Weighted-average cost of capital

11 June 2020

Somewhere between an aide-memoire and a terse primer, below are my notes on WACC. The angle here is market practice for corporate finance rather than theory.

Modern portfolio theory (“MPT”)

  • Markowitz (while at Rand, 1952)
  • ‘Efficient frontier’ whereby assets with given pairwise correlations are combined with certain weights to maximise expected return for a given level of risk (defined as the standard deviation of returns);
    • maximum μr\mu_r for given σr\sigma_r OR minimum σr\sigma_r for given μr\mu_r
  • No risk-free asset (i.e. no asset where σr=0\sigma_r = 0) in original treatment
  • Weights can be negative (i.e. you can be short)

Capital asset pricing model (“CAPM”)

  • MPT with risk-free asset, which like other assets can have positive or negative weights (i.e. long or short)
  • Theoretically, everyone now owns the same portfolio (the ‘market portfolio’)
  • You want to evaluate the required return for a given level of risk for an individual asset (specific)
    • Nobel-prize worthy smart (Sharpe, Markowitz, Miller 1990) but does not always stand up empirically
  • CAPM gives us beta
    • You know the systematic risk (the market portfolio) — the specific risk is the risk left over

Weighted-average cost of capital

WACC=e(d+e)×ke+d(d+e)×kd\text{WACC} = {e \over (d+e)} \times k_e + {d \over (d+e)} \times k_d

where ee = equity, dd = debt, kek_e = cost of equity, kdk_d = post tax cost of debt

  • Weighted average of debt, equity, anything else
  • Forward looking
  • Note the weights are for the optimal capital structure
  • For most public companies 8-10% sensible and this is why equity research analysts always guesstimate
    • BTW our decisions have to be more defensible
  • Do: always include preference shares/convertibles if outstanding
  • Do not: use the WACC from Bloomberg, it is always wrong

kek_e

ke=rf+β(rmrf)k_e = r_f + \beta (r_m - r_f)

  • rmr_m is the market return: you own the entire market, what is your earnings yield OR put another way, portfolio reflects basket of entire market, gives you a weighted average P/E, what is the inverse

  • rfr_f is the risk-free rate: asset where returns do not vary i.e. σr=0\sigma_r = 0

    • In practice, government bond for the asset you are trying to value e.g. UK or US
    • Tend to use 10 year maturity in practice
  • β\beta adjusts the equity risk premium (rmrf)(r_m - r_f) for specific risk of the asset

  • Note that kek_e is already/inherently post-tax

  • Use ‘CRP’ on Bloomberg to source latest rfr_f and rmr_m

  • Equity risk premium post GFC (QE and low interest rates) is much higher than it has been historically

  • Historically 4-6% typical

  • Low cost of debt post GFC offsets this in WACC

  • Cost of equity varies for different types of company. From low to high:

    • Defensive megacap: liquid, provides a product or service the world cannot do without, low beta, recurring progressive dividend; in short, bond-like returns
    • Small cap: illiquid, life will go on if it falls over, likely to have greater volatility in profits, may still be re-investing so lower dividend(s)
    • Private: same as small cap but more so
    • Early stage private i.e. venture: you can loose your equity value at any moment and there are no tangible assets
  • To adjust for this a size/liquidity premium of 1-3% is often added for small/mid-caps (c.f. Ibbotson Associates)

  • Use earnings yield as a sense check

β\beta

  • β\beta represents the idiosyncratic risk of the asset and acts to scale the equity risk premium
  • Use ‘BETA’ function on Bloomberg
    • What index do you use? FTSE all share (UK), S&P500 (US) …
    • Sampling period? Day, week, month? Over 1, 3, 5 years? Monthly seems to be standard but nothing wrong with taking an average
  • Use adjusted beta: βadj=13+23×β\beta_{adj} = \frac{1}{3} + \frac{2}{3} \times \beta
    • CAPM says all β\beta converge at 1 over the long term

βu=e(d+e)×βl\beta_u = {e \over (d+e)} \times \beta_l

  • Unless a company has no debt, the observed β\beta is βl\beta_l
  • When is the beta not the beta?
    • When the shares don’t trade i.e. illiquid small/mid-caps
    • This is why size/liquidity premium is used
  • What if beta is not observable i.e. the asset is not listed?
    • Take an average of the betas of listed peers
    • When taking an average the average of the unlevered betas (βu\beta_u) of the peers must be used, and then re-levered (βl\beta_l) for the optimal capital structure of the asset

kdk_d

  • There are multiple sources of cost of debt:
    • YTM/YTC on listed bonds if they have them (Bloomberg)
    • Weighted average interest rate on bank facilities (Annual report)
    • CDS spread (for large-cap)
  • If you have to estimate:
    • LIBOR (or other interest rate benchmark) plus spread
    • YTM/YTC on listed bonds at similar credit rating
  • Make sure post-tax: kd×(1t)k_d \times (1-t) if not

Target capital structure i.e. weights

  • Market values of debt and equity should be used where available
  • The more mature the company the more likely it is that the pre-existing capital structure is optimal
  • If you are unsure, an average of peers should give what is typical in industry
  • Leverage (net debt/EBITDA) and gearing (debt/equity) should be calculated as a sense check

WACC in context of DCF

  • Higher WACC gives lower NPV
  • Discount rate should also reflect opportunity cost
  • WACC is used to discount cash flows to whole firm (i.e. pre financing) i.e. to EV not to equity
  • Discount rate should not reflect probability of the forecasts being achieved — do that separately
    • Cost of financing does of course reflect the risk of the asset, in the round
  • The discount rate belongs to the cash flows of the asset: do not use acquirer discount rate on target
  • WACC is a key input to a DCF as well as PGR, margins and revenue growth
    • Should always sensitise WACC when doing DCF

Where else WACC is used

  • Goodwill impairment testing (IFRS), if you are an auditor
  • ROIC less WACC gives an indication of economic profit
  • Capitalising (pre-tax and pre-financing) synergies
  • Discounting the future value of EV to give value today