**Cost of Equity**

** The cost of equity** is the rate of return required on the common stock of a company. This minimum rate of return is essential for the company to earn so that it prevents its common stocks price from falling. There are several models such as capital asset pricing model (CAPM) and dividend discount model (DDM) that are used for estimating the cost of equity.

## Cost of Equity Formula

The cost of Equity= Risk-Free Rate + Beta coefficient * Market Risk Premium.

Now let us go back to the cost of debt and the cost of capital. Why all this is important? Well because remember, the interest rate, does not change during the life of the bond. The interest rate is always fixed at 10%. The interest payments are always 100 million and the principal never change. So if we are thinking about the cost of debt, as what investors are requiring at each particular point in time. Then the interest rate can never be a good indicator of the cost of debt. And the reason it can never be a good indicator is because this number never changes. Obviously as time goes by companies become riskier or less risky, but the interest rate is does not change. And the coupon payments that don’t change, so the interest rate could never be a good approximation to the cost of debt. But remember, the number that does change when prices change and when riskiness change, and that is that mean annual return that we calculated, that why. That you have in the slide. And that y, which we call yield to maturity. That’s why we call it, and we put the notation as y, that yield to maturity is basically the mean annual return that you get by paying the market price for the bond, $939 in the example that we’ve seen, and pocketing all the cash flows that you expect from the bond. That is, if you pay the market price, and hold the bond until it matures your mean annual return is what we call the yield to maturity. That is the measure of the cost of debt. Because that yield to maturity will be changing all the time, as market prices change and market prices will be changing all the time when the riskiness of the company goes up or down. So if we want to be accurate. If we want to properly capture what the company needs to deliver in terms of return, today then we will be looking at a number. That it actually fluctuates over time rather than a number that is constant over time that can never give us an updated. Fresh estimate of, of the cost of capital. So if we want to know what the companies cost of capital today, all we have to do is look at the yield to maturity that the company’s paying today in the bonds than the company has outstanding. Bottom line, the cost of debt is a bond’s yield to maturity. So for a company that has only one bond in the market, that cost of debt will be equal to the yield to maturity that the company is paying at this particular point in time. This is just to show you, this is just taken from the Financial Times it is published every day you can find it in the Wall Street Journal, you can find it online. I just wanted to highlight very quickly. Look at Australia. These are government bonds. And the only thing that I want to show you there, the four columns that you have. The first one is the, the one that says Redemption Date. R-E-D. A day that is Redemption Date. And that is the day that the bond. Or the date that the bond actually expires. So the first bond. The first Australian bond expires on June of 2016. The second bond expires on April of 2024. So that basically tells you that all bonds, or just about all bonds. It is not, I mean, there are bands that never expire, but that is a little corner of the market. But in general, all bonds have an expiration day. And everybody knows that expiration day. It is a public number. It is a number that you need to know when you buy a bond. All bonds. We will have a coupon. Remember the coupon is what percentage of the principle the company is going to be paying on an annual basis. And so the second column is showing those numbers. So for example in the bond that expires on June 16. The coupon on that bond in the case of Australia is 4.75. And that basically means that they will be paying 4.75% of the principle, on an annual basis. The second bond has a coupon of 2.75. Well it means the same thing. Between now and April 2024 the Australian government will be paying 2.75% of the principle. And the principle could be $100, $1,000, it doesn’t really matter, 2.75% of the principle every year until the bond expires. The last two columns are the most important ones, and they are most important because. They show you how much you have to pay today for that bond. And notice that next to each price, there’s what’s called a big yield. Big yield is what we called before the yield to maturity. That means that if you pay $104 for that bond, then your mean annual return, if you hold a bond until maturity is 2.6%. The second bond if you pay 9238 for that bond and you hold that bond until maturity, your mean annual return is going to be 3.68. And notice something that is important. Compare for the first bond the coupon with the yield. The coupon is 4.75. The yield is 2.60. In the second case, the coupon is 2.75 and the Mm. yield. Is 3.68. So as you see the coupon and the yield. And that again, again we’re calling yield. It is the yield to maturity. But we always call it yield. When you compare the coupon and the yield to maturity, these two numbers do not have to be the same. In fact, more often than not, they are going to be different. So here’s important thing, if you actually look at this in the paper today and tomorrow, and the day after, and the day after, those coupons will not change until the bond expire, none of those number in the coupon column will change. But if you actually look every day, today, tomorrow, and the day after, to the price and the yield, the last two columns. Those will change every day. That is why it is important that you keep in mind that the coupon, or the interest rate of the bond, could never be a good estimate of the cost of capital. Because. Companies riskiness change over time, but that is never reflected in the coupon, unless that the company has to issue it, or the bond has to issue it, or the government has to issue a, a new bond. But the prices, and the yields that go with those prices. That one change all the time. So bottom line. When we think of the cost of debt, we need to think of the yield to maturity of the bond that the company may have out, outstanding in the market. Now you can say well but not every company issue bonds. Well that is true. Some companies actually borrow money directly from a bank a, and we’ll get to that in just a second and we’ll get to that in just a second because we need to now start talking a little bit about the cost of equity. But the first point that we need to make about the cost of equity is related cost of debt and that is think about the numbers we’ve just seen, you now, if you look at the bond of any company the price that you have to pay. And the yield to maturity that goes with that price, that’s a number that is given by traders in the market, and that number for, from the point of view from the company, it’s sort of given. You know, the company is doing things every day, the investors are reacting to whatever the company is doing and they fix the prices, and they fix those yields to maturities. But from a managerial, if you will, perspective, what that means is my cost of debt is observable. By observable, I mean that I can always go to a trading screen and say that is my bond today and that is the yield to maturity that I have to pay. And because it is observable, as some people would also call it objective. Why objective? Well because I may like or not like the number but if you, I look at the number, and you look at the number, and someone else look at the number, that number is not going to change. It is going to be the same at a particular point in time. The number is whatever it is. Some people refer to the cost of debt as observable; some people refer to the cost of debt as objective. And some people actually refer to the cost of debt as observable and objective, both of them at the same time. Why had I brought up the issue of banks before? Well again, because some companies may not have a bond trading in the market and they may do business with a bank. Whenever they need, need debt they call their banker and they say, you know, we need 100 million. How much would you charge me today? And the bank would say well for that we’ll charge you 8%, 7%, 6%, whatever the number. But again notice that the same thing. That, that cost of debt now becomes observable. Someone tells me, what that cost is going to be, and again, it is subjective. They give me the number. I may like it or not. But if I’m hearing the number, you’re hearing the number, we’re going to be hearing the same number. So that becomes my cost of debt. So whether I have a bond trading in the market, or whether I’m borrowing money from the bank, in both cases, the cost of debt is both observable and objective. And the reason that this is important now that we start talking about the cost of equity, is because the cost of equity or the require return on equity is neither. That is first it is not observable. That means that we need to estimate it and that means that because you and I may be using different models. Or you and I may be using the same model but with different values for the parameters, then that cost of equity becomes subjective. Your number and my number may be different. That will never happen with the cost of debt. So that is a fundamental asymmetry that you need to keep in mind. That as far as the cost of debt is concerned, I observed that number and it becomes objective, but as far as the cost of equity is concerned I do not observe that number, I must estimate it and therefore it becomes subjective. Now, of course there are many ways of estimating the cost of equity that many models have been proposed a by far, the most widely used model is what we call the CAPM. And CAPM is just an abbreviation for the capital asset pricing model. And if you actually ask around, and by ask around I’m saying you do surveys of what models people tend to use, as you can see in that picture by far. Of the model most widely used to calculate the cost of equities this campaign that, that we’re going to explore. So again, this is not the only way of calculating the cost of equity, but what is important is two things. One. That we need to estimate somehow the cost of equity. And two, the CAPM is not the only model. But it’s by far the most widely used. And it’s also very intuitive as you’ll see in a minute in order to estimate that cost of Equity.