Cost of Capital

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# Cost of Capital - PowerPoint PPT Presentation

Cost of Capital. John H. Cochrane University of Chicago GSB. Standard approach. 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)

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### Cost of Capital

John H. Cochrane

University of Chicago GSB

Standard approach
• Question: Should we invest, buy asset or company?

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)
Warning: Most people misunderstand “Expected.”

What many people mean

What the formula means

• This may explain high required-return hurdles.

Profit

Profit

Risk

“Expected”

Expected

Risk

“Risk”

Time

Time

Warning 2: Valuation is very sensitive to growth, return assumptions. The cost of capital matters!P/D = 1/(r-g)

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!
Problem 2. Market Premium varies a lot through time.
• 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
Market premium varies a lot through time

Multifactor models are replacing the CAPM

Example: Fama-French model

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

Use Dynamic Multifactor Models?
• 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.

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!

Use Dynamic Multifactor Models?
• 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?
• 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.
Comparables?