Inputs required in the application of the real options model

As discussed in the previous sections, the RO approach utilizes the Black Scholes Option Pricing Model. The Black Scholes Options Pricing Model (BSOPM)187 is a valuation model with a built-in capability to replicate a non-arbitrage (risk-neutral) portfolio.

184

Trevor Vigfusson, CFO, Nike Global Retail, on new retail stores “risk assessment”: establishing store risk analogies and analyzing store attributes can improve risk predictability.”

185 _{Detailed reference see footnote in Literature Review. Here is a brief description for reference. The build}

option refers to most complex investments generate sequential decisions and cash outlays. The defer / delay option refers to the investments are delayed due to the internal resources limitation and/or the market (un)favorable conditions. The expansion option refers to changing operating scale, expand or contract capacity, following the evolution of the market. The option to abandon is the possibility to completely withdraw from the market and sell the facilities at their salvage value in an economically favorable environment. Divestment is considered as the Put Real Options. This application is for further research.

186

Actual investment details may not disclose for business confidentiality. Details disclosed here is only for the purpose of this study. The final presentation of this paper may only provide partial disclosure.

187 _{Black Scholes, op. cit. Black and Scholes (1973) stated, “it is possible to create a fully hedged position,}

Equation 2 indicates that the value of the call option in real assets depends on six variables. S is the present value of the underlying asset which is determined from

discounting and summing the expected cash flows from the investment. In our case studies, it is the management’s estimations of net cash inflows discounted by the corporate Weighted Average Cost of Capital (WACC). X is the option strike price. It is the cost in present value terms of the investment calculated by discounting and summing the estimated cash outflows using the risk free rate. Note that S minus X is the NPV.

The third variable is sigma (σ), which measures the volatility of the underlying asset value. We note here the counterintuitive implication of volatility and call value when compared to NPV. For example, if there is significant uncertainty or variance in the value of the underlying asset, sigma will have a higher value and from the BSOPM, the call option value will increase. This is counterintuitive because in the NPV approach, increased uncertainty is compensated by increasing the discount rate to account for the increased risk which should then lower the sum of the present value of the cash inflows, reducing NPV. In short, higher volatility increases the real option value of the investment, but higher volatility decreases computed NPV. Reliance on NPV alone becomes

problematic if real options, as hypothesized, are shown to have value. As stated before, the remodeling project or any real assets is not traded, thus, the value of sigma cannot be observed from the market and must be estimated.

The fourth variable is “t”, the time period for which the investment opportunity is valid. The fifth variable is “r”, risk-free rate, assuming that the investment outlay in present value terms is known with certainty. The final variable is delta, δ. In the financial

option application of the Black Scholes model, δ is the dividend yield that is foregone as an option holder and it is in the model to take into consideration that the payment of dividend reduces the underlying stock price. For the real option application, we will use a proxy to reflect the annual cost of delay, 1/n, if applicable. The reason being, each year of delay translates into one less year of value creating cash inflows from the life of the projects—equivalent to the foregone dividend yield.

Of the six input variables, sigma requires further explanation since the estimated value of the variance of the underlying asset has a significant influence on the value of the option. In the literature review section, we have identified extensively, and

summarized in Table 7, what prior studies have used to estimate the variance of the return of underlying asset.

Earlier in the methodology section we had proposed that the variance of the rate of change of sales be used as the basis for estimating sigma. Regression analysis

documents the relationship of 64 quarters of Nike sales and Nike stock prices188. Other financial variables, indicating cash flows and return on invested capital, were also tested against Nike stock price. However, results of the regression of sales and Nike stock price are the most robust. This provides us with confidence to propose the variance of the return on historical Nike stock price be used as the primary estimate for sigma.

188 _{When businesses are "publicly traded," their equity can be purchased and sold by investors in stock}

markets available to the general public. Stock prices are recognized and perceived by investors as one of the key valuation indicators when assessing the return of an investment. They also reflect market volatility and the industry’s specific risks and opportunities. The stock price has therefore been widely considered as one of the key performance indicators representing the company’s value. It is a perceptible manifestation of the company’s value, comprised of both current operational performance and future growth potential. It, the