A Lesson on the Cost of Capital

Cost of Capital

Cost of Capital should reflect the time value of money and the risk incurred in earning cash flows. It is a measure that reflects how much we are charging for the capital that we allocate to particular activities.

The first aspect of this definition is fairly straightforward. We value a dollar more today than a dollar in the future so cash flows in the future should be discounted at a higher rate. The second part of the definition requires greater judgement. Judgement is particularly important because the cost of capital is time-varying in nature, meaning that as our perception of risk through time changes so will the cost of capital.

Before we get into the the theory I'd like to address one point. A lot has been made about "excessive risk taking" in recent years. I think it is important to remember that we invest in the stock market (or markets) principally because we want companies to task risks. The allocation of capital is fundamentally based on rewarding risk, so we should not be penalising companies that take this path. What is and has been the problem recently has been the level of transparency surrounding  risk taking. If you are a high risk company and decorate yourself to portray a low risk company, then simple valuation analysis tells us that values are going to be highly (and erroneously) inflated (think about it from a DDM approach - Po = D1/r-g).

Now back to the cost of capital...

The cost of capital is the flip side of the cash flow valuation problem. This means that when we are examining cash flows that will be delivered to shareholders that the relevant hurdle rate is the cost/return on equity. On the other hand if we are examining cash flows that are returned to all stakeholders then the relevant hurdle rate should be the cost of capital. The latter is a weighted average of all the capital contributions to the firm. The first rule, therefore, in choosing an appropriate cost of capital is to identify where the cash flows come from.

So what is the cost of capital?

It is the weighted average contribution of equity and debt (and possibly preferred equity/debt) to the firm. To calculate WACC we require a proxy for the cost of capital and cost of equity as well as the relative contribution of debt and equity to the firm's capital structure. In its simplest form the WACC a markets assessment of the opportunity cost of investing a particular asset and therefore, for this figure to make sense it needs to be calculated from market based variables. This means it needs to be forward looking  rather than calculated from historical statements. Some other points worth remembering about the cost of capital are the following:

1. The weight of each component is the fraction of total long-term financing that each source represents. Therefore, when you are thinking about the proportion of D/V (and even E/v) all non-interest bearing liabilities such as accounts payable/receivable, unfunded pensions etc.. are excluded.
2. The cost of debt is multiplied by (1-tc). We use the after tax cost of debt rather than the gross value because we recognise that debt offers us particular tax advantages (creditors receive rd but the firm receives a net cost of rd(1-tc) that we benefit from (thus lowering the overall cost of capital). Since neither the cost of equity/ preferred stock is tax deductible we don't adjust these components for tax.
3. The cost of capital calculation assumes a constant capital structure. Because this capital structure is constant we should ensure that our D/V and E/V represent the long-run optimal capital structure mix. This is because value is primarily derived from the terminal value component of our calculation. To have the capital structure reflecting otherwise does not reflect the true cost of capital over the life of the firm.

The cost of Equity

The cost of equity should reflect the risk of cash flows to common equity holders who are the residual claimants of the firm's earnings. An estimate of the cost of equity is generally obtained through some pricing model like the CAPM or the Fama and French 3 factor model. These models assume that the marginal investor is well-diversified. Therefore, the only risk that is relevant is that which contributes to the overall volatility of a well-diversified portfolio. Given that the market is dominated by hedge and super funds, assuming the marginal investor has a diversified portfolio is not a stretch of an assumption.

The CAPM, its components and the issues in valuation

The CAPM is made up of of 3 factors: the risk free rate, the market risk premium, and the company beta. Most equity analysts will search for a beta (provided by Bloomberg, Reuters, or some other data provider), use some treasury bond as a risk free rate, and rely on some market talk that the market risk premium is around 4-6%. In undertaking a valuation analysis, although this will on average give us a rough but fair estimate, there are many times where it will not. For example, if we are valuing a company which earns a significant proportion of its cash flows offshore, can we continue to use the same risk free asset (or even market risk premium) as a company that earns 100% of its cash flows locally? The answer to this is a flat and resounding NO. Therefore, with companies like Brambles, BHP, and Macquarie to an extent, we need to think about possible work around solutions.

The market risk premium represents the difference between the market's expected return and the risk free rate. It is something that can be forward looking, historical in nature, or based on current data. In an analysis to work out the cost of equity, most analysts choose to base their estimate of the market risk premium on historical data. The reason for this choice is that it genuinely reflects an investors required return over the long term (through booms and bust periods). If we use a risk premium based on current market data, over the long term we face underestimating the risk of being involved in equities. While this may solve one of the issues related to the market risk premium, other points of concern worthy of mentioning include whether we should rely on arithmetic or geometric returns, how we deal with the huge standard estimates associated with having such a small set of data, and the endemic survivorship bias.

The final part of the CAPM estimation is the beta which measures the sensitivity of equity returns relative to the returns of the overall market portfolio. Beta is a measure of risk and is made up of two components: the operational risk of the firm (and the higher the sector/ industry risk the higher we would expect beta to be) and the financing risk (the more highly levered the higher we would also expect beta to be). Measuring beta is usually computed by looking at historical data, and its relevance is a function of how stable the firm is. If a firm has recently changed its capital structure as well as the nature of its operations then in all likelihood its beta estimate is nonsense.

Where you are confronted with this problem I recommend that you calculate beta by unlevering the beta of a range of companies perceived to have similar forms of operational risk and then re-levering this industry average unlevered beta to capture the effects of the firm's financial risk

Remembering the following lessons should hold you in good stead for deriving the cost of equity.

More to come...