How do you calculate the cost of equity?
Use CAPM. Cost of equity is the risk free rate plus beta times the equity risk premium, so 4% plus 1.2 times 5% is 10%. Use a long term government bond yield for the risk free rate. It should exceed the cost of debt.
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Example answer
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The cost of equity is the return shareholders require for owning the stock. There's no contract that states it, the way there is for debt, so I have to estimate it. The standard way is CAPM.
The formula is the risk-free rate plus beta times the equity risk premium.
The risk-free rate comes from government bond yields. Beta measures how much the stock moves with the market. The equity risk premium is the extra return investors want for holding stocks instead of government bonds.
So a company that moves more with the market has a higher cost of equity.
What holds it back
The formula and the three inputs are right, but it stops at definitions. There's no worked number, and nothing on where you'd actually find each input.
The cost of equity is the return shareholders require for owning the stock. There's no contract that states it, the way there is for debt, so I have to estimate it. The standard way is CAPM. The formula is the risk-free rate plus beta times the equity risk premium. I'll assume a risk-free rate of 4%, a beta of 1.2 and an equity risk premium of 5%. Beta times the premium is 6%, and adding the risk-free rate gives a cost of equity of 10%. The risk-free rate comes from government bond yields. I'd use the ten-year bond in the same currency as the cash flows. Beta measures how much the stock moves with the market. I can get it from a regression of the stock's returns against an index, or from comparable companies. The equity risk premium is the extra return investors want for holding stocks instead of government bonds. It's estimated from long-run history or implied from current market prices. So a company that moves more with the market has a higher cost of equity.
The cost of equity is the return shareholders require for owning the stock. There's no contract that states it, the way there is for debt, so I have to estimate it. The standard way is CAPM. The formula is the risk-free rate plus beta times the equity risk premium. I'll assume a risk-free rate of 4%, a beta of 1.2 and an equity risk premium of 5%. Beta times the premium is 6%, and adding the risk-free rate gives a cost of equity of 10%. The risk-free rate comes from government bond yields. I'd use the ten-year bond in the same currency as the cash flows. Beta measures how much the stock moves with the market. I can get it from a regression of the stock's returns against an index, or from comparable companies. I'd trust the peers more, because one company's regression is noisy. The equity risk premium is the extra return investors want for holding stocks instead of government bonds. It's estimated from long-run history or implied from current market prices. Nobody can observe it directly, so it's the input I'd hold least firmly. So a company that moves more with the market has a higher cost of equity. The logic is that investors only get paid for risk they can't diversify away. One company's bad news washes out in a portfolio, but its exposure to the whole market doesn't, and beta measures that exposure. Two checks. The answer has to sit above the company's cost of debt, because shareholders get paid after lenders. And I'd show a range. With a beta of 1.0 it's 9%, and with 1.5 it's 11.5%, so half a point of beta moves it by 2.5 points. For a small or private company, many practitioners add a size premium on top of CAPM. That's a convention, not part of the formula, so I'd say so if I used one.
The numbers, step by step
Assumed inputs: a 4% risk-free rate, a 5% equity risk premium and a beta of 1.2, then the same with betas of 1.0 and 1.5.
- Beta times the premium1.2 × 5%
- 6%
- Cost of equity4% + 6%
- 10%
- With a beta of 1.04% + 1.0 × 5%
- 9%
- With a beta of 1.54% + 1.5 × 5%
- 11.5%
- Effect of half a point of beta11.5% − 9%
- 2.5 points
What the interviewer listens for
- Do you know the CAPM formula without hesitating?
- Can you say where each of the three inputs comes from?
- Do you state your rates as assumptions instead of quoting the market?
- Do you understand why beta, and not total risk, drives the answer?
Common mistakes
- Multiplying beta by the whole market return.Beta applies to the premium over the risk-free rate, so the risk-free rate is only counted once.
- Quoting a bond yield or risk premium as today's fact.Say "I'll assume 4%" unless you checked it this morning.
- Using a risk-free rate in a different currency from the cash flows, which mixes two inflation outlooks in one valuation.
- Ending up with a cost of equity below the cost of debt and not noticing.Shareholders rank behind lenders, so they need more.
More finance technicals
- What is beta, and why would you unlever and relever it?
- Why do you subtract cash to get enterprise value, and can enterprise value be negative?
- Walk me through a comparable company analysis.
- Which valuation method usually gives the highest value, and why?
- When would you use EV/EBITDA instead of P/E?
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