Session 11: Estimating Hurdle Rates - More on bottom up betas

In session 11 of this 36-session corporate finance class, I'd like to build on the concept of bottom-up betas. First talking about estimating betas for global companies, and then talking about how to use this approach to estimate the beta for a private business. The last session I introduced the notion of bottom-up betas, where I estimated a beta for Disney by breaking it down into individual businesses. In fact, looking at the larger picture, we're still on the beta section of the hurdle rate. Because we need a beta to get a cost of equity. In this session, I'd like to build on the concept of bottom-up betas and extend it to the other companies in my domain. So let me start with Vale. Vale is a global mining company that happens to be incorporated in Brazil. The reason I emphasize the global aspect of Vale is Vale is Brazilian. But much of its revenues come from outside Brazil. In fact, China is its largest market. So I broke Vale down into four businesses. Actually, let me take that back. Vale broke themselves down into four businesses. And essentially, I did exactly what I did for Disney, for Vale. And with each business, I look for publicly traded comparable firms. Notice that for all four groups, I've used global companies as my comps. And I have a pretty large sample in each one. I get the regression betas, just like I did for Disney's comparable businesses. I unlever them. In other words, I do exactly what I did for Disney to come up with an unlevered beta by business. Then I estimate a value for each of Vale's four businesses. Again, I use the revenues and that multiple EV to sales ratio, the enterprise value to revenue multiple, to come up with an estimated value. And you can see, based on my estimates, that Vale is predominantly an iron ore company. It's about 76% iron ore, 24% everything else. But the weighted average of those unlevered betas, which is about 0.84, is the unlevered beta that I have for Vale's operations. In the table below, I use those unlevered betas in conjunction with the debt-to-equity ratio. And here I cheated a little bit. Unlike Disney, where I took the debt and I allocated it across different businesses, because I believe the movie business should have a different debt-to-equity ratio than the theme park business. In the case of Vale, I decided that the businesses were close enough in terms of their debt needs and how much debt they could carry, that I could use the same debt-to-equity ratio, which is about 55% for Vale, across all the businesses. That allows me to come up with a levered beta and a cost of equity for Vale. Notice also that I'm using the US dollar risk-free rate, because I'm going to assess Vale entirely in US dollar terms. Why? Even though it's a Brazilian company, as a commodity company, it actually reports its numbers in US dollars first. It's actually easier for me to assess things in US dollars than to go into nominal REI or a different currency. So my risk-free rate is the risk-free rate in US dollars. For the risk premium, I use the weighted average equity risk premium we computed for Vale of 7.38%. That reflects the fact that it's in multiple countries, especially China. And this is the weighted average equity risk premium. So I have the cost of equity by business and a cost of equity in US dollar terms of 11.23%. That's a US dollar cost of equity, right? Now, let's assume after you've done all this work and come up with a US dollar cost of equity, you decide that you'd rather have a nominal REI cost of equity. Well, you could go back to scratch and start with the nominal REI risk-free rate and build up, but there's a shortcut you can use. And this shortcut is actually an incredibly useful one to remember any time you want to move across currencies. Remember that 11.23%? That's a US dollar cost of equity. To convert it into a nominal REI cost of equity, I need two numbers. I need an expected inflation rate in US dollars and an expected inflation rate in nominal REI. The easier of those two numbers to get is going to be an expected inflation in US dollars. And here's how I would get it. I would take the difference between a 10-year T-bond rate, that's a nominal T-bond rate, and a TIPS rate, a 10-year TIPS rate. That's the inflation index treasury bond rate. In the case of the US, that yielded about 2% in November of 2013. So that's a difference between the T-bond rate, 2.75%, and the TIPS rate of 0.75% on that day. 2% is my expected inflation in US dollars. Expected inflation in Brazil is a little more difficult. I had the actual inflation rate from last year, but there are two problems with it. One is it's last year's inflation, not an expected number. The second is it is subject to manipulation by governments that determine what basket of goods they're going to use and what price controls they put. So I'll take it with a grain of salt. But if I assume that that inflation rate is about 9%, here's what I get as my cost of equity in nominal REIs. I take one plus the US dollar cost of capital, that's 11.23%. I take the 9% inflation rate in REIs, the 2% inflation rate in dollars, and I scale up my cost of equity in dollar terms to end up with an 18.87% nominal REI cost of capital. Of course, I could have done everything in nominal REI terms. I could have used a nominal REI risk-free rate. No, I've taken the beta, multiplied by the equity risk premium. I'd have ended up with a slightly lower cost of equity. I think starting with dollar numbers and adjusting for inflation is actually a better way of estimating a local currency, cost of equity or cost of capital, because so many of our risk premiums come from dollar-based markets. What I mean by that, the equity risk premiums I computed, the CDS spreads all come from dollar-based markets. So especially if you're working with a currency with a high inflation rate and you want to get a cost of equity capital in that currency, my suggestion is start in US dollars and do this conversion. So that's my valet cost of equity in both dollar terms and nominal REI terms. I computed the cost of equity for Tata Motors and Baidu, and I'm not going to go through the details because the process remains the same. These companies were, in a sense, easier to work with because they're both in single businesses. Tata Motors I treated as an automobile company and used the beta for global automobile companies to come up with a levered beta 1.10. And I used that to come up with a rupee cost of equity for Tata Motors using a rupee risk-free rate. Remember the 6.57% we computed, the beta 1.10, and the equity risk premium I computed for Tata Motors. For Baidu, I used a Yuan risk-free rate, I used the beta for online advertising companies as my beta for Baidu, and the equity risk premium I computed for Baidu to come up with a cost of equity for Baidu in Yuan. So make a currency choice, come up with a beta, in this case, a bottom-up beta, estimate the equity risk premium for the company, and you have a cost of equity for the company. Everything has its place. Your currency choice is in your risk-free rate, your business mix is in your beta, your country choices, your graphical breakdown is in your equity risk premium. So that is basically the bottom-up beta approach. I can use this to get a bottom-up beta for Deutsche Bank as well. Deutsche Bank, as I classified it, is in two businesses, commercial banking and investment banking. For commercial banking, I looked at European banks as my comparable companies. For investment banking, I used global investment banks, and that includes banks which are publicly traded in the US, because that's where the bulk of independent investment banks tend to be. I came up with the average beta for each of these comparable firms. That average regression beta is what I'm going to use as the beta for each business. Notice I've skipped a step. With Tata Motors and Baidu and Vale and Disney, I unlevered that beta first before I came up with a beta for the company. In the case of Deutsche, I'm going to skip that step, and here's why. Getting a debt-to-equity ratio for a bank is close to impossible, so I'm not even going to try. I'm implicitly going to assume that the levered beta is the beta for the business, and the weighted average of those betas is the beta that I'm going to use for Deutsche Bank. Those betas are what I'm also going to use to come up with a cost of equity for each of Deutsche Bank's businesses. And notice the investment banking business has a much higher cost of equity than the commercial banking business, but the weighted average reflects the weights that I see Deutsche getting from each of the two businesses. So if you're looking at a financial service company, my suggestion is steer away from unlevering and relevering betas. Stay with the levered beta by business. Take a beta for the company based on the values of the businesses, and move on. Now, here's an advantage you get with bottom-up betas that you could not have used regression betas for. The approach that I've just described for all of my companies, where I look at the businesses you're in and building up, I can use if you came to me with a private business or the division of a publicly traded company. In fact, it is true, there are some people who use accounting numbers to come up with betas for private companies. What I mean by that is they run a regression of accounting earnings for the company against accounting earnings in the S&P 500. I wouldn't even try that. Accounting earnings are not estimated frequently enough for a regression beta based on them to have any meaning. So stick with the bottom-up beta approach. So I'll take you through an example of a bottom-up beta computation for a private business. This is actually an independent bookstore in New York City called BookScape. The unlevered beta that I've computed for BookScape is based upon publicly traded book companies. Notice how I characterize this. Not publicly traded book retailers alone because there were too few of them. So I expanded my sample to include publishing companies. So essentially, I do exactly what I do for public companies. I take the average regression beta across these publicly traded book companies. I unlever them using the debt-to-equity ratio for public companies. And I look at the cash as a percent of firm value to come up with a pure play beta for being in the book business. I end up with a beta for being in the book business of 0.7584. I'm almost home, right? Because with a public company, here's what I would do next. I would take the market debt-to-equity ratio of that public company, like I did for Disney and Valley, to come up with a levered beta. But with a company like BookScape, one of the problems you face is there is no market debt and there's definitely no market equity. Rather than try to estimate it, you could try asking the owner what his or her target debt-to-equity ratios. And maybe you'll get lucky. But all too often with private businesses, getting a target debt-to-equity ratio is very difficult to do. So here's what I'm gonna assume for BookScape. I'm gonna assume that the debt-to-equity ratio that BookScape will use is the average debt-to-equity ratio across book companies of 21.41%. If I plug in that market debt-to-equity ratio in, I get a levered beta for BookScape of 0.8558. That 0.8558 is what I would use to come up with a cost of equity. The cost of equity, the risk-free rate of 2.75%. It's a U.S. dollar risk-free rate, 0.8558 beta. And the equity risk premium of 5.5% for BookScape is roughly 7.5%. But here's the catch. BookScape is a privately owned bookstore. The owner of BookScape is not diversified. And this is true for most private business owners. So let me ask you a question. If 7.5% is the cost of equity based on a beta, and beta measures only the portion of the risk that you cannot diversify away. And now I tell you that the owner of this business is exposed to the rest of the risk as well, because he or she is not diversified. Do you think I'm going to underestimate the cost of equity using a market beta or overestimate it? I'm probably going to underestimate it, right? Because I'm not counting all that other risk that this owner is going to be exposed to. So here's what I'd like to do. I'd like to bring in the rest of the risk that a private business owner is exposed to into the cost of equity. How am I going to do that? Here's a simple way to think about it. Remember those regressions from which I got the betas for publicly traded book companies? Let's assume that I looked at each of those regressions, which I should be able to, that I took the R-squareds from the regressions and I computed the average R-squared across those companies. The average R-squared across those publicly traded book companies was about 26%. So basically I'm taking the regression beta page and I'm averaging the R-squareds out. That R-squared tells me what proportion of variance in these companies is explained by the market, right? Here's a statistical artifact I've got to deal with. Beta is a standard deviation measure. It's not a variance measure. So I'm going to take the square root of the R-squared, which gives me roughly 51% as my correlation. That's the square root of the R-squared. Here's my final step. I have the beta that I got as a market beta of 0.8558. I'm going to divide that by the correlation of 0.51. What I end up with, I call it total beta, and that total beta 1.678 is what I'm going to use to come up with my cost of equity for BookScape. And that cost of equity is almost 12%, much higher than the 7.5% that I estimated on the prior page, but that is the cost of equity I would argue that this owner should be using in deciding whether to take investments in this book business or not. So if you're looking at a private business, remember that concept. Using a market beta is probably going to give you too low a hurdle rate. Adjusting that market beta for the extra risk the owner is exposed to because he or she could not diversify will give you a higher hurdle rate and a higher cost of equity. So if you look at your company, and I think this is a good way to start off by thinking about betas, break your company down into businesses, come up with a beta by business, and estimate a beta for your company based on a weighted average. If you have trouble getting betas by businesses, if you visit my website, I actually have betas by business estimated at the start of every year for US companies, emerging market companies, European companies, Japanese companies, and global companies. So if you want a quick fix, you can get betas by business from my website and build up a beta for your company. I think it's a much better way of estimating betas than running one regression, taking the slope from that regression and treating it as a beta for your company. Thank you very much for listening.