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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

Cost of Capital

John H. Cochrane

University of Chicago GSB

standard approach
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)
  • Spend a lot of time on β, use 6% for E(Rm-Rf)
warning most people misunderstand expected
Warning: Most people misunderstand “Expected.”

What many people mean

What the formula means

  • This may explain high required-return hurdles.










Warning 2: Valuation is very sensitive to growth, return assumptions. The cost of capital matters!P/D = 1/(r-g)
market premium 6
Market Premium = 6%?

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
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
Market premium varies a lot through time

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

multifactor models are replacing the capm
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 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.
  • 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!

use dynamic multifactor models1
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……
answer guess 1 comparables
Answer guess 1: Comparables?
  • 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?
answer guess 2 prices
Answer guess 2: Prices
  • 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.