To: Ana Bellario, Director of Market Strategy for Eurotel
Date: October 14, 2012
Subject: Regression Model for 3G License Valuation Estimation -------------------------------------------------
As part of the European expansion plan, Eurotel is planning to bid on 3G licenses in Hungary, Russia and Turkey. Usually, the operator determines the maximum price to bid following three steps: 1. NPV analysis
2. Market Indicator Considerations
3. Game theory
As a complement to this methodology, a multiple linear regression model will be proposed and evaluated. This memo includes the approach to the problem, the model reached, the results for Hungry, Russia and Turkey and the evaluation of the model.
Number of variables
To reach a robust model, a variety of variables have been considered to include information about industry status (competition, maturity, etc.), market size (number of mobile subscribers) and spending power (GDP, ARPU, etc.). All in all, eleven variables have been identified. However, following rule of thumb, n>5(k+2) and since the number of previous observations is thirty, only three variables can be supported in the model.
Since what Eurotel cares about the price of one license in a particular market, not the price of all the 3G licenses in a market, a new variable should be introduced: “Price per License” obtained dividing the “Price for All Licenses” by the “Licenses Available”.
One way to include the qualitative variable “Type of contest” in the model is to create a dummy variable, that will be equal to “1” when it is bidding and “0” when it is beauty contest.
The first step to build a multiple linear regression model is to study the linear relations among all the variables, i.e. to calculate the correlation among them to: 1. Select the independent variables that present the strongest correlation with the dependent variable (Price per License) 2. Avoid multicollinearity, discarding to include in the model two or more highly correlated variables in the left hand side of the regression equation.
The first positions of the correlation ranking can be found below (the full correlation matrix can be found in the appendix).
Variable vs. Variable| R|
Price/License (million) vs. GDP ($Bn)| 0.96803|
Price/License (million) vs. Mobile Subscribers (Million)| 0.96297| GDP ($Bn) vs. Mobile Subscribers (Million)| 0.94273|
Mobile Subscribers (Million) vs. Population (Million)| 0.93741| Price/License (million) vs. Population (Million)| 0.91955| GDP ($Bn) vs. Population (Million)| 0.91190|
As a result, the highest correlated variables with the Price per License are: 1. The GDP
2. Number of Mobile Subscribers
3. The population
However, these variables are strongly correlated among them. For example, GDP ($Bn) vs. Mobile Subscribers (Million) yields a correlation of 0.94273. To avoid multicollinearity, just one of these highly correlated variables should be kept in the model. Although GDP shows the strongest correlation with Price per License, the model regression build on GDP generates a negative price for the license in Hungary (see appendix). For this reason GDP is discarded. The second highest correlated variable with Price per License is Mobile Subscribers, which is the variable selected for building the model.
The regression equation for the Price per License based on the number of Mobile Subscribers obtained is:
Price per License ($Mn) = - 190.6147 + 54.1952 * Mobile Subs (Mn) (see appendix for regression details)
This equation yields the following results for Hungary, Russia and Turkey:
Country| Mobile Subs (Mn)| Price ($Mn / license)|
Hungary| 4.98| $79.28|
Russia| 5.20| $91.20|
Turkey| 19.65| $874.32|
Hurdle Valuation vs Regression Valuation