Investment decisions in mobile telecommunications networks applying real options

Abstract

This paper proposes a real options model for valuing the option to delay mobile telecommunications network investment decisions and a method for calculating the real options’ impact on mobile service costs. Ranges of option value multiples are calculated for the decisions to invest in a number of network elements, each representing a different part of the mobile network, subject to different demand and technological uncertainties. The value of the option to invest in each network element, net of future replacement options, is modeled as a function of the element’s total variable profit and the cost of investment in the element. The model and method are then applied to estimate the real options’ impact on mobile termination costs using real cost and volume data.

Appendices

Appendix 1: Dickey–Fuller test and procedure for estimating the volatility parameters

If $Y_{t}$ follows geometric Brownian motion with drift and volatility parameters respectively given by $\alpha _{Y}$ and $\sigma _{Y}$, then $\ln {\left( Y_{t}\right) } = \left( \alpha _{Y} - \frac{\sigma _{Y}^{2}}{2}\right) t + \ln {\left( Y_{0}\right) } + \sigma _{Y}N\left( 0, 1\right) \sqrt{t}$.

Writing the above equation for discrete intervals of time of length ${\triangle }t = \frac{1}{N}$ year(s):

$$\begin{aligned} \ln {\left( \frac{Y_{i}}{Y_{i - 1}}\right) } = \frac{a_{Y}}{N} + \frac{\sigma _{Y}}{\sqrt{N}}\varepsilon _{t}, \text { where } a_{Y} = \left( \alpha _{Y} - \frac{\sigma _{Y}^{2}}{2}\right) \text { and } \varepsilon _{t} \sim N\left( 0, 1\right) . \end{aligned}$$

The Dickey–Fuller test was performed running the linear regression model on $\ln {\left( \frac{Y_{i}}{Y_{i - 1}}\right) } = \frac{a_{Y}}{N} + \left( b_{Y} - 1\right) \ln {\left( Y_{i - 1}\right) } + \frac{\sigma _{Y}}{\sqrt{N}}\varepsilon _{t}$ and testing the null hypothesis $H_{0}: \left( b_{Y} - 1\right) = 0$. The alternative hypothesis was $H_{A}: \left( b_{Y} - 1\right) < 0$. The regression was based on monthly time-series data on mobile voice traffic and quarterly time-series data on mobile data traffic, respectively over the periods of six and eight years.

The tests showed that there is not enough evidence to reject the null hypothesis (i.e., the assumption that the stochastic variables follow geometric Brownian motion).

The backward-looking estimate of $\hat{\sigma }_{Y}$ was derived from the equation $\hat{\sigma }_{Y}^{2} = N\{$ sample variance of $\ln {\left( \frac{Y_{i}}{Y_{i - 1}}\right) }\}$.

Appendix 2: Actual cost and volume data

The cost and volume information used in this paper is based on the actual cost study of a mobile telecommunications operator for the project to build a mobile network in a small metropolitan area. The network was dimensioned to meet the forecast demand for the next six years, reaching a total of 40,000 mobile subscribers by 2020. A single MSC was assumed to serve a maximum of 125,000 subscribers. The number of BSCs was determined by the number of sites, since each BSC was assumed to serve a maximum of 20 sites. The geographic area was split into six dense, six medium and six rural sites. Each BTS was assumed to be connected to a single BSC. Table 6 shows the cost and volume information of all network elements used by the mobile call termination service, suitably modified to preserve the carrier’s anonymity.

Table 6 Network elements’ cost and volume information