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Cost of Capital

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Cost of Capital

John H. Cochrane

University of Chicago GSB

- Question: Should we invest, buy asset or company?
- Standard answer:
Value = Expected Profit / Expected Return

(Really, multiperiod version)

- ER? Use CAPM, ER = Rf + β E(Rm-Rf)
- Spend a lot of time on β, use 6% for E(Rm-Rf)

What many people mean

What the formula means

- This may explain high required-return hurdles.

Profit

Profit

Risk

“Expected”

Expected

Risk

“Risk”

Time

Time

My focus: using the CAPM for cost of capital

Problem 1. We don’t know E(Rm-Rf)! 6% is very rough!

- Statistical uncertainty – large with 18% σ
- Economic uncertainty. 6% (0.5 Sharpe) is HUGE. No economic explanation for 6%. Did our grandparents really know 6%?
- Suggests true ex-ante premium is lower!

- Returns are forecastable. Dividend (cashflow) growth is not forecastable.
- All variation in price / x is due to time-varying discount rate E(Rm-Rf).
- Your discount rate (cost of capital) should vary too; low cost when p/x is high!
- When p/x is high, it’s ok to invest in high p (high cost) projects

Forecasts made 5 (10) years ahead using D/P regression

Example: Fama-French model

E(Ri-Rf) = bi E(Rm-Rf) + hiE(HML) + si E(SMB)

- Use multifactor models (e.g. FF) with time-varying betas and time-varying premiums?
- Note betas and premium vary over the life of the project as well as over time (when project is started).
- Technically complex but straightforward. Much theoretical literature is headed this way.
- Better answers?

Problem 1: New premia just as uncertain and vary over time too!

Et(Ri-Rf) = bi Et(Rm-Rf) + hiEt(HML) + siEt(SMB)

What’s E(HML), E(SMB)? Same statistical problem. Even less economic understanding of value/size premium. Less still of how they vary over time. More of them!

- Problem 2: Lots of new “factors” and anomalies.
- FF fails on momentum, small growth (especially important here!), other anomalies.
- “Answer:” Many more factors! Momentum, small-growth, currencies, term premium, default premium, option returns and up/down betas……

- Renewed use of comparables. (Keeping fallacies and pitfalls in mind.)
- E(Ri) = Rf + β E (Rm-Rf)
- Why not just measure the left hand side? Avg returns of similar firms?
- Old answers:
- CAPM gives better measure. σ is lower (1/2) so σ√T is better. (Industry return may have been luck.)
- Need to make β adjustments. This project may be low β though industry (comparable) is high β.
- CAPM is “right” model.

- New answers:
- We don’t know (yet) that multifactor models give better predictions for ER going forward.
- Challenge for MF is now to explain patterns already well described by characteristics (size, book/market, momentum, industry etc.)
- Possible to be low β project with high ER characteristics, but how often does this really happen?
- Much less confidence that MF models are “True” vs. “Descriptive.” Who really cares about covariance with SMB?

- Why is the cost of capital different from the cost of tomatoes?
- Real question: If we issue stock for new investment or acquisition, will money raised = cost of investment?
- A: If new project is like your old projects, market / book ratio tells you the answer directly.
- Q theory: Invest whenever market / book > 1.