In this first session together, we are going to discuss the logical foundations of the estimation of a company's weighted average cost of capital, the WACC. Now before getting into it though, let's pause for a moment and briefly recap how we got to this stage in the first place. We began with the discussion of alternative attitudes towards risk, settling in on the concept of risk aversion as being the standard way that investors regard the risk return tradeoff. Specifically, we suggested that as risk increased, investors required a higher rate of expected return in order to generate the same level of utility or satisfaction. Our measure of risk in this early section was total variability in returns, as measured by an asset standard deviation of returns denoted by the Greek letter sigma. We then moved on and started to think about what would happen as we added assets together into a portfolio? And we found that we are able to eliminate some risk by doing this. So this led to the very important revelation that investors could demand compensation only for that risk that could not be diversified away. This risk is known as systematic or undiversifiable risk and a common measure of this is given by the Greek letter beta, which of course is the risk measure that arises under the capitalized pricing model the cap M. Now the beauty of the cap M, of course is that we have a very simple linear model of the relationship between expected return and systematic risk. And it's a model that is extremely, intuitively appealing. Now the problem is though, that the model doesn't do so well in explaining realized returns on an ex-post basis. This has led to the development of a series of increasingly complex multifactor models, such as the Fama-French three-factor model. So, all is looking pretty good now. Well that's until we look at some of the survey evidence of what discount rates managers use in practice. And here, we see that rather than using a risk match discount rate that is project specific, as the cap M would suggest is most appropriate, firms instead employ a company wide discount rate when undertaking discounted cash flow analysis, that is DCF, to assess new projects. One common interpretation of this result is that firms are using their weighted average cost of capital or WACC to evaluate new projects. So now let's have a look at the formula for a firm's WACC and then work out why this formula works as it does. So a firm's WACC is simply equal to the cost of their capital kd, measured on an after-tax basis, scaled by the ratio of the market value of debt to the market value of the firm's assets plus the cost of the firm's equity capita ke, scaled by the ratio of the market value of the firm's equity to the value of the firm's assets. Now, it's important to pause here and think about the two scaling factors. That is D divided by V and E divided by V. If you think of the value of the firm's assets being like a cake, then the claims on those assets simply determine how that cake is sliced. The cake is going to be eaten by either debt holders or shareholders. Hence, V=D+E. This is a finance course. So let's start working with some numbers. Let's assume that the firm's cost of debt capital kd is equal to 5% per annum. And its cost of equity capital, the required return on equity is 12% per annum. For the example, let's also assume that the corporate tax rate is 35% and that the current market value of debt is $1 million and the current market value of equity is also $1 million. Let's also assume that chair holders receive all of their returns via cash payments, via dividends. So 100% of all earnings are distributed. Let's also assume that the firm's debt level will be constant through time and the firm itself is a going concern that will generate its operating cash flows forever. Now this has the important implication that the market value of the firm can be estimated using a standard perpetuity formula, which is simply the regular cash flow divided by the relevant discount rate. Now with all of these assumptions in place, we can now demonstrate how we get to the formula of firms weighted average cost of capital, its WACC. So the first step, let's work out the regular cash flows required by debtholders and shareholders. Well, debtholders require a return of 5% on their $1 million. So the interest payment required each year is equal to $50,000. But of course, interest payments are tax deductible. So although the firm pays $50,000, the interest payment reduces their taxes by $17,500, which implies and after-tax net cash flow to debtholders of $32,500. That is the after-tax net cost of interest It's simply = kd * (1-tc) * D. So now what about our shareholders? What cash flows do they require? Well, the shareholders require a return of 12% on their equity, which implies regular dividends of $120,000 per annum, 12% of a million dollars. How are we going to use all of this information? Well, recall that the present values of perpetuity is simply the regular cash flow divided by the relevant discount rate. The value of the firm's assets therefore, can be estimated by dividing the annual cash flow required by all contributors of capital, by the firm-wide cost of capital. But we can rearrange this formula to solve for the firm-wide cost of capital, given the market value of the firm’s assets. So recall that the market value of the firm’s assets is simply equal to the market value of debt plus the market value of equity. Re-expressing our original equation using this formulation of V, gives us the second expression to my left. And we then simply rearrange that expression with a little simple algebra to end up with the formula for the firm-wide cost of capital or WACC. The next step will be to substitute for the annual cash flow, that is the actual cash flows required by both debtholders and shareholders on an annual basis. So, all this slide is doing is refining that original equation to specify kd and ke separately. As you can see, by the time we get to the bottom line, we have the formula that we started with at the very beginning of this session for a firm's weighted average cost of capital. Now let me pause for a moment. If you aren't really following the algebra here, don't worry. I've included it just in case you're asking yourself, but why does the WACC formula look like this? From our perspective, the main thing is that we understand that the WACC formula is founded on a set of assumptions about how cash flows are generated by the firm and how the mix of debt and equity is assumed to be constant. Let's now check how the numbers from our earlier example are plugged into the WACC formula. So, our regular annual cash flow required by debtholders is $32,500 and $120,000 from our shareholders. The total market value of the companies assets is $2 million, which implies a firm-wide cost of capital of 7.625% per annum. Alternatively, we can utilize the WACC formula directly. And lo and behold, we find that the firm's weighted average cost of capital is 7.625% per annum. So let's pause for a moment and identify some key elements of what we've just been through. Firstly, with respect to kd and ke, it's important that we utilize current costs of capital. That is that these measures reflect exactly what it is our debtholders and shareholders would require today to contribute capital to the firm. Current not historic. Secondly, we're interested in current market values for debt and equity, not book values. You see as good finance people, we're always forward-looking rather than backward-looking, like our friends and colleagues from the accounting discipline. But even after all of this, who really cares about a firm's WACC? If it's so important, then wouldn't firms regularly announce to the market exactly what their WACC is? Well, the answer is a most definite no. Most companies are extremely protective of their WACC, because it can impact upon their competitiveness in tendering for new assets in the market. Well, let's think about this a little bit more. Assume that a new project has just come up and we're in a competitive tendering process, where we need to essentially bid for the project. An auction style process, as we have seen most firms use discounted cash flow techniques, such as NPV or internal right of return to determine whether they're going to go ahead with the new project. The firm's WACC can be viewed as the discount rate that they might use to count the cash flows from the new project, which in turn informs us about the maximum price that we should be willing to pay for the project. That is that price that yields an NPV equal to zero. If a competing firm knew our WACC, then it could with the same predictions of the project's cash flows, backup the maximum price that we'd be willing to pay for the project, which might just give them the edge they need in order to win the tender. Now for this reason, it's extremely difficult to assess the WACC of a firm as an outsider of the firm. So as we go through our analysis of WACC over the next three modules, we'll assume that we're undertaking the process for our own firm. So that we can assume that we have access to all of the propriety information needed for the calculation with respect to the different sources and costs of capital for the firm. In this session, we've defined WACC as the after-tax cost of debt capital kd, scaled by the ratio of the market value of debt to the market value of the firm's assets. Plus the cost of equity capital ke, scaled by the ratio of the market value of equity to the market value of the firm's assets. We then went on to demonstrate the intuitive and logical foundations of the WACC formula, highlighting the reliance of the formula on market values and market required rates of return. We concluded by highlighting why firms might be expected to be reluctant to let the market know the precise WACC for fears that it might compromise their competitive position. So what's next? Well, let's demonstrate how we would estimate the WACC from a firm's internal perspective.
