Explain why beta measures only systematic risk and not total risk. Why is that the economically correct thing for CAPM to price?
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The answer
Beta measures only systematic risk because that is the only risk a diversified investor still bears. Total risk includes both systematic market-wide factors and company-specific idiosyncratic risk, but a rational investor holding a diversified portfolio has already eliminated that idiosyncratic risk for free, since the unrelated ups and downs of many different stocks tend to average out.
Because diversification costs nothing, the market does not compensate you for bearing risk you can easily get rid of, so the only risk that earns a return is the non-diversifiable, systematic risk that beta captures.
When CAPM prices a stock, it uses beta rather than total volatility because total volatility would double-count risk the market does not actually pay you to hold, and that makes beta the economically correct measure for determining the required return.
DCF timeline
| Line item | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
|---|---|---|---|---|---|
| Free cash flow | 50 | 54 | 58 | 63 | 68 |
| PV of free cash flow | 45 | 45 | 44 | 43 | 42 |
| Terminal value (Year 5 exit) | 1,001 |
| PV of terminal value | 621 |
| Implied enterprise value | 840 |
Also asked as
- Write the CAPM formula and define each of its three components in one sentence each.
- Why is a long-duration government bond yield (e.g., the 10-year Treasury) used as the risk-free rate, rather than a short-term rate?
- Compute the cost of equity given a risk-free rate of 4.2%, an equity risk premium of 5.0%, and a beta of 1.4.
- Why can't you directly average the levered betas of several comp companies with different capital structures? What do you do instead?
- You have two comps: Comp A with levered beta 1.25, D/E of 25%, tax rate 24%; Comp B with levered beta 1.60, D/E of 55%, tax rate 24%. Unlever both betas and compute the average unlevered beta.
- Using the average unlevered beta from the previous question, relever it to a subject company's target D/E of 45% (tax rate 24%), and compute its cost of equity given Rf of 4.0% and ERP of 5.5%.
- A comp has a distorted effective tax rate of 6% due to large NOL carryforwards, a levered beta of 1.35, and D/E of 40%. Explain why you should not use its 6% effective tax rate directly in the unlevering formula, what you should use instead, and compute the unlevered beta both ways (using 6% and using a normalized 25% marginal rate) to show the magnitude of the distortion.
- A subject company currently has D/E of 20% but plans a recapitalization that will bring it to a target D/E of 80% within the year. You've derived an average unlevered beta of 0.95 from a comp set (25% tax rate). Compute the cost of equity using (a) the current D/E of 20% and (b) the target D/E of 80%, given Rf of 4.5% and ERP of 5.5%, and explain which one is appropriate for valuing the company going forward and why.
- Explain the difference between a historical equity risk premium and an implied (forward-looking) equity risk premium, and describe a market environment in which the two would diverge significantly. If the implied ERP is currently 3.5% but the historical average is 5.5%, and you use the historical figure in your CAPM calculation, what direction of bias does this introduce into your DCF valuation relative to current market pricing?
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The rest of this topic
Beta: levered, unlevered, relevered