When do Firms Invest in Corporate Social Responsibility? A Real Option Framework

Abstract

In this paper, the process for firms to decide whether or not to invest in corporate social responsibility is treated from a real option perspective. We extend the Husted (J Bus Ethics 60:175–183, 2005) framework with an important extra parameter that allows us to understand the timing of CSR investment and explain why some companies drag their feet over CSR investments. Our model explicitly allows for the impact of the opportunity cost of delaying the CSR investment decision, providing firms with tools to determine the optimal moment of exercising the CSR investment option. We illustrate our timing model through a case study and analyze governmental support strategies for CSR from a real options perspective.

Appendix 1: The Black–Scholes Formula for Call Option Valuation

The valuation models for real options are based on the financial options’ models. The most commonly used model has been developed by Black and Scholes (1973) and Merton (1973) and is commonly referred to as the Black–Scholes model. Its popularity is derived from its closed-form solution, allowing computing the value much more simple, and in addition, the model makes it easier to conduct a sensitivity analysis using partial derivatives. The Black–Scholes analysis assumes the following (Hull 2000): (1) frictionless markets, i.e. no transaction costs or taxes, nor restrictions on short sales; (2) continuous trading is possible; (3) the risk-free (short-term) interest rate is constant over the life of the option; (4) the market is arbitrage-free; (5) the time process of the underlying asset price is stochastic and exhibits a geometric Brownian motion.¹⁰ This process assumes asset prices to be log-normally distributed and returns to be normally distributed. Obviously, any violation of some of these assumptions may result in a different option valuation model. The goal of this article is not to provide a precise estimate of the CSR option value, but to present a richer conceptual framework that provides additional insights compared to a more conventional NPV analysis. It will be left to future research which option valuation model is the most appropriate to value CSR options, whenever a more precise estimate of the option value matters. The option value C according to the Black–Scholes model can be calculated as:

$$C = V\,e^{{ - \delta \left( {T - t} \right)}} \;N(d_{1} ) - I\;e^{{ - r_{\text{c}} \left( {T - t} \right)}} \;N(d_{2} ), \quad {\text{where}}$$

(A.1)

$$d_{1} = \frac{{\ln \left( \frac{V}{I} \right) + \left( {r_{\text{c}} - \delta + \frac{1}{2}\sigma^{2} } \right)\left( {T - t} \right)}}{{\sigma \sqrt {T - t} }}$$

(A.2)

$$d_{2} = \frac{{\ln \left( \frac{V}{I} \right) + \left( {r_{\text{c}} - \delta - \frac{1}{2}\sigma^{2} } \right)\left( {T - t} \right)}}{{\sigma \sqrt {T - t} }} = d_{1} - \sigma \sqrt {T - t} ,$$

(A.3)

where V is the present value of the future FOCFs from CSR, I is the capital expenditure (CSR investment cost), T-t is the time to expiration (in years), σ is the annualized standard deviation of the CSR project return (V), r _c is the continuous risk-free interest rate, δ is the opportunity cost, and N(d) is the cumulative normal probability density function.

The effect of a change in one of the parameters on the value of the call option (the so-called Greeks), i.e. the first derivative, is calculated as follows

Sensitivity of C to	Name and symbol		Formula and sign of impact on C
Benefits of investment in CSR (V)	Delta	∆	e −δ(T−t) N(d 1) > 0
Investment cost of CSR (I)	Psi	Ψ	− e −r(T−t) N(d 2) < 0
Lifetime (T-t)	Theta	Θ	$\begin{gathered} \frac{{ - V\;n\left( {d_{1} } \right)\;\sigma \;e^{{ - \delta \;\left( {T - t} \right)}} }}{{2\;\sqrt {T - t} }} - r\;Ie^{{ - r\;\left( {T - t} \right)}} \;N\left( {d_{2} } \right) \hfill \\ + \delta \;V\;N\left( {d_{1} } \right)\;e^{{ - \delta \;\left( {T - t} \right)}} \hfill \\ \end{gathered}$ > 0
Risk-free interest rate (r)	Rho	$\rho$	I (T-t)e −r(T−t) N(d 2) > 0
Volatility (σ)	Vega	V	$V\;\sqrt {T - t} \;N\left( {d_{1} } \right)\;e^{{ - \delta \;\left( {T - t} \right)}}$ > 0
Opportunity cost (δ)	Ksi	≡	− V(T-t)e −δ(T−t) N(d 1) < 0

1. The value N(d ₁) is the derivative of the standard normal distribution function with respect to d ₁