In this next section together, dealing with the calculation of a firm's WACC, we're going to concentrate upon the other half of the WACC equation, equity. So the two elements that we need to get a handle on here, are ke, the cost of equity capital, and E, market value of equity. As we'll see, if the company's equity is listed, then it's going to be a very straightforward process. Firstly, let's consider ke, the cost of equity capital. As we saw in the last module of this course, there's a very well-structured approach encapsulated in the capital asset pricing model that clearly links discount rates to our measure of systematic risk, beta. So for Kellogg’s for instance, we ended up with the cost of equity capital of 7.41% per annum. Now calculating the market value of equity is even more straight forward when dealing with a listed firm like Kellogg’s. As we simply multiply the number of shares on issue by the price per share, giving us the total market value of equity, which is what we refer to as the firm's market capitalization. In this instance, that's $23.42 billion. So for listed firms, its really straightforward. But what about if our firm's equity is unlisted? If our firm's shares are not listed, then we won't be able to directly observe the way in which the returns for the company co-vary with the market, and hence we won't be directly estimate the beta for the company. So what we are going to have to do is be a little bit more creative in our approach. Specifically, we're going to identify another company that is listed and that operates in the same industry as our company. We'll then piggyback off of their measure of systematic risk, being very careful to make sure that adjustments are made for differences in systematic risk that might be induced by differences in strategic choices made by the firm, such as the level of leverage employed. Let's have a look at why this might be necessary. You might recall from the previous course in this specialization, <i>Corporate Financial Decision-Making for Value Creation</i>, that the higher the level of debt within a company, the greater the variability of return to equity holders. This effect reflects what we refer to as financial risk. And from our last module together in this course, we demonstrated that the beta for a portfolio was simply the weighted average of the betas of the assets within the portfolio. Similarly, the beta of a company's assets is the weighted average of the betas relating to the debt of the company and the company's equity. Because debt holders have a priority claim over both the cash flows and the assets of the firm, the market value of debt tends to be much less sensitive to changes in market wide returns than is the market value of equity. Or put another way, the beta of a company's debt would be lower than the beta of that same company's equity. Indeed, a common assumption made for firms with investment grade debt is that the company's debt beta is equal to zero. Well, we're going to make use of that common assumption to firstly de-lever the listed firm's equity beta. That is, take out the effective leverage to arrive at an estimate of the beta of the listed company's assets. The next step will be to relever up the unlisted firm's equity to reflect the unlisted firm's level of leverage. Now let's go through an example to demonstrate how this might work in practice. So let's assume that you run an established business, Protecta Ltd. This firm produces plastic shields for motorcycle helmets. The shares in your company are not yet listed, but you have identified another firm, Faceoff Ltd., that produces the same sort of product and operates in the same sort of markets. Now Faceoff is listed in the New York Stock Exchange, and you estimate that its equity beta is 1.30. Faceoff Limited has a debt to total value ratio of 0.5, whereas your own firm has a leverage level of 0.2. Now intuitively holding everything else constant, this implies that the equity bata for your own firm should be lower than that of Faceoff Limited, because of the low level of leverage. There is then this final assumption concerning the debt betas of both Faceoff and Protecta in that they can be assumed to both be zero. Well, let's have a look at how we might use this information to estimate the beta of Protecta's equity. So, the first step is to back out the implied beta for Faceoff's assets. That is, what is our measure of the systematic risk of the company's assets free of any debt effects? So, with an equity beta of 1.3, and a ratio of equity to total value of 0.5, we end up with a beta for Faceoff's assets of 0.65. Now this is what the beta of the company's equity would be in the absence of any debt at all in the company's capital structure. We now use this asset beta to work out what the implied beta is for Protecta, given its lower level of leverage. And as we go through this calculation, we end up with an equity beta of 0.8125. Plugging this number into the capital asset pricing model yields a required return on equity for our unlisted firm of 7.69% per annum. This can now be used in our estimation of WACC for our unlisted firm. So, in summary, in this session we've shown you how the estimation of the cost of equity capital and the market capitalization of equity is a very, very straight forward process when the equity is listed. For firms that are unlisted it gets a little trickier. But it's still possible to use a proxy company that operates in the same industry, and is subject to the same pressures and systematic risks. We use that proxy company to obtain an estimate of the cost of equity capital. Then the key is when working with that proxy company's data, that we make adjustments at differing levels of leverage between the two firms. These adjustments are part of the de-levering and re-levering beta prices. So, in our next session together, we're going to turn our attention to some of the pitfalls that might arise when companies employ their weighted average cost of capital as a discount rate in their evaluation of new project proposals. Stay tuned.
