www.charteredgrindschool.com 133 Study Unit 12 Contents Page A. The Opportunity Cost of Equity Capital 135 B. The Opportunity Cost of Debt Capital 137 C. The Weighted Average Cost of Capital 137
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www.charteredgrindschool.com 135 A. THE OPPORTUNITY COST OF EQUITY CAPITAL The Opportunity Cost of Equity (called K E the cost of equity) represents the discount rate a company with 100% equity financing should use in project evaluation. It represents the rate of return, which the company could get for an equivalent level of risk through investment in the capital market. There are basically 3 methods of arriving at this rate. We will look at each one in turn. (a) Using the CAPM to Derive the Opportunity Cost of Equity Capital At the start of the previous topic we said that one of two primary aims of the CAPM was to derive the Opportunity Cost of Equity Capital for use in discounting a risky project s future cash flow. So far, we have shown the CAPM has evolved as a method of estimating required return from an asset/portfolio with a given level of risk as measured by. The required/expected return is given by the formula: K E = R F + Equity [E(R Market) Rf] Application to Private Companies Private companies may also use the CAPM approach to derive the Opportunity Cost of Equity Capital because it represents the opportunity cost of their funds for a given risk level. For example, an unquoted company could look at the risk level of a particular level as measured by its beta and calculate an appropriate cost of equity capital for investment in that industry. (b) Deriving the Cost of Equity Using the Dividend Valuation Model The Dividend Valuation Model A company may be valued as a stream of future dividends onto infinity discounted at the rate which the market feels is appropriate for a given risk level. In this instance the company valuation will be the same as that for a perpetuity i.e. Value of Share = Dividend/K E. Suppose, the Dividend is 10 and the cost of the equity is 10%, then the value of the share will be 10/.1 = 100. Suppose though that we don t know the cost of equity. The value of the share will be apparent from the market as will the dividend. Thus, if the share price is 100 and the dividend is 10 we can infer that the cost of equity is 10%. Remember, Share Price = Dividend/K E so, by rearranging, K E = Dividend/Share Price The assumption here is that the dividend is a constant stream which will go on forever. However, if there is growth in dividends, then we can use the growing perpetuity formula: Share Price = Div 0 (1+g) / (K E g) where g is the growth rate in dividends Since Div 0 (1+g) = Div 1 (i.e. the Next Dividend), the Valuation Model can be expressed as: Share Price = Div 1 / (K E g) Suppose the last dividend was 10 cent, the growth rate in dividends is 5% and the K E = 10% - work out the share price. The Cost of Equity Capital From the Dividend Valuation Model By rearrangement, K E = Dividend 1 Share Price + g
136 www.charteredgrindschool.com Formula for Share Price Using The Dividend Valuation Model Share Price = Div 1 K E g Formula for Cost of Equity Using The Dividend Valuation Model K E = {Div 1 / Share Price} + g CAPM vs DVM Approaches to Cost of Equity Capital The CAPM and the Dividend Valuation Model (Discounted Dividend model (DDM)) are likely to give different values for the K E because of a number of factors: The estimates may be wrong e.g. in CAPM or g in Dividend Model The CAPM is a single period model; the Dividend Model is a multi-period model CAPM focuses only on Market Risk; the K E derived from the dividend model is based on many dimensions of total risk The CAPM is a Normative model focusing on what the K E ought to be given a share s market risk (Ex-Ante Model). The Dividend valuation model is a Positivist model focusing on empirical real world data (Ex-Post Model). The ideal approach is to use both in an effort to arrive at K E. In an exam context use whichever is most appropriate in the context of the data provided. (c) The Price/Earnings Model Approach The Earnings Approach to Valuation Another model which is often used to calculate K E is based on the Price/Earnings ratio. A company can be valued as a stream of future Earnings rather than Dividends. The Share Price in this case, assuming no growth in EPS and a constant EPS forever (in perpetuity) is: Share Price = EPS/K E The Earnings Approach to The Cost of Equity Capital By rearrangement K E = EPS/Share Price This is the inverse of the P/E ratios which is quoted in the financial press. This model can be used to accommodate growth in EPS in the same manner as the DVM model shown above. Calculating the Cost of Equity (K E) The choice of models to use for K E will depend on the type of information given CAPM Approach: K E = R F + (R M R F) DVM Approach: Earnings Approach: K E = {Div 1 / Share Price} + g K E = EPS/Share Price
www.charteredgrindschool.com 137 B. THE OPPORTUNITY COST OF DEBT CAPITAL We have already examined the various methods for calculating the cost of debt. However, one method which we haven t mentioned is as follows: Using the CAPM to Calculate the Cost of Debt In some circumstances, you might be told what the of Debt is (since Debt can also be a trade security). In these circumstances you simply apply the CAPM equation to find the cost of debt: K Debt = R F + Debt (R M R F) If the Debt = 0.3; R F = 6% and R M = 14%; calculate K Debt Summary Floating Rate Debt: K D = Floating rate x (1 T) Irredeemable Fixed Rate Debt: K D = Coupon Payment (1 T) / Market Value of Debt Redeemable Fixed Rate Debt: K D = IRR of After Tax Cash Flows Using the CAPM: K Debt = R F + Debt (R M R F) For Private Issues of Debt Approximate using Equivalent Public Issues of Debt C. THE WEIGHTED AVERAGE COST OF CAPITAL If a project is all equity financed the opportunity cost of capital is based on the opportunity cost of equity capital. However, if the project is partly financed by debt then this will not be the appropriate rate. The appropriate rate in this instance will be made up of a combination of the rates for equity and debt capital. Often the term Cost of Capital is used to refer to both the case of all equity financing and part equity/debt financing. This is incorrect and you should be aware, as the examiner points out, that there are two distinct types of Cost of Capital. 1. The Opportunity Cost of Capital (r): The expected rate of return offered in capital markets by equivalent-risk assets. This depends on the risk of the project s cash flow. If there are no financing side effects or none of significance use this rate. In our terminology this is the opportunity cost of equity capital. 2. The Adjusted Cost of Capital (r*): An adjusted opportunity or hurdle rate that reflects the financing side effects of an investment project. If financing side effects are significant calculate the NPV using the adjusted cost of capital rate. This is the WACC. According to the examiner The WACC approach will be most usually expected although candidates should be aware of other methods it will not be necessary to remember the various formulae in general examination questions will focus on the WACC approach 14 14 The 2 other adjusted cost of capital formulae (infrequently used) will be discussed when MM theory is being covered. APV approach is to be looked at that time also. The Weighted Average Cost of Capital
138 www.charteredgrindschool.com The most widely used adjusted cost of capital is called the Weighted Average Cost of Capital (WACC) and is made up of a weighted average of the following: The Opportunity Cost of Equity Capital (K E) (As Derived from the CAPM) and The Cost of Debt Capital (K D) which because of the tax advantages of debt is (1 T) (K D) The relative weightings given to K E and K D depend on the proportion of Debt (D) and Equity (E) in the firms capital structure. Note that sometimes the part of the formula D + E is represented as Firm Value (V): So WACC (i.e. r*) is given as: [{K E x (E/ D+E)} + {K D (1 t) x (D/D+E)}] Note that the relative values of Debt and Equity could be measured using Book Values or Market Values typically Market Values should be used but Book Values will suffice if these are not available. Strengths and Limitations of the WACC Approach Strengths 1. Simplicity: The WACC is comparatively simple to use and understand 2. Relative Accuracy: The WACC is not always appropriate as a method of calculating the cost of capital but the relative errors caused may not be significant. When you consider the impact that errors in cash flow estimation can have on the NPV approach, small errors in the cost of capital can be relatively immaterial. Of course, the significance of the errors caused by the incorrect use of the WACC will depend on the extent to which the WACC is actually inappropriate in a particular circumstance (see the discussion of limitations). Limitations of WACC WACC can only be used in situations where a number of restrictive assumptions apply 15. Use of the WACC when these assumptions do not apply leads to potential difficulties: 1. The Project Should be Financed in an Identical Manner to the Firm as a Whole: If the company has a 60/40 balance between debt and equity then the project should be financed in this manner also. If the project is financed in any other ratio of Equity/Debt the usual WACC can t cope with the adjustments caused by the increased riskiness of debt. 2. The Project Should Have a Level of Market Risk Identical to that of the Company s Average Market Risk: If all the company s business is focused in the one sector and the proposed project is in this sector then this problem does not arise. However, if the company enters a new area of business the WACC for the old area will not apply for example, banking vs drilling for oil is the same WACC applicable to both? While this is an extreme example, the use of the existing WACC for a new type of endeavour is not appropriate. 3. The Project Should be Small vis a vis the Firm as a Whole: The K E and K D represent the costs for marginal increases in equity/debt. If the project is very large vis a vis the size of the firm, these marginal rates will not apply as the circumstances will be completely altered. If these assumptions are not met adjustments are needed as described below. 15 Knowledge of the situations when WACC can/can t be used is mentioned as a key aspect of the syllabus Assumption 1: Not Met Use the MM Formula as per the Formula Sheet: Use Instead of Usual WACC if the Project Will Not Be Financed in the Same Manner as The Firm As A Whole:
www.charteredgrindschool.com 139 The MM formula for WACC, which is to be used when the project is to be financed in a manner different to the firm as a whole, is as follows: r* = r (1 (t x L)) Which you could think of as WACC = K EUG (1 (t x L)) Where L = Percentage of Debt Financing for the Project T is the rate of corporate tax as before. L we haven t come across before. In broad terms L can be thought of as the specific debt/equity ratio to be used for the particular project i.e. suppose the project was being financed by 60% Debt and 40% Equity then L would be 0.6. Example: If tax is 40% and the K EUG (ungeared cost of equity) of the project is 15% - work out the WACC (i.e. the adjusted cost of capital) using the MM formula when the project is financed by 30% Debt and the firm as a whole is financed by 50% debt. WACC =.15% (1 [.4 x.30]) =.132 = 13.2% This formula works if the project (a) generates a level perpetual cash flow and (b) supports permanent debt. If the project doesn t meet either of these requirements the MM formula will not work. However, it will give reasonably accurate estimates in either case typically if the assumptions aren t met it will result in an error in the NPV calculation of between 2% - 6%. However, as Brealy and Myers (1991) point out, this isn t too bad when an error in cash flow forecasts could put the NPV out by 20% either way. Assumption 2: Not Met Using the Geared/Ungeared Beta Approach Beta of Equity Geared and Ungeared A firm with debt financing is riskier than one with no debt financing. Since risk is measured by beta, it follows that the beta of a geared firm will be higher than that of an ungeared firm. The beta of a geared firm represents both business and financial risk while that of an ungeared firm represents business risk only. The geared and ungeared betas are called equity and asset betas respectively. The Beta of Equity of an Ungeared Firm ( EUG) Asset Beta (Business Risk Only) The Beta of Equity of a Geared Firm ( EG) Equity Beta (Business & Financial Risk) There is a formula linking the Asset (Ungeared) and Equity (Geared) Betas as follows 16. D is the percentage of debt in the total financing structure (using market values), E is the percentage of equity in the total financing structure (using market values) while T is the tax rate. EUG = [{ Debt x (D (1 T) / (D (1 T) + E))} + { EG x (E / (D (1 T) + E))}] Which if the beta of debt is zero simplifies to: EUG = EG x [E / E + D(1-t)] Note that the EG i.e. the beta of equity of a geared firm is sometimes called the Equity Beta and the EUG i.e. the beta of the firm if it was all equity financed is sometimes called the Asset Beta as it only reflects the beta of the firm s business risk as distinct from business and financial risk. Practical Usefulness of Geared & Ungeared Betas: Example Firm in Beer goes into Fish Farming: Suppose Beer Limited has 80% Equity and 20% Debt. Its Beta of Equity is 1.3. It is considering going into business in the fish farming area but doesn t know the appropriate discount rate to charge. It looks at the average statistics for companies in the Fish Farming Industry and finds that: Average Beta of Equity = 1.5; Average Debt/Equity Ratio = 30% Debt and 70% Equity
140 www.charteredgrindschool.com Beta of Debt = Zero; Tax = 40%; E(R Market) = 15%; R F = 5% To arrive at the appropriate opportunity cost of capital for its Fish Farming venture can Beer: Use its own beta of 1.5 or use the fish farming beta of 1.35? The answer in both cases is NO. Its own beta is inappropriate for assessing the risk of a venture in a new business. The beta of equity in the fish farming industry is also inappropriate as that beta reflects both business and financial risk. All Beer Limited is interested in is the business risk of fish farming. This is where the formulae for converting Geared Betas (equity betas) to Ungeared Betas (asset betas) and Geared Costs of Equity to Ungeared Costs of Equity come in useful. The basic steps are to: Ungear the FF Equity Beta to reflect business risk only (use the FF gearing to do this) i.e. arrive at the FF Asset Beta Regear the FF Asset beta to reflect the business risk of FF and the financial risk of Beer i.e. arrive at Beer s Equity Beta For This Particular Project (use Beer s gearing to do this) Use Beer s Equity Beta For This Particular Project to calculate the Cost of Equity Capital (using the CAPM) and in turn plug this cost of equity into the WACC formula. The precise steps are as follows: Step 1: Calculate the EUG (i.e. the Asset Beta) of Fish Farming (i.e. the business risk as of fish farming as opposed to the business risk plus the financial risk of companies in the fish farming industry). EUG = { EG x (E / (D (1 T) + E))}] (assuming the debt beta is zero) EUG (Fish Farming) = {1.5 x 70 / (30 (1 -.4) + 70} = 1.19 Thus, the beta of the actual business risk of fish farming is 1.19. 16 If this formula is needed it will be provided in the exam Step 2: Convert the Fish Farming Ungeared (Asset) Beta to Reflect the Financial Gearing of Beer Limited Use the same formula as before except plug in the appropriate figures for Beer Limited EUG = { EG x (E / (D (1 T) + E))}] Remember, that we are calculating a Geared Beta for Beer Limited so we apply Beer Limited s gearing levels. 1.19 = { EG x 80 / (20 (1 -.4) + 80)} So EG (Beer s Fish Farming Project) = 1.37 = Beta for Business and Financial Risk This is the geared beta to reflect both the business and financial risk of Beer Limited s appraisal for the fish farming project. Step 3: Utilise the CAPM to work out the Appropriate Cost of Equity Capital K EG (Beer s Fish Farming Project) = R F + EG (E (R M R F) = 5% + 1.37 (15% - 5%) = 18.7% Step 4: Derive the WACC in the Normal Fashion
www.charteredgrindschool.com 141 Assume that the pre-tax cost of debt is 8.33% giving an after tax cost of debt of 5% (equivalent to R F since Debt = 0). To derive a WACC for the project we simply use the usual WACC formula: WACC = {18.7% x (80 / 100)} + {8.33% (1 -.4) x (20 / 100)} = 15.96% Thus, the project s after tax net cash flows should be discounted at 15.96% This might seem complex at first but practice and you will get the hang of it! Candidates frequently have difficulty in adjusting cost of capital for changes in capital structure particularly when this involves ungearing and re-gearing betas. This is a matter of practice. An Alternative Approach: Use of the Geared/Ungeared Cost of Equity Capital Approaches Instead of using the geared/ungeared beta approaches Beer Limited could take an alternative route to arrive at the same answer. First we need to examine the link between the geared and ungeared cost of equity. Cost of Equity Geared and Ungeared K EG = K EUG + {D (1 T) / E} (K EUG KD) 17 Step 1: Work out the Cost of Equity Geared/Ungeared in the Fish Farming Industry K EG (Fish Farming) = 5% + 1.5 (15 5) = 20% This represents the cost of equity in fish farming which includes both business and financial risk. To isolate the business risk component only Beer Limited can use the formula to convert geared and ungeared costs of equity as follows: 17 Again, this formula will be on the exam script if required. In general, even if a formula is published on the paper it does not always mean that it has to be used! Be careful! K EG = K EUG + {(D (1 T) / E) x (K EUG K D) 20% = K EUG + {(30 (1 -.4) / 70) x (K EUG 5) K EUG (Fish Farming) = 16.9% Again, this gives the rate to use to reflect only the business risk of the fish farming industry. Step 2: Convert the Ungeared Cost of Equity in Fish Farming to Reflect Beer Limited s Gearing K EG (Beer s Fish Farming Project) = 16.9% + {20 (1 -.4) / 80) x (16.9% - 5%) = 18.7% Step 3: Apply this Cost of Equity in the WACC Formula as Before You should make sure that you understand and are able to use both approaches as a question could provide information which was more applicable to one rather than another. If Assumption 3 Not Met i.e. The Project is large Vis a Vis The Firm As A Whole In this instance the WACC formulae break down completely since they are all concerned with the marginal cost of capital. In this case you must use an approach called Adjusted Present Value described later. Conclusion on WACC A popular argument advanced by many commentators is that the WACC used in the US and UK is much higher than that used by Japan and Germany and that this can help to explain the relative decline of the US and UK. The structure of the equity and corporate bond markets in the latter counties receives much
142 www.charteredgrindschool.com of the blame for this phenomenon. However, like many debates in finance, there is no definitive answer to this issue. Checklist for Calculating WACC Adjustments If the project is not to be financed in the same manner as the firm as a whole: Use the MM formula for WACC If the project doesn t have a level of market risk identical to that of the firm as a whole: Follow the Geared/Ungeared Beta/Cost of Equity Approach If the project is not small (marginal) vis a vis the firm as a whole WACC breaks down completely Use APV approach