Investment Appraisal

What is Real Options in Investment Appraisal?

The concept of real option in investment appraisal attempts to classify and value flexibility or choices which is present when financial advisors are deciding on whether to undertake an investment project. These are flexibility in capex investment decisions which represent choices or existence of options which may alter the financial outcome in between the project tenure.

These represent options on real physical assets which have a value in addition to conventional NPV. Strategic NPV = Conventional NPV + Value of real option.

These are like: options to delay the project at the start of it or in-between, option to expand the project, option to abandon or sale the project in-between, or option to redeploy.

Real option methodology considers the time available before a decision on the option to be made and the risk & uncertainties attached to the project. The value of the real option can be estimated through BSOP model (Black-Scholes Options Pricing Model).

In BSOP model, for real options Pe is the capital investment required for future expansion in case of call options or the amount to be received when put option would be exercised. Pa is the present value of future cash flows arising from the project after Option expire date.

Here’s a breakdown of the formula and its components, considering both call and put options:

Call Option Formula:
C = Pa * N(d1) – (Pe * N(d2) * e^-rt)

Put Option Formula:
P = c – Pa + Pe*e^-rt

Where:
C: The value of the call option
P: The value of the put option
d1: The first price difference =(ln(Pa/Pe) + (r + 0.5s^2) * t) / (s * sqrt(t))
d2: The second price difference =d1 – s * sqrt(t)
N(d): The cumulative standard normal distribution function in excel =NORMSDIST( )

Key Variables:
Pa: Present value of the underlying asset’s future cash flows after real option expiry date
Pe: Exercise price, i.e., cost to invest in the project in case of call option like expansion or selling price to be received in case of put option like divestment
t: Time to expiry of the option in years
r: Risk-free interest rate
s: Volatility of cash flows: standard deviation
e = 2.71828, exponential constant, in excel =EXP(1)

However, the BSOP model has certain assumptions which may act as limitation for certain scenarios. For example, the BSOP model assumes that the real option is a European style option, which can only be exercised on the option expiry date which may not be true for all real options. Similarly, assumptions like accuracy of volatility, constant value of interest rates & volatility, accuracy of time to expiry and other information may not be perfect for real options.

Furthermore, real options are available on large, once-off projects, for which there would be little or no historical data available and are not traded in financial market, hence accurate availability of variables could be a challenge but could be estimated using simulation models.