Session 21: Optimal Financing Mix V - Alternate Approaches

In session 21 of this 36 session corporate finance class, I'd like to look at alternative ways of coming up with the optimal mix of debt and equity for your company. In particular, I'd like to talk about the adjusted present value approach, or the APV approach, for coming up with an optimal mix, as well as setting your debt ratio based on what everybody else in the sector is doing, or a relative assessment. In these last three sessions, we used the cost to capital approach to come up with the optimal financing mix for a company. In this session, I'd like to move past the cost to capital approach and look at different ways of coming up with the optimal, alternative ways. In particular, I'd like to focus on two. The first is called the adjusted present value approach, or the APV approach, and I'd like to pay some attention to that. And the second is the most common way in which most companies set their debt ratios. They look at what everybody else in the sector is doing. I'm going to call this relative analysis, or sector-based financing mix, and let's talk about when that works, when that might not work, and how we can refine it. So let's start the process. Let's talk about the adjusted present value approach. In the cost to capital approach, the cost to capital carries the burden of showing what happens as you change your financing mix. In the adjusted present value approach, use a different set of steps to get to the optimal mix. In fact, you start off by estimating what the value of a business would be with no debt. That's called the unlevered firm value. Then you bring in the effects of debt by looking at both its advantages, and you value those, and its disadvantages, and you cost those. The net effect is captured in your adjusted present value. So if you break it down, there are three steps to the adjusted present value approach, and here are the three steps. The first step is to estimate the value of your business as if it had no debt, an unlevered firm value, and there are two ways you can do this. The first is to do a full-fledged valuation. We project the cash flows to the business, and discount it back at a cost of capital that they would have had with no debt, which you can get by using an unlevered cost of equity. That's a lot of work. There's a shortcut you can use. If you start with the market value of the business, which you should have if it's a publicly traded company, and you back out of it the effects of debt, you're and add back the expected bankruptcy cost. In other words, ask yourself what that value would have been if they did not have their existing debt. You can come up with an estimate of unlevered firm value, but that's your starting point, is the value of the business as if it had no debt. Second step in the process, estimate the present value of the tax benefits you get from the debt that you're considering taking on, and that should be relatively simple to do. After all, the tax benefits of debt flow from the interest expenses you have, and the marginal tax rate you face as a company. Take the present value of those tax savings over time, that's the present value of the tax benefits added on from debt. The third and final step is messy. You've got to estimate the expected bankruptcy cost you're going to create by taking on that extra debt. To do this, you've got to estimate the probability of bankruptcy that you will have if you go to that new debt level, and your cost of bankruptcy. And as we've talked about in earlier sessions, that's a tough number to estimate, because it includes both the direct cost, which is what happens after you go bankrupt, and the indirect cost, which is what the perception that you're in trouble creates for you as a cost. In fact, it's a third step that gives people trouble, and most people who claim to use the APV approach actually start off with the first step, they get the unlevered firm value. Do the second step, they add the tax benefits, but they get to the third step, and they throw up their hands and they ignore it. If you do that, you're going to find that your value as a business will always increase as you borrow more money, because you're counting the good stuff, but not the bad stuff. So let's talk a little bit about that third step. To estimate the expected bankruptcy cost, I need two numbers. I need a probability of bankruptcy, and that probability will go up as I borrow more money, but I need a specific number. So you need to tell me if you borrow an extra 10, 20, or 30 billion, what will happen to that probability? What will that number look like at different probabilities? In a sense, we've laid the foundations for being able to estimate this number in the cost of capital approach, and we'll return to that foundation. The second is that cost of bankruptcy. The direct cost of bankruptcy, as I noted, is what happens after you go bankrupt, and that cost is going to be relatively similar across most companies, maybe 5% to 10%. It's the indirect cost of bankruptcy, the perception that you're in trouble causing your trouble, that's going to vary across companies. There are studies that have looked at these costs, and they come back with a range. They said this cost could range anywhere from 10% of the value of the business to as high as 40%. Where you put your company will give you a very different optimal debt ratio for the company. So let's think about that first number, the probability of bankruptcy, and let's think about how something we did in the cost of capital approach can help us estimate that number for different debt ratios. So let's say you decide to go out and borrow an extra 20 billion. I could compute an interest coverage ratio and a synthetic rating for your company, right? We did that in the cost of capital approach. Let's assume that I can estimate a synthetic rating for your company. If you can estimate a rating for your company, there is a way in which you can convert that rating into probability of default. And to do this, you have to look at a study. A colleague of mine at the Stern School of Business at Altman every year updates a study where he looks at bonds from a decade ago. He classifies them based upon their rating from triple A all the way down to D, and he looks at the percentage of bonds within each ratings class that default within those 10 years. In other words, he's estimating the probability of default over a 10-year period given the rating at the start of the period. That's what I'm going to use to make my judgment. To give you an example, Disney's existing rating is single A. If you look at this table, the probability of default for a single A rated company is 0.66%. If your rating changes, I can tell you what the probability is by going to this table. So let's start and try to see if we can apply this approach to Disney. Let's start with the unlevered firm value. I'm going to use the shortcut. I'm going to start with the existing market value of the firm, which I obtained by adding the market value of equity, which I get as multiplying the share price by the number of shares to the estimated market value of debt. Notice I'm continuing to use the $15,961 that I estimated in a prior session. From this, I'm going to take out the effects of debt, and here's what I mean by taking out the effects. The existing debt of $15,961 creates a tax benefit for me. There's a shortcut I can use to estimate the tax benefit. If I assume that the interest tax savings are going to occur in perpetuity, the present value of the tax benefits from this debt can be computed by multiplying the marginal tax rate by the total dollar debt. The interest rate actually drops out of the equation. I'm going to add, I'm going to take out those tax benefits because I'm trying to answer the question, what would happen to my value if I did not have the debt? So without the debt, there'd be no tax benefits. But now I'm going to also add back the expected bankruptcy cost, because if you did not have the debt, you wouldn't have those costs, right? We estimated the property of default based on their existing rating at 0.66%. And for simplicity, I'm going to assume that the bankruptcy cost at Disney will be roughly 25% of the value, right in the middle of that range between 10 and 40%. I'm going to multiply that 25% by the existing value of the business. What I'm in effect doing is estimating the expected cost of bankruptcy that's being subtracted out right now to get to the value of the business. I'm adding it back saying if you did not have the debt, that property of default will disappear. I come up with an unlevered firm value of $132.2 billion. That's what you're going to see me use, or $132.3 billion, which is what you're going to see me use for the rest of this assessment. Because once I get that unlevered firm value, the rest, as they say, is pure mechanics. I take each debt ratio. I compute the dollar debt. I come up with an interest coverage ratio. I use it to compute a rating. And here's where the APV approach kicks in. I use that rating to come up with a probability of default using the table I showed you just a couple of pages ago, and an expected cost of bankruptcy using 25% of the value of the business. I compute that expected bankruptcy cost at every debt ratio, the tax benefits at every debt ratio. And I do factor in that beyond the 70% debt ratio, you run out of operating income to cover your interest expenses. I have my unlevered firm value from the prior page. I add the expected tax benefits, and I subtract out the expected bankruptcy cost. I have my estimated levered value for the business in the last column. My objective is to maximize value, right? And based on this table, on the adjusted present value approach, the APV approach, the optimal debt ratio for Disney is 40%. That is very convenient. You know why? Because when we did the cost of capital approach, that's exactly the optimal we came up with. Do not expect this on every company you're assessing. The two approaches take slightly different pathways to the optimal, and you can actually end up with different optimal debt ratios using the two approaches. If you do, which one should you use? It depends on how much confidence you have in that expected bankruptcy cost in the APV approach. If you feel pretty confident about it, use the APV approach. If not, stick with the cost of capital approach. So that's the APV approach, and if you're going to do it, do it right. Bring in the expected bankruptcy cost. Now let's look at the other way you can approach setting an optimal financing mix for your company. You can look at what everybody else in the sector is doing and try to stay as close as you can to the industry average. The advantage of doing this is if you screw up, you're going to always have lots of company, and that's a good thing because you're not going to lose your job as a CFO if everybody else is making the same mistake. Having said that though, if you're going to look at the sector, you're going to look at industry averages, apply some common sense. What I mean by that is if your company is very different from the rest of the sector, bring that into the assessment. So if you're an Irish company in a sea of other European companies, remember your tax rate is lower than everybody else's. You should expect to have a lower debt ratio than everybody else. If you're a larger and safer company than the other companies in the sector, you should have a higher debt ratio than everybody else. If you have more insiders running your company, you have less need for discipline. You should need less debt than everybody else. So what you do as a company should reflect not just what business you're in, but how different you are from everybody else in the sector. So let me start off by showing you what the industry averages look like for the four companies that I assessed. I start with Disney, and for each company I report four debt ratios. One is a market debt ratio, one is a market debt to capital ratio. The second is a book debt to capital ratio. Remember debt to capital, I take the total debt and divide by total debt plus market equity, or total debt plus book equity. So I start off by looking at those ratios. I also report a net debt ratio. What's net debt? I subtract out cash from gross debt and compute the ratios, and then I then compare these numbers to the industry averages for each company. For Disney I used entertainment companies, and again I get a very convenient finding. Remember that with both the cost to capital approach and the APV approach, I found that Disney was under levered. It had too little debt. Well the sector comparison confirms that conclusion. Disney has too little debt relative to the other companies in the sector. That makes my sales pitch even easier to make to Disney if I'm trying to convince them to borrow more money. With Vale and Tata Motors, I get confirmation as well. Both Vale and Tata Motors look like they have too much debt relative to other companies in the sector using both the gross and net debt ratios, and there again they confirm my finding that they should be borrowing less money, not more. And at least with Tata Motors, where we found that over leverage, here's something else that backs up that over leverage. With Baidu, we look at the rest of the sector and we notice that the rest of the sector is just as reluctant to borrow money as Baidu is. Kind of confirms our conclusion that Baidu should probably continue to do what they're doing, which is borrow very little money. In effect, I'm allowing the sector averages to guide my thinking and confirm what I found using my intrinsic approaches, the cost-to-capital approach and the APV approach. But it's always good to know what the rest of the sector is doing before you make a recommendation to a company to borrow more money, less money, or do what they're doing right now. Now when you do look at sector averages, you're looking at the average, and in the process you're throwing out a lot of data, right? What I mean by that is there are 25 other companies in the sector. There is information in why the debt ratios vary across sectors. There is a way in which you can use the rest of the information, and this will draw on Stat 101. I don't know whether you remember the multiple regression chapter of that book, of the statistics book. The multiple regression that you probably saw had a dependent variable and independent variables. You try to explain the dependent variable with the independent variables. That's what we're trying to do in this assessment. We're trying to explain differences in debt ratios across companies using variables that we think matter, like tax rate and how variable your earnings are, and how much you have as cash flows, which I measure by looking at how much EBITDA each firm has as a percentage of market value. I run a regression across the sector. I use that regression in conjunction with the numbers for your specific company to come up with a predicted debt ratio for your company. I compare that predicted debt ratio to the actual debt ratio. Sounds abstract, right? Let me try this on global automobile companies and use Tata Motors as my example. There are 56 automobile companies in my sample. I ran a regression of debt ratios against their tax rates, against how much they had in cash by looking at EBITDA as a percentage of firm of enterprise value, and what their capex needs were. The regression is an R squared of 21%. Not great, but not too bad. I plug in the values for Tata Motors into the regression, and I get a predicted debt ratio of 18.54%. You say, what does that tell me? Given how other automobile companies are setting debt ratios, I would expect Tata Motors to have a debt ratio of 18.54%. Their actual debt ratio is much higher. Again, it confirms what we found when we assess Tata Motors' optimal debt ratio using the cost of capital approach. Tata Motors is too much debt, so using the sector regression kind of adds to that conclusion. Now, of course, you could extend your sample to look at the entire market, and that's basically what I do at the start of every year with the U.S. market. I run a regression of debt ratios against the variables that should drive debt ratios, including tax rates, how variable your earnings are, what you have as cash flows, and perhaps what the institutional holdings are as a percentage of outstanding shares. Again, when you try these regressions, it might turn out that one or more of these variables doesn't work. Don't push the data. If it doesn't work, take it out. The R squared of this regression is only 8%, so keep that in mind when I use it to get a predicted value. There's going to be a lot of noise in my estimate. I take this regression, and I plug in the values for Disney into this regression. I get a predicted debt ratio for Disney of 18.86%. Again, you might say, what does this tell me? Given how the rest of the companies in the market are setting debt ratios, I would expect Disney to have a debt ratio of about 19%. Their actual debt ratio is only 11.5%. That would suggest, again, that Disney has too little debt. Again, the conclusion you're drawing is based on how other companies are borrowing money. With both the sector regressions and the market regressions, you're going to build in whatever mistakes others are making into your prediction. Put differently, if everybody else is borrowing too much money, you're going to borrow too much money as well, but that's a flaw any time you look at everybody else and making a judgment of what to do as a company. Let me pull these numbers together for my companies. With Disney, I have multiple predictions of what the right debt ratio is given the different approaches. With the cost of capital approach, I got a 40% optimal unconstrained. I got a slightly lower optimal if I constrained the rating. I went back to a 40% with the APV approach. I get a lower optimal if I look at the sector average or a market regression, but overall, my conclusion is the same using all of my predictions. Disney is underleveraged. You can look at Tata Motors and Vale and draw your own conclusions, but you can see that based on my assessment, Tata Motors looks overleveraged on every prediction. These are all factors that you will take into account when you try to decide what the right mix of debt and equity for your company is. There is no magic bullet or one approach that's going to work every single time. So do your best. Try the different approaches and make your best judgment on what the right mix of debt and equity is for your company. Thank you very much for listening.