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The Weighted Average Cost of Capital – Strategy @ Risk

Series: The Weighted Average Cost of Capital

  • The weighted average cost of capital

    The weighted average cost of capital

    This entry is part 1 of 2 in the series The Weighted Average Cost of Capital

     

    A more extensive version of this article can be read here in .pdf format.

    The weighted cost of capital (WACC) and the return on invested capital (ROIC) are the most important elements in company valuation, and the basis for most strategy and performance evaluation methods.

    WACC is the discount rate (time value of money) used to convert expected future cash flow into present value for all investors. Usually it is calculated both assuming a constant cost of capital and a fixed set of target market value weights ((Valuation, Measuring and Managing the Value of Companies. Tom Copeland et al.)) , throughout the time frame of the analysis. As this simplifies the calculations, it also imposes severe restrictions on how a company’s financial strategy can be simulated.

    Now, to be able to calculate WACC we need to know the value of the company, but to calculate that value we need to know WACC. So we have a circularity problem involving the simultaneous solution of WACC and company value.

    In addition all the variables and parameters determining the company value will be stochastic, either by themselves or by being functions of other stochastic variables. As such WACC is a stochastic variable– determined by the probability distributions for yield curves, exchange rates, sale, prices, costs and investments. But this also enables us – by Monte Carlo simulation –to estimate a confidence interval for WACC.

    Some researchers have claimed that the free cash flow value only in special cases will be equal to the economic profit value. By solving the simultaneous equations, giving a different WACC for every period, we will always satisfy the identity between free cash flow and economic profit value. In fact we will use this to check that the calculations are consistent.

    We will use the most probable value for variables/parameters in the calculations. Since most of the probability distributions involved are non-symmetric (sale, prices etc), the expected values will in general not be equal to the most probable values. And as we shall see, this is also the case for the individual values of WACC.

    WACC

    To be consistent with the free cash flow or economic profit approach, the estimated cost of capital must comprise a weighted average of the marginal cost of all sources of capital that involves cash payment – excluding non-interest bearing liabilities (in simple form):

    WACC = {C_d}(1-t)*{D/V} + {C_e}*{E/V}

    {C_d} = Pre-tax debt nominal interest rate
    {C_e} = Opportunity cost of equity,
    t = Corporate marginal tax rate
    D = Market value debt
    E = Market value of equity
    V = Market value of entity (V=D+E).

    The weights used in the calculation are the ratio between the market value of each type of debt and equity in the capital structure, and the market value of the company. To estimate WACC we then first need to establish the opportunity cost of equity and non-equity financing and then the market value weights for the capital structure.

    THE OPPORTUNITY COST OF EQUITY AND NON-EQUITY FINANCING

    To have a consistent WACC, the estimated cost of capital must:

    1. Use interest rates and cost of equity of new financing at current market rates,
    2. Be computed after corporate taxes,
    3. Be adjusted for systematic risk born by each provider of capital,
    4. Use nominal rates built from real rates and expected inflation.

    However we need to forecast the future risk free rates. They can usually be found from the yield curve for treasury notes, by calculating the implicit forward rates.

    THE OPPORTUNITY COST OF EQUITY

    The equation for the cost of equity (pre investor tax), using the capital asset pricing model (CAPM) is:

    C = R+M*beta+L

    R  = risk-free rate,
    beta  = the levered systematic risk of equity,
    M  = market risk premium,
    L  = liquidity premium.

    If tax on dividend and interest income differs, the risk-free rate and the market premium has to be adjusted, assuming tax rate -ti, for interest income:

    R = (1-t_i)*R  and  M = M+t_i*R.

    t_i = Investor tax rate,
    R  = tax adjusted risk-free rate,
    M = tax adjusted market premium

    The pre-tax cost of equity can then be computed as:

    R/(1-t_d)+{beta}*{M/(1-t_d)}+{LP/(1-t_d)}

    C_e(pre-tax) = C_e/(1-t_d) = R/(1-t_d)+{beta}*{M/(1-t_d)}+{LP/(1-t_d)}

    Where the first line applies for an investor with a tax rate of -td, on capital income, the second line for an investor when tax on dividend and interest differs  ((See also: Wacc and a Generalized Tax Code, Sven Husmann et al.,  Diskussionspapier 243 (2001), Universität Hannover)) .

    The long-term strategy is a debt-equity ratio of one, the un-levered beta is assumed to be 1.1 and the market risk premium 5.5%. The corporate tax rate is 28%, and the company pays all taxes on dividend. The company’s stock has low liquidity, and a liquidity premium of 2% has been added.

    cost-of-equity_corrected

    In the Monte Carlo simulation all data in the tables will be recalculated for every trial (simulation), and in the end produce the basis for estimating the probability distributions for the variables. This approach will in fact create a probability distribution for every variable in the profit and loss account as well as in the balance sheet.

    THE OPPORTUNITY COST OF DEBT

    It is assumed that the pre-tax debt interest rate can be calculated using risk adjusted return on capital (RAROC) as follows:

    Lenders Cost = L_C+L_L+L_A+L_RP

    L_C = Lenders Funding Cost (0.5%),
    L_L = Lenders Average Expected Loss (1.5%),
    L_A = Lenders Administration Cost (0.8%),
    L_RP= Lenders Risk Premium (0.5%).

    The parameters (and volatility) have to be estimated for the different types of debt involved. In this case there are two types; short -term with a maturity of four years and long-term with a maturity of 10 years. The risk free rates are taken from the implicit forward rates in the yield curve and lenders cost are set to 3.3%.

    In every period the cost and value of debt are recalculated using the current rates for that maturity, ensuring use of the current (future) opportunity cost of debt.

    THE MARKET VALUE WEIGHTS

    By solving the simultaneous equations, we find the market value for each type of debt and equity:

    And the value weights:

    Multiplying the value weights by the respective rate and adding, give us the periodic most probable WACC rate:

    As can be seen from the table above, the rate varies slightly from year to year. The relative small differences are mainly due to the low gearing in the forecast period.

    MONTE CARLO SIMULATION

    In the figure below we have shown the result from simulation of the company’s operations, and the resulting WACC for year 2002. This shows that the expected value of WACC in is 17.4 %, compared with the most probable value of 18.9 %. This indicates that the company will need more capital in the future, and that an increasing part will be financed by debt. A graph of the probability distributions for the yearly capital transactions (debt and equity) in the forecast period would have confirmed this.

    In the figure the red curve indicates the cumulative probability distribution for the value of WACC in this period and the blue columns the frequencies. By drawing horizontal lines on the probability axis (left), we can find confidence intervals for WACC. In this case there is only a 5% probability that WACC will be less than 15%, and a 95% probability that it will be less than 20%. So we can expect WACC for 2002 with 90% probability to fall between 15% and 20%. The variation is quite high  – with a coefficient of variation of 6.8 ((Coefficient of variation = 100*st.dev/mean)).

    VALUATION

    The value of the company and the resulting value of equity can be calculated using either the free cash flow or the economic profit approach. Correctly done, both give the same value. This is the final test for consistency in the business model. The calculations are given in the tables below, and calculated as the value at end of every year in the forecast period.

    As usual, the market value of free cash flow is the discounted value of the yearly free cash flow in the forecast period, while the continuing value is the value of continued operation after the forecast period. All surplus cash are paid, as dividend so there is no excess marketable securities.

    The company started operations in 2002 after having made the initial investments. The charge on capital is the WACC rate multiplied by the value of invested capital. In this case capital at beginning of each period is used, but average capital or capital at end could have been used with a suitable definition of capital charge.
    Economic profit has been calculated by multiplying RIOC – WACC with invested capital, and the market value at any period is the net present value of future economic profit. The value of debt as the net present value of future debt payments – is equal for both methods.

    For both methods using the same series of WACC when discounting cash the flows, we find the same value for the both company and equity. This ensures that the calculations are both correct and consistent.

    Tore Olafsen and John Martin Dervå

    reprint_fen

  • WACC, Uncertainty and Infrastructure Regulation

    WACC, Uncertainty and Infrastructure Regulation

    This entry is part 2 of 2 in the series The Weighted Average Cost of Capital

     

    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.

    Wacc-and-Wacc-weights

    Calculating Wacc for a specific company for a number of years into the future ((For some telecom cases, up to 50 years.)) 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):

    Riksbank_dec09

    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:

    Wacc-2012

    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