equal to T, the investor cannot trade assets optimally to maximize the value of the portfolio.

Longstaff derived a model that measures the loss in value resulting from the opportunity cost imposed by the period of time during which the asset is not liquid. This model is as follows:

(14.1)

where

σ = standard deviation of the company’s daily stock returns (annualized)

T = length of time that the shares are illiquid

N(d) = probability that a standardized, normally distributed, random variable is greater or less than d, where

This model calculates the largest percentage discount for the absence of liquidity that ...