Understanding Modigliani-Miller Theorem Case 3

In the previous two videos, we looked at the Modigliani-Miller theorem, Propositions 1 and 2, which looked at the capital structure of the firm, as well as the weighted average cost of capital. And in Case 1, there were no corporate taxes and no bankruptcy costs. In case two, we added corporate taxes, but we still didn't have bankruptcy costs. And here we're going to add the third case. We're going to make it more realistic. We're going to have corporate taxes and bankruptcy costs. There are a couple of different kinds of bankruptcy costs. There's the obvious one, the direct costs, things like legal and administrative costs. Costs of bankruptcy is not cheap. You have to hire attorneys. go through the court system. It's very expensive. Enron, for example, spent around a billion dollars to cover its bankruptcy. WorldCom, around 600 million. Bondholders may also lose out. They may not receive the amount of money they were promised, so there's another direct cost. There are also indirect costs of bankruptcy, which can actually be larger than the direct cost, but are difficult to measure. For example, as management spends time dealing with the bankruptcy, they may take time away from running the business, and that may cause sales or revenues to go down. There may also be lost sales. For example, if you think the company that you're doing business with is going to be bankrupt, you may be concerned that they're not going to honor their warranties, that you may not be able to get parts to repair. whatever it is you purchase from them. For example, a number of years ago during the financial crisis when General Motors was going through financial difficulty, a lot of people were concerned about buying a GM car. Would GM honor the warranty? You buy a car, it has a three-year warranty or a five-year warranty, and you expect that to be honored. Now, the government stepped in and said, We will honor the warranty. So your warranty is good. But even that was a bit of a concern because part of the reason you buy a car is, or buy a certain car, is the dealership is close by. You may need to have service done and you don't want to drive 100 miles to the nearest dealership. to have the warranty work done. So the talk that General Motors was going to close up a lot of dealerships may have been a concern too. I mean, there's a big difference between having a dealership that's two or three miles from your home and having to drive 50 or 60 miles to get your car repaired. So again, that was a problem. And so there probably were people who chose not to buy a GM car because of the bankruptcy. You may also have other types of concerns. Employees may have concerns. If you think the company you're working for is going bankrupt, you may go and look for another job and they may lose a highly skilled, valued employee. Alright, so let's look at case three with bankruptcy costs. As the debt equity ratio goes up, the probability of bankruptcy also goes up. As the probability of bankruptcy goes up, the expected... bankruptcy costs go up. Quite logical. So what happens here? This is one of the basic tenets of economics. Is that there are trade-offs. Using more debt gives you a bigger... interest tax yield, but it also increases the bankruptcy cost, which will offset some of that gain. And so what will happen? There's going to be a point where using too much debt actually decreases the value of the firm and causes the weighted average cost of capital to increase. So let's see what that looks like graphically. If we eliminate this pink colored line, this curved line here, this is the graph that we saw that compared the unlevered firm, the firm with no debt, with the levered firm. And the levered firm was equal to the value of the unlevered firm plus the tax yield. And the tax yield was computed as the corporate tax rate times the amount of debt. All right. And we found in case two that if there were no bankruptcy costs, the optimal capital structure was to use all debt. That led to the lowest cost of capital and that led to the highest value for the firm. Now, if you add bankruptcy costs, you get this curve. Now, in the early part, adding extra debt doesn't affect. the risk of bankruptcy or the financial distress cost as they call it here very much okay someone making someone making a million dollars a year can easily borrow twenty five thousand dollars to buy a car That's not going to have much impact. They can easily buy a $200,000 house and pay the mortgage. But if somebody making a million dollars a year goes out and buys a $10 million house, they may have a real impact. risk of bankruptcy. So at some point you get to the point where the tax yield is offset by the financial distress. And what happens is there's an optimal capital structure. We have a curve here. And what you want to look at is, because this is value of the firm on this axis, you want this to be as high as possible. So you want to hit it right at its peak before it starts to turn down. So up until this point, point, over here, the tax yield gain was more than the financial distress cost. After we get past this point, the financial distress costs are greater than the gain from the tax yield. So you start to lose value. This line from the value of the unlevered firm to the levered firm is the the tax yield benefit and this difference here is the financial distress cost. At some point this becomes big enough to offset this and you get to the point where you're using too much debt in your capital structure. Let's take a look at one more graph which will illustrate Proposition 2, the weighted average cost of capital. It's a little bit hard to see. It's kind of small. So, let's take a look at Proposition 1. So, let's take a look at Proposition 2. but this is the same picture up here we had before the previous diagram down here this is the weighted average cost of capital and when we did when we had the case where there were no bankruptcy costs then the cost of capital curve this bottom one approached the rate on debt however when you have bankruptcy costs at some point it starts to turn up. That is, again, this is the same part or same point where there's an optimal capital structure for the value of the firm that would be the same optimal capital structure for the weighted average cost of capital. So again, three lines here, case one, which is no taxes, no backward. CRIPSY COSTS, WEIGHTED AVERAGE COST OF CAPITAL DOESN'T CHANGE. CASE TWO, WHICH IS THE BOTTOM ONE, SAYS THAT AS YOU INCREASE DEBT, YOU SIMPLY REDUCE THE COST OF CAPITAL. of capital because there are no bankruptcy costs. And then case three, which is this blue line in the middle, says that, again, at some point, the benefits from the tax savings are offset by the additional cost of bankruptcy, which increase the cost of capital. And that starts to cause this to curve upwards. So again, there's an optimal capital structure. They call it D, D slash E star, which leads to the best, the highest value for the firm and the lowest weighted average cost of capital.

And here we're going to add the third case. We're going to make it more realistic. We're going to have corporate taxes and bankruptcy costs.

There are a couple of different kinds of bankruptcy costs. There's the obvious one, the direct costs, things like legal and administrative costs. Costs of bankruptcy is not cheap. You have to hire attorneys.

go through the court system. It's very expensive. Enron, for example, spent around a billion dollars to cover its bankruptcy.

WorldCom, around 600 million. Bondholders may also lose out. They may not receive the amount of money they were promised, so there's another direct cost.

There are also indirect costs of bankruptcy, which can actually be larger than the direct cost, but are difficult to measure. For example, as management spends time dealing with the bankruptcy, they may take time away from running the business, and that may cause sales or revenues to go down. There may also be lost sales.

For example, if you think the company that you're doing business with is going to be bankrupt, you may be concerned that they're not going to honor their warranties, that you may not be able to get parts to repair. whatever it is you purchase from them. For example, a number of years ago during the financial crisis when General Motors was going through financial difficulty, a lot of people were concerned about buying a GM car. Would GM honor the warranty?

You buy a car, it has a three-year warranty or a five-year warranty, and you expect that to be honored. Now, the government stepped in and said, We will honor the warranty. So your warranty is good.

But even that was a bit of a concern because part of the reason you buy a car is, or buy a certain car, is the dealership is close by. You may need to have service done and you don't want to drive 100 miles to the nearest dealership. to have the warranty work done. So the talk that General Motors was going to close up a lot of dealerships may have been a concern too.

I mean, there's a big difference between having a dealership that's two or three miles from your home and having to drive 50 or 60 miles to get your car repaired. So again, that was a problem. And so there probably were people who chose not to buy a GM car because of the bankruptcy. You may also have other types of concerns. Employees may have concerns.

If you think the company you're working for is going bankrupt, you may go and look for another job and they may lose a highly skilled, valued employee. Alright, so let's look at case three with bankruptcy costs. As the debt equity ratio goes up, the probability of bankruptcy also goes up.

As the probability of bankruptcy goes up, the expected... bankruptcy costs go up. Quite logical. So what happens here? This is one of the basic tenets of economics.

Is that there are trade-offs. Using more debt gives you a bigger... interest tax yield, but it also increases the bankruptcy cost, which will offset some of that gain.

And so what will happen? There's going to be a point where using too much debt actually decreases the value of the firm and causes the weighted average cost of capital to increase. So let's see what that looks like graphically.

If we eliminate this pink colored line, this curved line here, this is the graph that we saw that compared the unlevered firm, the firm with no debt, with the levered firm. And the levered firm was equal to the value of the unlevered firm plus the tax yield. And the tax yield was computed as the corporate tax rate times the amount of debt.

All right. And we found in case two that if there were no bankruptcy costs, the optimal capital structure was to use all debt. That led to the lowest cost of capital and that led to the highest value for the firm.

Now, if you add bankruptcy costs, you get this curve. Now, in the early part, adding extra debt doesn't affect. the risk of bankruptcy or the financial distress cost as they call it here very much okay someone making someone making a million dollars a year can easily borrow twenty five thousand dollars to buy a car That's not going to have much impact.

They can easily buy a $200,000 house and pay the mortgage. But if somebody making a million dollars a year goes out and buys a $10 million house, they may have a real impact. risk of bankruptcy.

So at some point you get to the point where the tax yield is offset by the financial distress. And what happens is there's an optimal capital structure. We have a curve here. And what you want to look at is, because this is value of the firm on this axis, you want this to be as high as possible.

So you want to hit it right at its peak before it starts to turn down. So up until this point, point, over here, the tax yield gain was more than the financial distress cost. After we get past this point, the financial distress costs are greater than the gain from the tax yield.

So you start to lose value. This line from the value of the unlevered firm to the levered firm is the the tax yield benefit and this difference here is the financial distress cost. At some point this becomes big enough to offset this and you get to the point where you're using too much debt in your capital structure. Let's take a look at one more graph which will illustrate Proposition 2, the weighted average cost of capital.

It's a little bit hard to see. It's kind of small. So, let's take a look at Proposition 1. So, let's take a look at Proposition 2. but this is the same picture up here we had before the previous diagram down here this is the weighted average cost of capital and when we did when we had the case where there were no bankruptcy costs then the cost of capital curve this bottom one approached the rate on debt however when you have bankruptcy costs at some point it starts to turn up.

That is, again, this is the same part or same point where there's an optimal capital structure for the value of the firm that would be the same optimal capital structure for the weighted average cost of capital. So again, three lines here, case one, which is no taxes, no backward. CRIPSY COSTS, WEIGHTED AVERAGE COST OF CAPITAL DOESN'T CHANGE. CASE TWO, WHICH IS THE BOTTOM ONE, SAYS THAT AS YOU INCREASE DEBT, YOU SIMPLY REDUCE THE COST OF CAPITAL.

of capital because there are no bankruptcy costs. And then case three, which is this blue line in the middle, says that, again, at some point, the benefits from the tax savings are offset by the additional cost of bankruptcy, which increase the cost of capital. And that starts to cause this to curve upwards.

So again, there's an optimal capital structure. They call it D, D slash E star, which leads to the best, the highest value for the firm and the lowest weighted average cost of capital.

Transcript for:Understanding Modigliani-Miller Theorem Case 3

Transcript for:
Understanding Modigliani-Miller Theorem Case 3