in the previous video we looked at the Modigliani Miller theorem of capital structure and cost of capital propositions one and two under the case where there were no taxes no corporate taxes and no bankruptcy costs so what we want to do is we want to look at the model now under case two the case where we have corporate taxes and here's how it works in the United States interest on debt is tax deductible so when a firm adds debt to its capital structure it winds up reducing its taxes and what happens when you reduce your taxes you happen to increase cash flow now this will result in a reduction in net income obviously because you're paying money to the government but you're going to increase your cash flow so let's take a look at an example here here we have a case of the unlevered firm we'll call it U and a levered firm will call it l they both have earnings before interest and taxes of a th000 in the unlevered case there's no interest so taxable income is ebit is the full $1,000 if we assume the taxes are 30% or the tax rate is 30% there's $300 in taxes so net income is 700 let's look at the leverage firm same $1,000 in ebit $80 in interest which means that we have $920 in taxable income and what's the case here we have $276 in taxes 30% of 920 which gives us $644 in net income so what we're really interested in is cash flow from Assets Now if we assume there's no depreciation and here we don't see any depreciation uh well actually depreciation would be above ebit we're going to assume no depreciation then cash flow from assets is simply going to be ebit minus taxes so in this case it's the same 1,000 minus 300 is 700 in the case of the levered firm it's going to be ebit minus 276 or 724 so what you see is there's 24 extra dollars in cash flow and that comes from what we call the interest tax shield let's see how that affects the value of the firm here we have the case where and again here are the assumptions we have the tax rate times the uh interest payment the interest expense is going to be $80 we're assuming 8% debt and $1,000 in in debt so $80 in interest the tax shield is going to be 30% the tax rate times the interest expens or $24 now if we assume that the company is going to maintain this tax uh this tax shield forever that is they're going to maintain their debt they're not going to pay off their debt they're going to maintain this $1,000 in debt we can figure out the present value of this of this interest tax shield it's $300 okay so it's going to be uh a couple ways you can do it it can be debt times the rate on debt times the uh tax rate divided by the rate on debt okay Rd cancels so you get debt time time the tax rate so ,000 time3 $300 let's see how that looks graphically what we have here is the case where if there is no debt okay we have the unleveraged firm okay down here is the total debt that's being used then this sort of pinkish line here shows that the value of the firm doesn't change because you're not using any debt so it's always the same on the other hand if you choose to use debt VL value of the levered firm is going to be equal to the value of the unlevered firm plus this tax shield so you can see that that's the difference here a firm that uses more debt actually winds up increasing the value of the firm if there are corporate taxes and those taxes are are are I'm sorry if there are corporate taxes and if the interest expense is tax deductible and remember we're not assuming any bankruptcy costs so using more debt doesn't increase the risk of bankruptcy here so in this case if you want to Value if you want the greatest value for the firm you should simply use 100% debt in your capital structure let's see how this looks for proposition two which deals with the weighted average cost of capital here's the case that we have where we have the return to the unleveraged firm and we know that the return on Equity from proposition from case one proposition two is upward sloping if there's more debt in the capital structure there's going to be more risk so so stockholders are going to re require a higher return but what happens here it turns out because of this tax deductibility of the interest payments that the weighted average cost of capital goes down as we add debt to our capital structure and you can see what it does is it approaches the rate on debt so if you used 100% debt in your capital structure it would be equal to the rate on debt that would be your weighted average cost of capital because the um percentage of equity used to finance The Firm would be zero so this is the case where again if you want the lowest cost of capital and you want the highest value of the firm what should you do in this case you should use all debt to finance The Firm now in the next video we'll take a look case three where we add bankruptcy costs and this is a much more interesting case but in this case the optimal capital structure is to use all debt in your um all debt to finance The Firm