CF 5-1A – Dividend Discount Model – Corporate Finance

Let's take a look at problem five, one, a, this explores the dividend discount model. What the dividend discount model says is to value a company's stock value, the cash flows it's going to produce and what are the cash flows of a stock? Dividend. So to basically figure out how many dollars worth of dividends we're going to get over time, discount those cash flows to today's dollars. That'll tell you the price of the stock or what you, the value of the stock, I guess, is a different way of saying it. So suppose Benson industries has just paid a $5 per share dividend, and it is announced that it plans to increase dividends by, uh, 3% per year going forward. The company's equity cost of capital is 10%. Okay. Uh, so what's the price of the stock today? We're going to use this formula. This is the dividend discount model with a growth rate, uh, to the dividend, uh, and that this is the formula. So P zero is just the value of the stock today. So, uh, the price today or the appropriate price today, that equals D one, which is the dividend amount in one year. So our expected dividend in one year, uh, divided by R, which is our required rate of return, our discount rate, and G is the dividend growth rate. And in this question, we're just given all this information or most of it. We certainly have enough information to go on to, to solve the problems. Let me change my ink color and let's get to it. So what's the stock price today. So we're solving for this P zero. Uh, well, what is the dividend going to be in a year? We know the dividend is $5 yesterday. What's it going to be a year from now? Well, it's going to grow by 3%. So $5 times 0.03. I can do that in my head. I think it's 15 cents. Five times 0.03 is a 0.15. So it's going to grow by 15 cents. So it's going to go from $5 to $5 15. That'll that's 3% growth. So D one is 5.15. We'll divide that by R minus G. Uh, R is our required rate of return or equity cost of capital in this case, 10%. And the dividend is going to grow by woes. That was crazy. Uh, things slipped away on me there. Uh, 10% minus 3%. That's our growth rate. So 5.15 divided by 10 minus three, uh, 5.15 divided by I'll put 0.07 into my calculator. So 5.15 divided by 0.07 equals $73 and 57 cents. That's the value that the dividend discount model would put on this stock. Now there's millions of other factors that go into an actual stock price, but this is one way of considering the value of the stock. So that's A and we've solved. Let's move on to B. What's the price going to be in five years? Well, revisiting our formula here. P5 equals D6, right? P0 equals D1. Well, P5, we got to figure out what's the dividend in six years divided by R minus G. So R minus G are the same. We got to figure out D6 in this whole equation. So what is the dividend at time six? Well, we know the dividend at time zero is $5 and we know it grows by 3% a year. So we're going to say times 1.03 to the sixth power. And that's going to give us our dividend at time six. So 1.03 to the power of six, 1.19 times five. So our dividend, if it keeps growing at 3% after six years, it's going to be $5 and 97 cents. So our D6 is 5.97. We'll divide that by R minus G, 10 minus three. It's still 7% or 0.07, I guess is what I'll do. So 5.97 divided by 0.07, $85 and 29 cents. Okay. So there we have what we would anticipate the stock price to be in five years. What about in 20 years? Well, we say price at 20 is the 21 divided by required rate of return minus the growth rate, dividend growth rate. So five times 1.03 to the 21st power, 21 years of dividend growth. Uh, going to be a big number here. 1.03 to the power of 21, 1.86 times five, 9.3, basically 9.3, 9.301. Um, okay. So that's my D at time 21, my dividend at time 21, 9.301 divide by again, R minus G is still the same. 10 minus three, uh, is 0.07. Now again, projecting for 21 years, companies change their dividend and growth rates change over time. But this is just a, you know, an exercise, like a calculation exercise, 9.3 divided by 0.07. 1 32.88. So our answer to a 73 bucks answer to be 85 bucks. And our answer to see 1 32 bucks. I hope I helped you with this. And as always, if I helped you, I hope you'll help me have a great day. Bye-bye.