2. Estimating the Valuation Parameters

We have seen in the section on option valuation that we generally need to know 6 parameters to estimate the value of the option: 

  • S: Current value of the underlying asset
  • X: Exercise price; Expenditures required to acquire the asset
  • T-t: Length of time until the option can be exercised
  • r: Risk-free rate of return (time value of money)
  • y: Dividend yield; benefits (negative if costs) of owning the asset during the life of the option
  • σ: Riskiness of the project (u and d in the case of the binomial model we considered)

 

The question is how to get estimates for these key variables in the context of real options. Here are some recommendations:

 

Parameter Estimation / Approximation
Value of underlying asset (S)
  • Use current market price if available (rarely the case for real options)
  • If there is no market value, conduct a discounted cash flow (DCF) analysis. Specifically, estimate the present value of all future cash flows (EXCLUDING THE INVESTMENT X!) if you take the project now.
Volatility of the underlying asset (σ)
  • Use the volatility of the change in asset value of comparable firms (rarely possible)
  • Use the cash flow variance from firms with similar assets (rarely possible)
  • Simulate many different scenarios for your project (how you derived S, see above) and obtain the volatility of the estimated present values. Theis requires assumptions about the cash flows under different scenarios as well as the probabilities of different outcomes.
Exercise price (X)
  • Estimate the cost of making the investment in the project. Check if that cost is more or less constant over time
Time to maturity (T-t)
  • Estimate for how many years (periods) the option grants you exclusivity.
  • In the case of a license or a patent, time to maturity could be the life of the license / patents
  • In other constellations, time to maturity could be how long it takes competitors to catch up with your investments and learning curve
Risk-free rate of return (r)
  • Government bond yield for the duration of the option (T-t) and denominated in the currency in which you value the project.
  • If the country of the reference currency is not "risk-free" use U.S. bond yields and translate them into your home-country rate using purchasing power parity (as an approximation, add the expected inflation differential between the reference country and the U.S.).
Dividend yield (y)
  • If the underlying investment project has a finite lifetime, postponing the investment decision imposes a cost of delay, because postponing the investment decision translates into one less year of value-creating cash flows!
  • In the case of a patent, for example, the investment opportunity might be worthless at the end of the patent because competitors will be able to replicate the idea.
  • To approximate the cost of delay in such situations, you could assume that:
     
    Annual cost of delay = y = 1/lifetime of the patent