# WACC, Uncertainty and Infrastructure Regulation

There is a growing consensus that the successful development of infrastructure – electricity, natural gas, telecommunications, water, and transportation – depends in no small part on the adoption of appropriate public policies and the effective implementation of these policies. Central to these policies is development of a regulatory apparatus that provides stability, protects consumers from the abuse of market power, guard’s consumers and operators against political opportunism, and provides incentives for service providers to operate efficiently and make the needed investments’ capital (Jamison, & Berg, 2008, Overview).

There are four primary approaches to regulating the overall price level – rate of return regulation (or cost of service), price cap regulation, revenue cap regulation, and benchmarking (or yardstick) regulation. Rate of return regulation adjusts overall price levels according to the operator’s accounting costs and cost of capital. In most cases, the regulator reviews the operator’s overall price level in response to a claim by the operator that the rate of return that it is receiving is less than its cost of capital, or in response to a suspicion of the regulator or claim by a consumer group that the actual rate of return is greater than the cost of capital (Jamison, & Berg, 2008, Price Level Regulation).

We will in the following look at cost of service models (cost-based pricing); however some of the reasoning will also apply to the other approaches. A number of different models exist:

• Long Run Average Total Cost – LRATC

• Long Run Incremental Cost – LRIC

• Long Run Marginal cost – LRMC

• Forward Looking Long Run Average Incremental Costs – FL-LRAIC

• Long Run Average Interconnection Costs – LRAIC

• Total Element Long Run Incremental Cost – TELRIC

• Total Service Long Run Incremental Cost – TSLRIC

• Etc.

Where:

**Long run**: The period over which all factors of production, including capital, are variable.

Long Run Incremental Costs: The incremental costs that would arise in the long run with a defined increment to demand.

Marginal cost: The increase in the forward-looking cost of a firm caused by an increase in its output of one unit.

Long Run Average Interconnection Costs: The term used by the European Commission to describe LRIC with the increment defined as the total service.

We will not discuss the merits and use of the individual methods only direct the attention on the fact that an essential ingredient in all methods is their treatment of capital and the calculation of capital cost – Wacc.

### Calculating Wacc a World without Uncertainty

Calculating Wacc for the current year is a straight forward task, we know for certain the interest (risk free rate and credit risk premium) and tax rates, the budget values for debt and equity, the market premium and the company’s beta etc.

There is however a small snag, should we use the book value of Equity or should we calculate the market value of Equity and use this in the Wacc calculations? The last approach is the recommended one (Copeland, Koller, & Murrin, 1994, p248-250), but this implies a company valuation with calculation of Wacc for every year in the forecast period. The difference between the two approaches can be large – it is only when book value equals market value for every year in the future that they will give the same Wacc.

In the example below market value of equity is lower than book value hence market value Wacc is lower than book value Wacc. Since this company have a low and declining ROIC the value of equity is decreasing and hence also the Wacc.

Calculating Wacc for a specific company for a number of years into the future^{1} is not a straight forward task. Wacc is no longer a single value, but a time series with values varying from year to year.

Using the average value of Wacc can quickly lead you astray. Using an average in e.g. an LRIC model for telecommunications regulation, to determine the price paid by competitors for services provided by an operator with significant market power (incumbent) will in the first years give a too low price and in the later years a to high price when the series is decreasing and vice versa. So the use of an average value for Wacc can either add to the incumbent’s problems or give him a windfall income.

The same applies for the use of book value equity vs. market value equity. If for the incumbent the market value of equity is lower than the book value, the price paid by the competitors when book value Wacc is used will be to high and the incumbent will have a windfall gain and vise versa.

Some advocates the use of a target capital structure (Copeland, Koller, & Murrin, 1994, p250) to avoid the computational difficulties (solving implicit equations) of using market value weights in the Wacc calculation. But in real life it can be very difficult to reach and maintain a fixed structure. And it does not solve the problems with market value of equity deviating from book value.

### Calculating Wacc a World with Uncertainty

The future values for most, if not all variable will in the real world be highly uncertain – in the long run even the tax rates will vary.

The ‘long run’ aspect of the methods therefore implies an ex-ante (before the fact) treatment of a number of variable; inflation, interest and tax rates, demand, investments etc. that have to be treated as stochastic variable.

This is underlined by the fact that more and more central banks is presenting their forecasts of macro economic variable as density tables/charts (e.g. Federal Reserve Bank of Philadelphia, 2009) or as fan charts (Nakamura, & Shinichiro, 2008) like below from the Swedish Central Bank (Sveriges Riksbank, 2009):

Fan charts like this visualises the region of uncertainty or the possible yearly event space for central variable. These variables will also be important exogenous variables in any corporate valuation as value or cost drivers. Add to this all other variables that have to be taken into account to describe the corporate operation.

Now, for every possible outcome of any of these variables we will have a different value of the company and is equity and hence it’s Wacc. So we will not have one time series of Wacc, but a large number of different time series all equally probable. Actually the probability of having a single series forecasted correctly is approximately zero.

Then there is the question about how long it is feasible to forecast macro variables without having to use just the unconditional mean (Galbraith, John W. and Tkacz). In the charts above the ‘content horizon’ is set to approximately 30 month, in other the horizon can be 40 month or more (Adolfson, Andersson, Linde, Villani, & Vredin, 2007).

As is evident from the charts the fan width is increasing as we lengthen the horizon. This is an effect from the forecast methods as the band of forecast uncertainty increases as we go farther and farther into the future.

The future nominal values of GDP, costs, etc. will show even greater variation since these values will be dependent on the growth rates path’s to that point in time.

### Mont Carlo Simulation

A possible solution to the problems discussed above is to use Monte Carlo techniques to forecast the company’s equity value distribution – coupled with market value weights calculation to forecast the corresponding yearly Wacc distributions:

This is the approach we have implemented in our models – it will not give a single value for Wacc but its distribution. If you need a single value, the mean or mode from the yearly distributions is better than using the Wacc found from using average values of the exogenous variable – cf. Jensen’s inequality (Savage & Danziger, 2009).

### References

Adolfson, A., Andersson, M.K., Linde, J., Villani, M., & Vredin, A. (2007). Modern forecasting models in action: improving macroeconomic analyses at central banks. *International Journal of Central Banking*, (December), 111-144.

Copeland, T., Koller, T., & Murrin, J. (1994). *Valuation*. New York: Wiley.

Copenhag Eneconomics. (2007, February 02). *Cost of capital for broadcasting transmission *. Retrieved from http://www.pts.se/upload/Documents/SE/WACCforBroadcasting.pdf

Federal Reserve Bank of Philadelphia, Initials. (2009, November 16). *Fourth quarter 2009 survey of professional forecasters*. Retrieved from http://www.phil.frb.org/research-and-data/real-time-center/survey-of-professional-forecasters/2009/survq409.cfm

Galbraith, John W. and Tkacz, Greg, Forecast Content and Content Horizons for Some Important Macroeconomic Time Series. Canadian Journal of Economics, Vol. 40, No. 3, pp. 935-953, August 2007. Available at SSRN: http://ssrn.com/abstract=1001798 or doi:10.1111/j.1365-2966.2007.00437.x

Jamison, Mark A., & Berg, Sanford V. (2008, August 15). *Annotated reading list for a body of knowledge on infrastructure regulation* (Developed for the World Bank). Retrieved from http://www.regulationbodyofknowledge.org/

Nakamura, K., & Shinichiro, N. (2008). The Uncertainty of the economic outlook and central banks’ communications. *Bank of Japan Review*, (June 2008), Retrieved from http://www.boj.or.jp/en/type/ronbun/rev/data/rev08e01.pdf

Savage, L., S., & Danziger, J. (2009). *The Flaw of Averages*. New York: Wiley.

Sveriges Riksbank, . (2009). The Economic outlook and inflation prospects. *Monetary Policy Report*, (October), p7. Retrieved from http://www.riksbank.com/upload/Dokument_riksbank/Kat_publicerat/Rapporter/2009/mpr_3_09oct.pdf

- For some telecom cases, up to 50 years. [↩]

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