Appendix B Weighted Average Cost of Capital

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1 Appendix B Weighted Average Cost of Capital The inclusion of cost of money within cash flow analyses in engineering economics and life-cycle costing is a very important (and in many cases dominate) contributing factor in understanding the respective costs. Cost of money reflects the fact that the use of money to support a product (e.g., to fund design, manufacturing, and sustainment) is not free, i.e., the money has to come from some source and it is likely that that source will require some form of compensation over time. In general there are three sources of funding available to a company to fund its operations: retained earnings, borrowed money (debt financing), and selling equity (e.g., stocks). If the money to support a project is obtained via a loan (debt financing), then the cost of that money is the interest paid to the loan provider. If all of the money is obtained via a loan then the interest rate on the loan is set when the money a company uses is obtained and the interest rate can simply be used to modify future cash flows as in (1.4), however, rarely is the case this simple. Usually companies are funded by, and fund projects via, a combination of debt and equity capital. Most engineering economics texts refer to the rate paid for money as simply the interest rate and many engineers will more generally call it the discount rate. Both of these terms infer the source of the money interest rate infers debt financing, the discount rate is defined as the interest rate charged to commercial banks and other depository institutions for loans received from the Federal Reserve Bank s discount window (or the rate used by pension plans and insurance companies for discounting their liabilities). A more general term is the weighted average cost of capital or WACC, which attempts to capture and combine the cost of all the sources of money. 1

2 2 Electronic Systems Cost Modeling This appendix describes the general calculation and use of the WACC. It also describes how the WACC can change over time and issues with using the WACC in long (calendar) time calculations. B.1 The Weighted Average Cost of Capital (WACC) A wide variety of methods can be used to determine the rate for cost of money, but in many cases, these calculations resemble art more than science. One common strategy is to apply the concepts of the weighted average cost of capital (WACC). The WACC is essentially a blend of the cost of equity and the after-tax cost of debt. B.1.1 Cost of Equity Equity is a stock or any other security representing an ownership interest in a company. Companies, whether public or private raise money by selling equity. Unlike debt, for which the company must pay at a set rate of interest, equity does not have a set price that the company must pay. But this doesn't mean that there is no cost of equity. Equity shareholders expect to obtain a certain return on their equity investment in a company. From the company's perspective, the equity holders' required rate of return is a cost, because if the company does not deliver this expected return, shareholders may sell their shares, causing the stock price to drop. The cost of equity is basically what it costs the company to maintain a share price that is satisfactory (at least in theory) to investors. The most commonly accepted method for calculating cost of equity comes from the capital asset pricing model (CAPM), 1 R e = R f + β(r m - R f) (B.1) where R e = cost of equity 1 Developed by William Sharpe from Stanford University who shared the 1990 Nobel Prize in Economics for the development of CAPM [B.1].

3 Weighted Average Cost of Capital 3 R f = risk free interest rate, the interest rate of U.S. Treasury bills or the long-term bond rate is frequently used as a proxy for the riskfree rate R m = market return β = sensitivity (R m - R f) = R p, Equity Market Risk Premium (EMRP). β measures how much a company's share price moves against the market as a whole. If β = 1, indicates that the company moves in sync with the market. If β > 1, the share is exaggerating the market's movements. If β < 1, the share is more stable. If β < 0, the share price moves in the opposite direction to the broader market. EMRP represents the returns investors expect over and above the risk-free interest rate, to compensate them for taking extra risk by investing in the stock. In other words, it is the difference between the risk-free rate and the market rate. There are several services (e.g., Barra and Ibbotson) that provide EMRP and β for public companies. 2 Once the cost of equity is calculated, adjustments can be made to take into account of risk factors specific to the company, namely: the size of the company, pending lawsuits, concentration of customer base and dependence on key employees. These adjustments are entirely a matter of investor judgment and they vary from company to company. B.1.2 Cost of Debt Debt is an amount of money borrowed by one party from another. Corporations use debt as a method for making large purchases that they could not afford under normal circumstances. A debt arrangement gives the borrowing party permission to borrow money under the condition that it is to be paid back at a later date, usually with interest. Compared to the cost of equity, the cost of debt is more straightforward to calculate. The rate applied to determine the cost of debt (R d) should be the current 2 If you are interested in finding EMRP or β for a non-public company, you should search for a public company with a similar business and use their EMRP or β.

4 4 Electronic Systems Cost Modeling market rate the company is paying on its debt. If the company is not paying market rates, an appropriate market rate payable by the company should be estimated. Since companies benefit from the tax deductions available on interest paid on debt, the net cost of the debt is actually the interest paid less the tax savings resulting from the tax-deductible interest payment. Therefore, the after-tax cost of debt is R d (1 - corporate tax rate). This is referred to as a tax shield that arises from the interest expense. B.1.3 Calculating the WACC The WACC is the weighted average of the cost of equity and the cost of debt based on the proportion of debt and equity in the company's capital structure 3 WACC = R e (E/V) + R d (1 T e) (D/V) (B.2) where V = the company's total value (equity + debt) D/V = the proportion of debt (leverage ratio) E/V = the proportion of equity T e = effective marginal corporate tax rate. 4 Figure B.1 shows the variation of WACC with the ratio of D to E. Note, in Fig. B.1 that the costs of equity and debt vary with the company s debt to equity mix, for example, the cost of debt for a company increases as more of the company is financed via debt (because lenders infer more risk and therefore charge a higher interest rate). Also note that as the cost of debt increases, the cost of equity also increases why? The costs of debt and equity track each other because equity holders are always taking more risk than debt holders and therefore require a premium return above that of debt holders. It is also important 3 In Chapters 1, 12, 13, 16, 17, and 20 of this book, WACC is referred to as the discount rate and represented with the symbol r. 4 The effective tax rate is the actual taxes paid divided by earnings before taxes.

5 Weighted Average Cost of Capital 5 Equity WACC Debt 0 0% Debt 100% Equity Debt to Equity (D/E) Ratio Fig. B.1. Variation in WACC with D/E ratio. 100% Debt 0% Equity to point out that there is an implicit assumption in Fig. B.1 that the company s value does not change with the D/E ratio. In the calculation of the WACC one can subdivide the cost of equity into different types of equity, e.g., common and preferred stock. Also, sometimes the rate of return on retained earnings is also included as a separate term in (B.1). Be careful: (B.2) seems easier to calculate than it really is. Rarely will two people calculate the same WACC, and even if two people do compute the same WACC, other applied judgments and valuation methods will likely ensure that each has a different opinion regarding the components that comprise the company's value. As a simple example of computing the WACC, consider a semiconductor manufacturer that has a capital structure that consists of 40% debt and 60% equity, with a tax rate of 30%. The borrowing rate (R d) on the company's debt is 5%. The risk-free rate (R f) is 2%, the β is 1.3 and the risk premium (R p) is 8%. Using these parameters the following can be computed: R e = R f + β(r m - R f) = (0.08) = D/V = 0.4/( ) = 0.4 E/V = 0.6/( ) = 0.6

6 6 Electronic Systems Cost Modeling WACC = R e (E/V) + R d (1 corporate tax rate) (D/V) = 0.124(0.6)+0.05(1-0.3)(0.4) = The WACC comes to 8.84% (this is a beta-adjusted discount rate or risk-adjusted discount rate ). Actual values of WACC for companies vary widely. It is not uncommon for WACCs to range from 3-4% up to 20% or more. Various web sites provide WACC estimates for publicly traded companies. 5 All the discussion in this section assumes there is no time dependence in the WACC, i.e., this is all valid at an instant in time and may have no validity at other times. The irony of the WACC calculation is that WACC is used to model the time value of money as in (1.4), but the WACC that is calculated is only valid at one instant in time. B.2 Forecasting Future WACC One of the biggest problems with WACC is that while it may accurately reflect what a company believes its cost of money is at the current time, the dynamics of the broader economy and the company s capital structure change with time. Therefore the WACC is not constant over time. Specifically the WACC is dynamic because: 1) a company s debt to equity ratio changes over time; 6 2) the cost of equity (R e) may change with time; 3) the cost of debt (R d) may change over time; and 4) the tax rate (T e) will be a function of profitability and tax breaks allowed for certain industries in certain locations during certain periods of time. Computing the WACC for a future time is difficult, but really important. Assuming that today s WACC will remain constant into the future may be a source of significant errors in life-cycle cost modeling. For 5 Does the US Government have a WACC? Yes, it s the rate on 3, 5, 7, 10, and longer-term treasury securities (T-Bills). 6 Depending on the form that the debt takes the D/E ratio may or may not remain constant. For example, the D/E ratio remains unchanged for debt in the form of a bond for which only the interest (coupon) payments are made, which is replaced by an equivalent bond at its maturity date. In the case of a loan whose balance reduces as payments are made, the D/E ratio drops over time.

7 Weighted Average Cost of Capital 7 example, at a macro-level, world economics dictate whether interest rates on debt rise or fall and high profile corporate disasters increase the perceived risk of equity investments. Many other factors affect the WACC associated with specific companies in specific business sectors. For example, for companies that operate wind farms (a relatively new and growing business sector), Increasing experience amongst operators of wind farms will reduce the risk premium that investors can demand thus lowering R e over time. In interest rates for debt are climbing due to the recovery of the global economy, increasing R d. The equity and debt ratios will change over time as well. For example, as risk decreases, companies are able to take on a larger share of debt (D/V increases and E/V decreases), which companies tend to do because usually R d < R e. The corporate tax rate will change because the company becomes profitable and the expiration of tax breaks granted by local and national governments. The trends over time in R d can be modeled with a yield curve. 7 R e has to be modeled using a capital asset pricing model (CAPM), in which β is the primary parameter that trends over time. In reality all the parameters used to determine WACC are probability distributions. Therefore, the resulting WACC is a probability distribution. Monte Carlo analysis can be used to determine the appropriate probability distribution for the WACC in each year of an analysis. In addition, the WACC is a non-stationary process. 8 In the case of WACC, not only does the distribution s mean shift over time (driven by the trends in the parameters), but its variance also becomes 7 Found by calculating a forward interest rate, which is an interest rate that is applicable to a future financial transaction. 8 A stationary process is a stochastic process whose joint probability distribution does not change when shifted in time or space (time is the relevant parameter for us).

8 8 Electronic Systems Cost Modeling larger as time progresses. Note, if non-stationary methods are used to estimate future WACC, the coupling (non-independence) of parameters must be respected. B.3 Comments What engineers often call discount rate would be referred to as weighted average cost of capital (WACC) by business analytics people. The WACC is not the inflation rate! In actuality, WACC is neither a cost nor a required return, it is a weighted average of a cost and required return [B.2]. Net present value (NPV) is the present value of future net cash flows (benefits) less the present value of implementation costs (investment costs). However, in many instances both investments and costs are discounted using the same WACC, which is wrong. 9 B.3.1 Trade-off Theory The cost of debt is lower than the cost of equity. Does this mean that a company (or projects) should be financed only with debt? What is the fallacy here? The WACC is actually effectively independent of the D/E ratio (see Problem B.7). In reality, using cheap debt increases the cost of equity (because its financial risk increases). Company management seeks to find a debt/equity ratio (D/E) that balances the risk of bankruptcy (i.e., large D/E) with the risk of using too little of the least expensive form of financing, which is debt (i.e., small D/E). 10 According to the trade-off theory [B.4], there is a best way to finance a company, i.e., an optimal D/E ratio that minimizes a company s cost of capital Fig. B.1 shows this concept graphically. 9 The benefits should be discounted at the WACC, but the investment should be discounted at a reinvestment rate similar to the risk-free rate [B.3]. 10 The after-tax cost of debt will always be lower than the cost of financing with equity.

9 Weighted Average Cost of Capital 9 B.3.2 Social Opportunity Cost of Capital (SOC) The concept of the Social Opportunity Cost of Capital (SOC) is sometimes invoked to specify the return governments require when making investments on behalf of the community, [B.5]. The social opportunity cost rate of discount is the rate that reduces the net present value of the best alternative private use of the funds to zero. It is the rate at which society is willing to forgo present consumption for the sake of future consumption. With this discount rate, the discounted value of future consumption goods equals the value of forgone present consumption goods. It is thus the consumption-based opportunity cost of capital. This means that the social opportunity cost reflects the cost in financial market terms. This leads to an approach where the government takes into account what similar projects would provide in returns if undertaken in the private sector. References B.1 Sharpe, W. F. (1964). Capital asset prices A theory of market equilibrium under conditions of risk. Journal of Finance XIX(3): pp B.2 Fernandez, P. (2011). WACC: Definition, misconceptions and errors, IESE Business School, University of Navarra, Working Paper WP-914. B.3 Mun, J. (2006). Real options analysis versus traditional DCF valuation in layman s terms. m.pdf B.4 Kraus, A. and Litzenberger, R. H. (1973). A state-preference model of optimal financial leverage, Journal of Finance 28(4): pp B.5 Harberger, A. C. (1969). The discount rate in public investment evaluation. Proceedings of the Committee on the Economics of Water Resources Development, Western Agricultural Economics Research Council, Report No. 17, Denver Colorado, pp Problems B.1. Why does paying more taxes reduce the WACC? Explain this. Companies want to decrease their WACC, so why is moving the

10 10 Electronic Systems Cost Modeling company to a state with a higher tax rate not a good approach for reducing the WACC? B.2 Why do equity holders require a greater return than debt holders? B.3 If a company borrows money at a 6.5%/year rate (after taxes), pays 9% for equity, and raises its capital in equal proportions of debt and equity, what is its WACC? B.4 A company currently has the following capital structure: Source of Funding Amount of Funding Expected Rate of Return Retained Earnings \$100M 11% Loans \$35M 3.4% Bonds \$150M 8.75% Preferred Stock \$60M 7% Common Stock \$110M 10.5% Note, the interest paid on the bonds is not tax deductible. Assuming a corporate tax rate of 25%: a) What is the current WACC of the company? b) If the company expects the total capital to remain the same, but the debt to equity ratio to increase 10% (via an increase in the debt and an across the board decrease in equity financing) and the cost of debt to increase 50% in the next 2 years, what will the WACC be after these changes? B.5 A semiconductor fabrication company is installing a new process that requires \$2,000,000 in new equipment. a) The company has two financing options: 1) 40% equity funds at 9% per year and a loan for the rest at 10% per year. 2) 25% equity funds at 9% per year and the rest of the money borrowed at 10.5% per year. Which alternative results in a smaller WACC? Assume a corporate tax rate of 5% per year. b) Yesterday the finance committee in the company decided that the WACC for all new projects must not exceed the 5 year historical average WACC in the company of 10% per year. With this restriction what is the maximum loan interest rate that can be incurred for the two options in part a)? B.6 A contract manufacturer of printed circuit boards plans to raise \$5 million in debt capital by issuing five thousand bonds (each has a face value of \$1000). The bonds pay 8%/year, paid annually (coupon interest rate) and have a 10 year life. Assume the effective tax rate of the company is 23% and the bonds are sold at a 2% discount. Calculate the cost of this debt equity before and after taxes. Assume discrete compounding. B.7 If the tax rate (T e) is zero, under what conditions is WACC independent of D/V?

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