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in this video we will discuss capital structure theory my name is Kirby Arkin death I have a PhD from the University of Illinois at urbana-champaign I'm a chartered financial analyst and a certified financial planner I'm currently chair of accounting and financial management at the Graduate School of the University of Maryland's University College during the 1950s and 1960s Franco Modigliani and Burton miller developed capital structure theory the objective of capital structure theory is to determine what capital structure ie mix of debt equity preferred stock and other forms of financing will minimize the cost of capital for a firm and therefore maximize its stock price bug DeLeon II and Miller both won the Nobel Prize for these efforts although in different years 85 and 90 the objective of capital structure theory is to find the correct mix of financing that will maximize the stock price this is the same thing as minimizing the weighted average cost of capital are the cost of financing for the firm if we consider a very simple firm with only debt and equity financing then whack the weighted average cost of capital has this equation where the fraction financed with debt plus the fraction financed with equity adds up to 1 KD is the cost of debt KS is the cost of equity and since interest payments on debt may be written off on corporate taxes the KD cost of debt is corrected by a 1 minus TC where TC is the corporate tax rate and science it is common to start with very simple but very unrealistic assumptions to try and understand a complex problem gradually complexity is then added to the problem a common joke is to consider starting with a spherical cow when module eonni and Miller tried to understand capital structure they started with a fairy tale world with no taxes no brokerage costs and no bankruptcy costs a world with complete transparency of information when everyone paying the exact same interest rates this is clearly unrealistic but then you can gradually add the complexity and figure out how the complexity affects the model if we start in this world then MacDill eonni and Miller found the capital structure theory doesn't matter it doesn't matter how much data firm has how much equity financing it has are any other type of financing they engage in no matter what the firm does the value of the firm is the same for example the value of a leveraged firm equals the value of an unleveraged firm so what creates complexity and what changes the value of the firm is everything that is left out so now we can start adding a few levels of complexity consider the simple model but then add merely corporate taxes in most countries with corporate taxes the interest that the firm pays on its debt is tax deductible on the corporate tax rates and Madhu Leone and Miller found this simple equation the value of the leverage firm is now the value of the unleveraged firm plus the corporate tax rate times the amount of debt financing the firm engages in note the correspondence principle if the TC the corporate tax rate goes to zero we return to the previous equation so each time we add complexity we should note that if you take away whatever the complex object is in this case corporate tax rates we should return to the simple equation of value of leverage firm equals value of unleveraged firm so now if we only add the complexity of corporate tax rates we find the more debt the firm adds the more valuable it is because as equity financing goes down and debt financing goes up the firm pays lower and lower taxes so under this unrealistic situation a firm would want to have no equity and 100% debt financing that would be optimal this is clearly not realistic because if you have close to 100% debt financing your probability of bankruptcy becomes quite high consider a company that is initially 100% equity finance and decides to refinance with 50% equity and 50% debt if the unleveraged value of the firm is a hundred million dollars and the firm is subject to a 40% corporate tax rate that according to the mmm model with corporate taxes what will the new leverage value of the firm be so initially we have a hundred percent equity then we go to 50 percent equity and 50 percent debt financing as a result of this additional 50 million in debt financing our firm increases in value to 100 plus 0.4 times 50 our 20 to 120 million dollars note again the higher the corporate tax rate is the more valuable the debt financing is if we were to graph out this situation showing the value of a leveraged versus an unleveraged firm versus debt again here is the value of the unleveraged firm at a hundred million and as the percentage of that hundred million financed with debt increases all the way up to a hundred the value of the leveraged firm increases in this case up to a hundred and forty million dollars since under this example we are again subject to a forty percent corporate tax rates if on top of corporate taxes personal taxes on both debt and equity income or added the mmm model for the valuation of a corporation becomes this somewhat complex equation the value of a leveraged firm equals the value of a none leverage firm plus one minus one minus the corporate tax rate times 1 minus the personal tax rate on equity income also known as capital gains divided by 1 minus the personal tax rate on interest altogether times D the amount of debt that the firm finances with when looking at a complex equation like this it is good as a check to use the correspondence principle meaning in this case if TS and TD the tax rate on both capital gains income and interest income go to zero will this return to our previous equation so if both of these terms go to 0 we get a 1 here a 1 here and we have a 1 minus 1 minus the corporate tax rates the ones cancel out and we just end up with the corporate tax rate times the dollar amount of debt so we have our previous equation for mmm with corporate taxes it is also good to understand how the value of the leverage firm changes with each of these variables we showed earlier that as the corporate tax rate goes up the value of the leverage firm goes up as we have debt so therefore organizations that issue debt like commercial banks would tend to prefer a high corporate tax rate if we look instead at the tax rate on individual taxes on capital gains as this goes up well we have a negative and another negative making a positive so just like with the corporate tax rate on debt it income we see that as the personal tax rate on capital gains goes up the value of the leverage firm goes up with the increasing amount of debt this would be since individuals since this is a personal tax rate are not going to want to buy equities if that personal tax rate on capital gains go up and instead will buy debt therefore the value of the debt to a firm will increase if the individual tax rate on interest income on the other hand goes up we have a 1 minus this so as this term goes up this becomes smaller so one over it becomes bigger and we have a negative in front of that which means this term will become smaller so as the personal tax rate on interest income goes up then the value of debt financing to a firm will in fact go down since individuals then will then not want to buy debt we can do a numerical example of this equation so consider again a company with initially 100% equity financing decides to refinance with 50 percent equity and 50 percent debt once again the unleveraged value of the firm is a hundred million dollars and we will say that the average investor in the firm is subject to a forty percent tax rate on interest but only a twenty percent tax rates on equity income or capital gains and using the MM model with corporate taxes and personal tax rates we ask what is the new leverage value of the firm so we have a hundred million we have a forty percent tax rate again on corporate income we have a twenty percent tax rate on personal capital gains and a forty percent tax rate on personal interest received times 50 million in debt finance and for the firm so the firm is again going from initially a hundred percent equity financing to fifty percent debt and fifty percent equity this rather complex equation here turns into a point two and we end up with the leverage value of the firm increases from one hundred million to one hundred and ten million not as much as it did under the previous situation what about if we add the possibility of bankruptcy so in the case of bankruptcy affirms death holders are not going to be paid off so they're going to be more worried about investing in debt therefore as the firm increases its debt financing they will become more and more worried and investing in the firm will become more and more risky and now we will examine how in putting this into the mm equation will affect its valuation so again we have a firm that's initially financed with a hundred percent equity and now we're going to decrease the amount of equity and increase the amount of debt well as the equity ratio is shifted towards debt again the firm is going to become more risky but initially since debt is cheaper financing that equity the weighted average cost of capital should become cheaper the value of the firm should go up but then as we increase more and more debt there's going to be a point where the risk of debt financing outweighs the advantage of cheaper debt financing and then the cost of capital of the firm will go up and the value of the firm will go down in this graph we look at the weighted average cost of capital the cost of debt financing the cost of equity financing all versus the debt over assets ratio so here we have the debt over assets ratio here we have the cost of each of these components so in debt over assets is zero in red here we have the interest rate on the firm it will be the lowest when there's very little debt since there's very little risk of bankruptcy and when debt over assets a zero the cost of equity capital shown in green is the total whack shown in blue since there is no interest financing gradually as you increase debt well as risk goes up banks are going to charge the firm more and more an interest and then the whack of the firm will diverge downward away from the cost of equity as we've added more and more interest finance and debt financing versus equity at a certain point here around 30% we find that whack is minimized and then starts to go back up this is the point at which the riskiness of adding more and more debt and increasing the possibility of bankruptcy starts to outweigh the advantages of cheap debt financing so in this example this would be the optimal mix are the optimal or weighted average cost of capital would be around 30% debt to ass and 70 percent equity to assets which will also be the point that will in fact maximize the stock price here we show again the same type of whack equation and it becomes minimized around 30 percent debt but now we also show the value of the firm and we show the point where the blue line whack is the minimum is the point where the red line the value of the firm is the maximum the cheapest financing gives you the highest valuation for a company how these graphs were derived is going to be from equations such as this the value of the company can be calculated using the constant growth stock model and in this case the free cash flow discount model where for a constant growth stock the value of the firm is the firm's free cash flows times 1 plus the growth rate divided by whack minus the growth rate and in whack we can embed the riskiness of the firm by using the Amana equation so as an American example we consider a company with a whack of 10% an expected growth rate of 6% 10 here 6% here and an expected free cash flow of 100 million then the value of the firm will be 250 million dollars if the company has outstanding debt of a hundred million than the value of the equity of the firm this V is now the total value of the firm so the value of the equity firm is going to be the 250 million total value minus 100 million debt value so 150 million in equity and then you would have to divide by the number of shares to get the value per share structure of the banking industry in the United States is somewhat unique compared to the rest of the world due to the glass-steagall laws that were passed in 1933 which separated investment and commercial banking investment banks sell stocks commercial banks and make loans we showed earlier the equation of the value of the firm as a function of corporate tax rates and personal tax rates on both debt and equity and we noted that as corporate tax rates increase the companies have a stronger incentive to finance their firms with debt therefore commercial banks which were separated under glass-steagall from investment banks are going to like a high corporate tax rates so commercial banks as noted like high corporate tax rates investment banks on the other hand would like low corporate tax rates similarly as we discussed in the complex equation commercial banks like high dividend taxes and investment banks like low dividend taxes the equation we used to embed risk into the previous WAC equation to make the graphs showing that as the possibility of bankruptcy increased the value of the firm went down was the hamada equation the effect of increasing debt on equity can be developed by this equation which was created by Robert Hamada at the University of Chicago around 1970 the beta of a leveraged firm which is the risk measurement of the firm is the beta of an unleveraged firm times one plus one minus the corporate tax rate times debt over equity in dollars financed for the firm so if debt is 0 beta unleveraged equals beta leveraged 1 minus corporate TC is going to be a positive number so as debt increases the beta of the leveraged firm increases relative to the beta of an unleveraged firm more and more debt more and more risk as an example we could consider a firm subject to a corporate tax rate of 40 percent financed with 70 percent equity and 30 percent debt if the unleveraged beta for the firm is 1.1 its leveraged beta is going to be 1 plus 1 minus 0.4 the corporate tax rate or 0.6 times 30 percent debt over 70 percent equity over 3 7 s 1.1 times this is 1.4 and the beta leveraged is in fact 1.4 higher risk than the unleveraged firm another topic commonly discussed with module e on e and Miller is signaling theory managers of course know more about a firm than the general public and they generally own stock or have stock options in the firm they manage they therefore may do what is in the best interest of them the managers versus the general stock owning public a new stock issue spreads potential profits or losses among investors so for a well established firm it is generally considered a negative signal and the stock firms may drop the reason for this is if a manager thinks the firm isn't doing too well they might issue new stock to sell we say spread the pain among new investors on the other hand a new debt issue will increase the return on equity for a profitable firm and is considered a positive signal this is considered a hoarding the wealth since if the management thinks the firm is going to do very well they will want to have fewer stockholders to spread their profits among and they might in fact borrow debt buy back stock and hoard the wealth to themselves and the other insiders at the firm I thank you for watching this video on capital structure theory