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MIT 15 414 - Discount Rates for Use in Capital Budgeting

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Recitation V Jiro E. Kondo Summer 2003Today’s Recitation: Discount Rates for Use in Capital Budgeting. I. Quick Review of the CAPM. II. Beta of Equity vs. Beta of Assets. III. Beta of Assets vs. Beta of Project. IV. Long-term Projects and Discount Rates.I. Quick Review of the CAPM. • CAPM gives us a theory of valuation (i.e. expected returns) for individually traded secu -rities. → Linear relationship between expected return and security’s beta. Described by SML: E[Ri]= Rf + βi(E[Rm] − Rf ). (1) • Beta of security i’s return is determined by: Cov(Ri,Rm)βi = (2)Var(Rm) where Rm is the return on the market (often replaced with the value-weighted market return or S&P500 index). → Estimating this beta with historical data can be done using a linear regression: Ri = ai + biRm + i. (3) → bi is an estimate of βi. → Problems with using historical beta?I. Continued... • Problem with using a long history of return data to estimate the equity beta... → On the one hand, using a longer estimation window is good because it reduces the estimation error in our predicted betas. → However, we run into a problem of changing betas. → It is reasonable to assume that a firm’s beta might change over time (e.g. firm undertakes projects in new industries, nature of industry changes, etc). In most cases, this process is slow and gradual (e.g. through or-ganic growth), though it can occur quickly (e.g. some diversification mergers). In an example, we’ll see later that, when a company is leveraged, the beta of its stock can change even without underlying shifts in business risk. → Why does this create problems in estimation? Be-cause it makes our beta estimates ambiguous in mean-ing. To illustrate, suppose that XYZ Corp had a beta of 2 in the 80s but, through mergers, lowered its beta to 1.5 in the 90s. In this case, it’s current beta is 1.5, which would roughly obtain using 90s data. Meanwhile, we’d likely get a beta estimate of about 1.75 (average of 1.5 and 2) if we used 80s and 90s data. → The main point is that you want to estimate betas using a long enough time series to reduce estimation er-ror while not extending back so far that changing beta problems can cloud your results.II. Beta of Equity vs. Beta of Assets. • Beta is easiest to calculate for common stock because it is most actively traded and stock re-turn data is readily available. → Called beta of equity. • Should we use the beta of equity to calculate the firm’s cost of capital? → No. The beta of equity is only used to cal-culate the firm’s cost of equity. Unless the firm is all equity financed, the beta of its underlying assets will almost surely be different from its beta of equity. The same thing holds true for expected returns. • Why? → Most common reason is the presence of debt in the firm’s capital structure. → How does debt make beta of assets differ-ent from beta of equity? Best seen with an example.Fact: Holding business risk constant, the more levered a company (i.e. more debt), the riskier its equity and the higher its cost of equity. → Intuition: So long as debt is roughly riskless, eq-uity ends up picking up all the variability in firm value (including the variability that’s correlated with the mar-ket). As more debt is issued, this variability per unit of equity value becomes larger which increases the beta of equity. This in turn increases the cost of equity.• Intuition: Recall that interest payments on corpo-rate debt (reflected by the cost of debt E[RD]) reduce accounting profits. Subsequently, this lowers the com-pany’s tax burden. On the other hand, dividend pay-ments (reflected by the cost of equity E[RE ]) do not reduce its accounting profits or tax burden (double-taxation: as profits for the firm, as dividend income for the investor). Through this difference in tax treat-ment, the government in some sense ’pays’ part of the cost of debt but not some of the cost of equity. This payment is larger as the corporate tax rate increases. This explains the presence of a tax adjustment on the cost of debt with no similar adjustment for equity in the WACC formula.III. Beta of Assets vs. Beta of Project. • Of course, the firm’s cost of equity really only gives us a measure of the cost of financ -ing all of the firm’s existing projects in their current state. That is, this gives us an idea of the cost of capital that’s appropriate for a project whose risk is the same as that of the firm’s typical project. • This measure does not apply to all the firm’s projects. • Alternative approach to estimating beta: com -parables method. → Other reasons to use comparables? • Examples: - Company in industry X evaluates a project in industry Y. Can estimate project beta using beta of assets of pure-plays in industry Y. - Company in industry X evaluate a project in industry X and industry Y. Can estimate project beta using an average of own beta of assets and an average of beta of assets of pure-plays in industry Y. Alternatively, can estimate the beta of assets of a firm operating in both industries X and Y.III. Continued... • Keep in mind that methods 1 and 2 will give slightly different answers. Method 1 runs into the problem that highly (low) levered firms might have more (less) risky debt/equity than our firm (which would make for poor compar-ison). Meanwhile, method 2 makes the as-sumption that comparable firms have the roughly the same WACC which could ignore differences in the tax treatment of debt and equity if they have varying leverage ratios. → Method 2 is most commonly suggested.IV. Long-term Projects and Discount Rates. • What we’ve said about a project’s cost of capital: ... using the CAPM, we can find a single discount rate E[RA] and


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MIT 15 414 - Discount Rates for Use in Capital Budgeting

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