## 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 $\mu_r$ for given $\sigma_r$ OR minimum $\sigma_r$ for given $\mu_r$
• No risk-free asset (i.e. no asset where $\sigma_r = 0$) 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

### $\text{WACC} = {e \over (d+e)} \times k_e + {d \over (d+e)} \times k_d$

where $e$ = equity, $d$ = debt, $k_e$ = cost of equity, $k_d$ = 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

## $k_e$

$k_e = r_f + \beta (r_m - r_f)$

• $r_m$ 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

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

• 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
• $\beta$ adjusts the equity risk premium $(r_m - r_f)$ for specific risk of the asset

• Note that $k_e$ is already/inherently post-tax

• Use ‘CRP’ on Bloomberg to source latest $r_f$ and $r_m$

• 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

## $\beta$

• $\beta$ 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: $\beta_{adj} = \frac{1}{3} + \frac{2}{3} \times \beta$
• CAPM says all $\beta$ converge at 1 over the long term

## $\beta_u = {e \over (d+e)} \times \beta_l$

• Unless a company has no debt, the observed $\beta$ is $\beta_l$
• 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 ($\beta_u$) of the peers must be used, and then re-levered ($\beta_l$) for the optimal capital structure of the asset

## $k_d$

• 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)
• 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: $k_d \times (1-t)$ 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