The Weighted Average Cost of Capital


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WACC, Uncertainty and changes over time

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.

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The Weighted Average Cost of Capital

  1. 1. - Strategy @ Risk - -WACC, Uncertainty and Infrastructure RegulationPosted By S@R On February 8, 2010 @ 5:18 pm In Balance sheet simulation, Costs, Inflation, Interestrates | 1 CommentTable of contents for The Weighted Average Cost of Capital 1. The weighted average cost of capital [1] 2. WACC, Uncertainty and Infrastructure RegulationThere is a growing consensus that the successful development of infrastructure – electricity, naturalgas, telecommunications, water, and transportation – depends in no small part on the adoption ofappropriate public policies and the effective implementation of these policies. Central to these policiesis development of a regulatory apparatus that provides stability, protects consumers from the abuseof market power, guard’s consumers and operators against political opportunism, and providesincentives 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 (orcost 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 accountingcosts and cost of capital. In most cases, the regulator reviews the operator’s overall price level inresponse to a claim by the operator that the rate of return that it is receiving is less than its cost ofcapital, or in response to a suspicion of the regulator or claim by a consumer group that the actualrate 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 thereasoning 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 definedincrement to demand.Marginal cost: The increase in the forward-looking cost of a firm caused by an increase in its output ofone unit.Long Run Average Interconnection Costs: The term used by the European Commission to describeLRIC 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 factthat an essential ingredient in all methods is their treatment of capital and the calculation of capitalcost – Wacc.Calculating Wacc a World without UncertaintyCalculating Wacc for the current year is a straight forward task, we know for certain the interest (riskfree rate and credit risk premium) and tax rates, the budget values for debt and equity, the marketpremium and the company’s beta etc.  1
  2. 2. There is however a small snag, should we use the book value of Equity or should we calculate themarket value of Equity and use this in the Wacc calculations? The last approach is the recommendedone (Copeland, Koller, & Murrin, 1994, p248-250), but this implies a company valuation withcalculation of Wacc for every year in the forecast period. The difference between the two approachescan be large – it is only when book value equals market value for every year in the future that theywill give the same Wacc.In the example below market value of equity is lower than book value hence market value Wacc islower than book value Wacc. Since this company have a low and declining ROIC the value of equity isdecreasing and hence also the Wacc. [2]Calculating Wacc for a specific company for a number of years into the future1 [3] is not a straightforward task. Wacc is no longer a single value, but a time series with values varying from year toyear.Using the average value of Wacc can quickly lead you astray. Using an average in e.g. an LRIC modelfor telecommunications regulation, to determine the price paid by competitors for services provided byan operator with significant market power (incumbent) will in the first years give a too low price andin the later years a to high price when the series is decreasing and vice versa. So the use of anaverage 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 themarket value of equity is lower than the book value, the price paid by the competitors when bookvalue 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 avoidthe computational difficulties (solving implicit equations) of using market value weights in the Wacc  2
  3. 3. calculation. But in real life it can be very difficult to reach and maintain a fixed structure. And it doesnot solve the problems with market value of equity deviating from book value.Calculating Wacc a World with UncertaintyThe future values for most, if not all variable will in the real world be highly uncertain – in the long runeven the tax rates will vary.The ‘long run’ aspect of the methods therefore implies an ex-ante (before the fact) treatment of anumber of variable; inflation, interest and tax rates, demand, investments etc. that have to be treatedas stochastic variable.This is underlined by the fact that more and more central banks is presenting their forecasts of macroeconomic variable as density tables/charts (e.g. Federal Reserve Bank of Philadelphia, 2009) or as fancharts (Nakamura, & Shinichiro, 2008) like below from the Swedish Central Bank (Sveriges Riksbank,2009):[4]Fan charts like this visualises the region of uncertainty or the possible yearly event space for centralvariable. These variables will also be important exogenous variables in any corporate valuation asvalue or cost drivers. Add to this all other variables that have to be taken into account to describe thecorporate operation.Now, for every possible outcome of any of these variables we will have a different value of thecompany and is equity and hence it’s Wacc. So we will not have one time series of Wacc, but a largenumber of different time series all equally probable. Actually the probability of having a single seriesforecasted correctly is approximately zero.  3
  4. 4. Then there is the question about how long it is feasible to forecast macro variables without having touse just the unconditional mean (Galbraith, John W. and Tkacz). In the charts above the ‘contenthorizon’ 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 effectfrom the forecast methods as the band of forecast uncertainty increases as we go farther and fartherinto the future.The future nominal values of GDP, costs, etc. will show even greater variation since these values willbe dependent on the growth rates path’s to that point in time.Mont Carlo SimulationA possible solution to the problems discussed above is to use Monte Carlo techniques to forecast thecompany’s equity value distribution – coupled with market value weights calculation to forecast thecorresponding yearly Wacc distributions: [5]This is the approach [1] we have implemented in our models – it will not give a single value for Waccbut its distribution. If you need a single value, the mean or mode from the yearly distributions isbetter than using the Wacc found from using average values of the exogenous variable – cf. Jensen’sinequality (Savage & Danziger, 2009).Adolfson, A., Andersson, M.K., Linde, J., Villani, M., & Vredin, A. (2007). Modern forecasting models inaction: 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 . Retrievedfrom Reserve Bank of Philadelphia, Initials. (2009, November 16). Fourth quarter 2009 survey ofprofessional forecasters. Retrieved from  4
  5. 5. Galbraith, John W. and Tkacz, Greg, Forecast Content and Content Horizons for Some ImportantMacroeconomic Time Series. Canadian Journal of Economics, Vol. 40, No. 3, pp. 935-953, August2007. Available at SSRN: or doi:10.1111/j.1365-2966.2007.00437.xJamison, Mark A., & Berg, Sanford V. (2008, August 15). Annotated reading list for a body ofknowledge on infrastructure regulation (Developed for the World Bank). Retrieved from, K., & Shinichiro, N. (2008). The Uncertainty of the economic outlook and central banks’communications. Bank of Japan Review, (June 2008), Retrieved from, 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 [1]Previous in series [6] 1. For some telecom cases, up to 50 years. [↩ ]Article printed from Strategy @ Risk: http://www.strategy-at-risk.comURL to article: in this post:[1] The weighted average cost of capital:[2] Image:[3] 1:[4] Image:[5] Image:[6] ↩: Click here to print. Copyright © 2009 Strategy @ Risk. All rights reserved.   5