##### CFA Level I Cost of Capital Lecture — Part 1 — by Mr. Arif Irfanullah

## собственный основной капитал

welcome to the CFA level one presentation on cost of capital so cost of capital is the rate of return that suppliers of capital which is bondholders and owners ie equity holders required as a compensation for their contribution of capital each source becomes a component cost of capital and marginal cost is the cost of raising additional funds for a potential project of potential investment project this is also referred to as MCC or marginal cost of capital so what’s the basic idea here so for a given firm there are two primary sources of capital one is money coming in from the owners this can be referred to as equity capital and the other source of money is coming in from the lenders these could be bond holders or the bank but basically somebody who is loaning money so this would be dipped so both these suppliers of capital expect a return the lenders expect to return in the form of an interest rate equity holders expect a return in terms of dividends capital gains and so on and essentially cost of capital is the overall or the average return that a firm needs to give to the suppliers of capital in this simplistic case we have two components one component is the equity component so there will be a cost of equity which we will generally denote as our e and there will be a cost of debt which we denote as our d marginal cost means what’s the cost of raising additional funds so if a firm has already raised 10 million and for this 10 million let’s say that the average cost or the cost of capital was 12% now the fun is going out to raise another 1 million and to raise this additional 1 million if the cost of capital is 14% then we say that the marginal cost of capital is 14% cost of capital is an extremely important concept it is used in investment decision-making by a company’s management it is also used but in the valuation process by investors a company invests in projects that produce a return in excess of the cost of capital so in the earlier reading we studied the concept of IRR which essentially is the return on a project let’s say that a return on a given project is 13% this return has to be compared with the cost of capital so if the cost of raising funds for a given company is 14% and the internal rate of return on a project is 13% then it does not make sense to go ahead with this project and so we will reject the project on the other hand if the internal rate of return is greater than the cost of capital then we will accept the project given given this extremely in for usage the estimation or of the cost of capital is a central issue in corporate financial management so any nature company will have a figure for the cost of capital because that is the basis for often the basis for accepting and rejecting projects this number the cost of capital is also sometimes referred to as the hurdle rate because this is the hurdle level that must be cleared in order for our project to be considered and as a general point the riskier are given investments cash flows the greater its cost of capital and we will study this in more detail later if you are just given that a company’s cost of capital is 14% this means that this is the cost of capital for a average project and very quickly if a project has more risk than average then the cost of capital will be more than 14% if a project has less risk than average then the relevant cost of capital that we take should be less than 14% more on this later so now here is the central equation that you must know and you should put this down on your formula sheet but what this says is that the weighted average cost of capital and you will see soon why we call this the weighted average is given by this equation and here we are assuming that there are three components of capital the is dead there is refered shares and there is regular equity or common shares so the formula for weighted average cost of debt is equal to the weighted of debt times the cost of debt times 1 minus T plus the weight age of preferred shares times the cost of issuing preferred shares plus the weighted of common equity times the cost of common equity and now we are going to understand these terms in a little more detail so when we say we tidge of debt preferred shares and equity we are referring to the relative market value so to take a simple case let’s say that for a given company the market value of debt is 20 million the market value of preferred shares is 30 million and the market value of common shares or equity is 50 million so in this case the total market value for all three components is equal to hundred the wait edge of debt will be 20 over 100 which is 0.2 the wait edge of preferred shares is .

### структура основного капитала

going to be 30 over 100 which is 0.3 and the we tidge of equity is 50 over 100 which is 0.5 our D refers to the cost of debt so this is the return that debt holders or bondholders are expecting so in this simple example let us say that bondholders are expecting 10 percent or 0.1 so we say 0.2 into 0.1 and then since the interest paid to debt holders is tax-deductible that effectively reduces the cost of debt and hence we multiply by 1 minus the tax rate so let’s say that the tax rate is 30% then you do 1 minus 30% which is 1 minus 0.3 which is 0.7 let’s say that the cost of preferred shares is 12% so that is 0.12 and finally let’s say that the cost of equity is 15% so here we would say wait times cost which is 0.15 so that’s a quick explanation we will see these items in more detail very soon let’s first look at a quick example and this just reinforces what we were talking about assume that IFT corporation has the following capital structure 30 percent debt 10 percent preferred stock 60 percent equity IFT wishes to maintain these proportions as it raises new funds which before tax cost of debt is 8 percent cost of preferred stock is 10 percent cost of equity is 15 percent if the marginal tax rate is 40 percent what is the WAC so again we are using the same formula it’s very simple but important enough that we look at it twice so this is the 30% debt so that’s the WD is 30% x this is the the for tax cost of debt that’s the Rd and this is the 1 minus T so 1 minus the tax rate again we do 1 minus T here because the interest paid on debt is tax deductible plus 0.1 into 0.1 this comes from the 10% preferred stock so weight age of preferred stock multiplied by the cost of preferred stock here is 10% so that’s the R P plus 0.6 is the weight age of equity which is given right here so this is weighted of equity and 15% is the return on equity so that is our e so we do the maths and we get 11.4% now let’s look at another example you gather the following information about the capital structure and before-tax component costs for a company the company’s marginal tax rate is 40 percent what is the cost of capital now here the core point is that given both book values and market values you are supposed to use the market value very often for debt the market value and book value will be quite similar but core point is that if you have both use market values so how do we do this the again the overall sum of for all three sources of capital is 303 94 10 so for 10 so we again take the component each component and multiply it by the so each weight is and multiplied by the component so what’s the weight edge of debt is ninety over four hundred and ten multiplied by eight percent zero point zero eight multiplied by one minus the tax rate which is zero point four plus we then do preferred shares twenty over four hundred and ten into the ten percent which is zero point 1 plus 300 over four ten in to 0.14 which comes from here so then you can just do the maths and get the the weighted average cost of capital and by now I’m sure you realize because why we call this weighted average because we are waiting each of these returns based on the relative percentage of each component of capital so weights in the calculation of AK should be based on the firm’s target capital structure so this is another important point on the earlier slide we talked about the importance of using market values rather than book values on this slide we talked about the importance of using target capital structure rather than current or past capital structure so the target capital structure is the portion based on market values of debt preferred stock and equity that a firm expects to achieve over time so the idea here is very simple if a company currently has debt 50% and equity 50% but is headed towards debt equal to 40% and equity equal to 60% then in the usage in our weightages we need to use these these relative weights of debt and equity so we need to use the target capital structure and not the current or the past capital structure in the absence of any explicit information for a funds target capital structure and analysts should use the current capital structure based on market values so this is one possibility so essentially we are saying if we don’t have any information about the target capital structure then then it might be reasonable to just use the current structure we can also look at the trend in the firm’s capital structure so if you see a trend whereby the percentage of equity is going up then we can extrapolate from that trend and come up with the most likely target capital structure and use that in our calculation and finally another strategy is to use the average of comparable companies so if you have no information at all about the capital structure then we can look at comparable companies and take an average here is a small example that gets a lot of people confused and hence I will cover it here suppose a company announces that the debt to equity ratio is equal to 0.4 and it says that this ratio reflects its capital structure so we simply have two components debt and equity so in our rack formula what weights should we use now a quick response that some people come up with is 0.4 and point 6 and that will be wrong so we need to figure out what in this example what’s WD and what is w/e the way you can think of this is just come up with some imaginary numbers the way we have 0.4 .

#### отношение основного капитала

over here you can say if debt is equal to 1 and equity so so actually let’s say debt is equal to 0.4 and equity is equal to 1 this is going to give debt over equity of 0.4 over 1 which is 1 so essentially this is saying that for one dollar of equity we have 0.4 dollars of debt so what is our total funding debt plus equity it is 1.4 so debt as a percentage of total then is 0.4 divided by 1.4 and equity as a percentage of total is 1 divided by 1.4 and using the calculator very fast so 0.4 divided by one point four is equal to so this is equal to 0.2 0.2 nine and this is equal to one divided by 1.1 actually 1 divided by one point one four is zero point seven one so obviously these two need to add up to one now let’s talk about the concept of optimal of the optimal capital budget and here we are looking at two two lines or two graphs first let’s look at the marginal cost of capital which is what we’ve been talking about all along so as you can imagine if we have the amount of new capital on the x-axis and the cost of capital on the y-axis then as you try to raise more and more capital the cost of capital will increase the idea being that for the first 20 million that you borrow the cost might be relatively low but as you keep trying to borrow after that the cost will rise so that’s why while this might not be a perfect straight line in reality but clearly the general trend will be upwards for the marginal cost of capital the other line that we look at is the investment opportunity schedule or I Oh s this refers to the sort of return that we are getting on projects and as you can imagine for the initial money that we invest in projects clearly we will do the most profitable projects first so the first 20 million that we invest will give us a relatively high IRR so let’s say that initially in our projects we can actually get an IRR of 30% and then as we try to do more projects then the return on those projects goes down so and as we keep doing projects eventually we will run out of profitable projects and then we might be somewhere over here where for money spent large amounts of money present when they are black spending uh you know 200 millionth dollar the return on projects then or the IRR is very low so clearly the investment opportunity schedule is downward-sloping and the point to remember is that the optimal capital budget is at this point where the investment opportunity schedule is equal to the marginal cost of capital and this should remind you a little just as a quick refresher in Econ you studied about the profit maximizing point being the point where marginal revenue is equal to marginal cost these are roughly analogous but the basic point is this let’s say that we are at this point a and at this point a notice that the IRR or the return on projects is more than the cost of capital so it makes sense to keep going and invest some more on the other hand if you are at point B then the cost of capital is greater than the return and hence it makes sense to scale back so the optimal point being this point X which is the point where the two lines intersect and that would be the optimal cap the optimal capital budget for a company now let us talk about the rule of marginal cost of capital the marginal cost of capital or the WAC for additional units of capital should be used as the discount rate when calculating a projects in PV for capital budgeting decisions so in the last presentations on capital budgeting the discount rate that we use is what we are talking about here so that discount rate should be the weighted average cost of capital however adjustments to the cost of capital are necessary when a project differs in risk from the average risk of firms existing projects so if the if we come up with a number that vac is equal to 14 percent this 14 percent is for average-risk projects if you have a high-risk project so high-risk project then you should use a rate that is greater than 14 percent and for low-risk projects you should use a rate that is less than 14 percent and more details on this later when we talk about how to measure risk and when we talk about the cap m formula so the discount rate should be adjusted upwards for high-risk projects and downwards for Lotus projects as illustrated above now let’s get into the details of how we come up with the different costs of capital so how do we come up with our dr4 preferred shares and our for equity each source of capital has different costs because of the differences among the source such as seniority contractual commitments potential value as a tax shield and so on and the primary sources of capital are debt preferred equity and common equity so before we get into the details just as a basic point investors will demand a higher return so they will demand a higher return if they are taking on a higher risk so in the case of debt preferred equity and common equity the common shareholders are taking the highest risk and hence they will demand the highest return and so after that comes preferred equity so they are taking lower risk than common shareholders so their return will be or expected or required return will be less than common equity and debt holders are taking the lowest risk relatively speaking because when a company makes money there is a contractual obligation to first pay the interest to debt holders and hence the required return for debt typically is the lowest of these three .