SECTION HANDOUT #5. MBA 203 December 5th, 2008

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1 SCTION HNOUT #5 MB 203 ecember 5th, 2008 I. sset, quity, and ebt Betas Last week we learned that we can use the Capital sset Pricing Model to find the required rate of return for a security. The only risk we care about is market risk, and the CPM (beta) tells us how sensitive a stock s return is to the return on the market. Recall that the expected return on stock i is related to the market return by the CPM equation: 1 r i = r f + i (r m r f ). The application of the CPM is not restricted to stocks alone. The CPM should hold for any asset, whether it s debt, equity, any firm s assets, or any series of future cash flows. In this section we re going to look at the firm s assets. To do so, it is useful to decompose the beta of the firm s assets. Remember that the beta of a portfolio is the weighted average of the betas of the individual assets in the portfolio. Suppose there is a firm whose outstanding securities include both equity and debt. Then the value of firm s assets () is equal to the market values of debt () and equity (): = +. If we owned all of the assets of the firm, we would have a portfolio of the firm s debt and the firm s equity that entitled us to all of the firm s future cash flows. This means that our asset beta is a weighted average of the debt beta and the equity beta: = +, Prepared by Sara Holland. Sebastien Betermier and Vijay Balakrishnan contributed to earlier versions of these notes. 1 In this equation, r m is the market return, r f is the risk-free rate, and r m-r f is the market risk premium. 1

2 where the debt beta and the equity beta represent the exposure to market risk that debt and equity holders bear, respectively. Be careful when using this relation! ven though we re writing the asset beta as a weighted average of the debt and equity betas, we re not implying that it necessarily depends on these two betas. In fact, is there any right-to-left causality? oes the asset beta, and, consequently, the value of the firm s assets, depend on how much debt the firm takes on? We ll tackle these questions in the next section. II. Valuing the Firm a. Without the ebt Tax Shield In a world without the debt tax shield, 2 the value of the firm s assets is independent of the way it is financed. Think about any firm, for example, pple, which has many upcoming projects producing better computers and MP3 players. s long as pple has the cash to finance these projects, it doesn t matter whether that cash comes from debt or equity. What does this irrelevance result imply about the distribution of risk among the firm s claimants? Rearrange the terms of the portfolio beta equation to find an expression for the equity beta in terms of the asset and debt betas: = e Note that if debt is risk free, then d, d = e =. = / e. This formula is key. The asset beta,, is independent of how the firm is financed, so as financial leverage increases, so does the equity beta,. So, how do we value a firm in this world? Well, we saw that the firm s value is the present value of all its future cash flows. few weeks ago, we learned how to estimate 2 ctually we need more assumptions: no taxes, no bankruptcy costs, no transaction costs, and no asymmetric information. 2

3 these cash flows. nd last week, we learned about the CPM model, which allows us to estimate discount rates. ccording to the CPM, in order to get the discount rate of the firm s assets (r ), we need the asset beta. With the portfolio beta formula it s easy to estimate the firm s asset beta: estimate the firm s leverage ratio, get the equity beta from data on stock returns, and assume a low value for the debt beta (usually close to 0). xample: 10.P.9, 10.P.10 b. With the ebt Tax Shield In a world without taxes, cash flows from the firm were shared between equity holders and debt holders. What happens when we introduce taxes? Now, cash flows from the firm are split into three pieces equity, debt and taxes. The value of the firm depends on the capital structure when we introduce taxes because of the difference in treatment between the interest paid to debt holders and dividends paid to shareholders. For the firm, interest expense is tax deductible, but dividend payments are not. Hence, there are tax advantages to issuing more debt. n increase in the proportion of debt in the firm will increase the total value of the equity and debt. Note that under these conditions every firm will always choose debt over equity to fund projects. But this is not what we observe in reality. Firms typically have leverage ratios between 20% and 40%. There must be some reason why firms continue to finance with equity. What else might be going on? We have not considered personal taxes on income or personal taxes on capital gains. Remember that we re still in a world with no bankruptcy costs and no asymmetric information. If we relax these assumptions, we might find an advantage to equity. If you take the Corporate Finance (MB231) course, you will see how the results change once we account for these other factors. 3

4 In the meantime, let s learn how to value a firm in the presence of the debt tax shield. The beta ( ) and the expected return to the assets (r ) remain the right risk measure and discount rate, respectively, but the tax shield complicates the regular PV formula. We will not explain the problem in this handout, but you will understand it in MB231. There are two methods to get around it and value the firm in the presence of a debt tax shield: the djusted Presented Value (PV) method and the Weighted verage Cost of Capital (WCC) method. Which method you should use depends on your assumption of the firm s future level of debt. i. PV Method The idea in the PV method is to value the firm without the tax shield and then to add the extra present value generated by the tax shield. Valuing the firm without the tax shield isn t hard. Remember that in the tax-free world, the value of the firm is independent of its financial leverage. So all we have to do is to assume that the firm has no debt (hence, no tax shield) and value this all-equity firm. The following steps are involved in using the PV method: Forecast the firm s or project s all-equity cash flows, i.e. the free cash flow from the firm and the after-tax interest (to get the tax shields) iscount the above cash flow using r to get the base PV dd the PV of all tax shields If the firm is planning to hold a constant amount of debt forever, then the PV is the best method to use to value the firm. It s also the most flexible method in general. xample: 20.Q.8, 20.P.16, 20.P.19 ii. Weighted verage Cost of Capital (WCC) s in the PV method, we need to calculate the cash flows for the firm assuming there is no debt. Then, we just discount the cash flows at an adjusted discount rate to obtain the 4

5 value of the firm. It s a one-step procedure, where the discount rate already takes into account the tax shield. The PV method accounts for the tax shield by adjusting the present value (we just tack on an extra term), whereas the WCC method uses an adjustment to the discount rate. This discount rate is called the WCC and is defined by: WCC = (1- Tc ) * r + d + r + where: - and are the amounts of ebt and quity in the firm, - T c is the tax rate of the firm, and - r d and r e are the required return on debt and equity respectively for the firm. e Important note: For WCC to be applicable, one important assumption must hold. The firm or project that we are valuing should maintain a constant debt/equity ratio for the remaining life of the firm or project. xample: 20.Q.1, 20.Q.2, 20.P.11 5