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“And welcome to this session. In which we re going to be working with chapter chapter 8 chapter. 8. Discuss common stock valuation we looked at different model we look valuing stock with zero growth model.
Where the dividend is the same d 1 equal to d 2 equal to d. 3. Which is constant we look at the constant growth model where the dividend is growing at a constant rate in this session. We re gonna what we re gonna be looking at is the non constant growth model and this is more realistic than the other two models because that s that s what actually happened in the real world you don t grow at a constant rate.
You don t throw at a constant rate constantly and you don t see the dividend doesn t stay the same so this is a non constant great model again we re gonna be doing some simplification. But this is a senior that could that could happen so the next case. We consider as a non constant growth. The main reason to consider this case is to allow for super normal growth rate over some finite length of time.
Ok what does that mean it means when a company start if the company is really doing well like it s it s it s a new startup. And you know they re new in that industry and they re doing great like apple computers when they started the iphone or the ipad. The company was growing a lot same thing with amazon amazon still growing at a high growth rate. Same thing as netflix right now but at some point these companies will level off in other words.
They might be growing at 20 to 30 percent now but this growth rate cannot be maintained forever. At some point. They re gonna be growing for example at 5 forever or 6 or 7. It s a at a look at a lower growth rate.
So this non constant growth rate will help us find the value of the stock. So as we discussed earlier the growth rate cannot exceed the required rate of return indefinitely. But it certainly can do so for some number of years so you re growing faster than your required rate of return that could happen to avoid the problem of having to forecast and discount. An infinite number of dividend.
We will require that the dividend start growing at a constant rate sometime in the future. So. We say is maybe this growth rate will be there for seven here s and then the growth rate will level off. So we ll make that assumption.
So let s take a look at a simple example to illustrate this point for a simple example of non constant growth rate. Consider the case of a company that s currently not paying any dividend. Okay you predict that in five years. The company will pay a dividend for the first time so on a timeline.
And this is worth the time value of money. What we learned is extremely important so this is zero period one period to period three period for period five period six. Period seven. Forever so the dividend will be 050 per share.
Then the dividend will grow at ten percent. So here s what we re saying they ll pay the first dividend at 050. Per share five years from now. This is the first time they paid ever and they re gonna pay half a dollar then going forward this dividend will grow it will grow at a 10 rate so g equal to a ten percent so in year six they re gonna pay you fifty five cent and in year seven fifty five cent times one point ten so on and so forth.
So it s gonna be a constant growth and all in this example. The required rate of return equal to twenty percent. So now what s the stock price today. What s the stock price today well basically what we have to do it s correct.
It s kind of like a two problems all we have to solve it in two different ways the first what we have to do is what we can do is we know that it s the we know the required rate of return equal to 20. We know the growth rate equal to 10 giving this information given this information. What we can find out we can find out the price at year for the price at year for what we learned from the prior session. If you don t know how how i m doing this make sure you go back and view.
The prior session. The price at year four equal to the dividend of year five divided by r minus g. And we already know the dividend that year five. We know the dividend at year five equal to 50 cent.
So another way to look at dividend that year. 5 is d. 4 d. 4.
Times 1 plus g. But we are giving this the 5 who are giving this as 15 as 50 cent per share. So if we take 50 cent per share. This is the dividend in year.
5 and we discounted rate of return equal to. 02. Minus the growth rate equal to 01. So 50 cent.
Divided by point 1. The price of the stock is 5. So now we find out is the price of the stock at year 4. So p.
4. Equal to 5. That s good that s before i m not looking for p 4. I m looking for and whatever what i want to find out it s what s p 0.
The price today well this is simple then if i know my growth. I know my growth rate. My growth rate growth rate is my required rate of return is 20. All what i have to do now is discount this 5 to the present now it s basically discounting the 5.
So basically to find p0 equal to you know p..
4. Divided by 1 plus r raised to the 4th power. So p 4. Equal to 5.
So basically on this count how much should i pay for 5 that i m gonna be getting. 4. Years. From now.
I will discounted 1 plus. R. 1. Plus.
1. Plus. The rate of return is point. 2 raised to the fourth.
Power. So. 5 that s the stock price four years from now 12. Let me see this.
Clear 1 point 2 raised to the. Fourth power that s. 20 seven divided by 207. 5.
Divided by two point zero seven. The present value factor is two dollars and forty one cent. So i ll pay for this stock today two dollars and forty one cent. Okay.
Today today why if i buy if i if i pay for it. Today. This stock should be worth five dollars four years from now. It should be worth five dollars.
How did i know it s worth five dollars. I discounted the dividend based on their growth rate okay so this is how i find out i ll pay so i ll pay today two dollars and forty one cent. Because they want the price today and hopefully we can see this so basically this was at two in a sense. It was a to two problems first we have to find the price at p for them from p for discount.
The price to p zero. Okay and this is the explanation in the book. So let s take a look at another example and try to solve the problem. Okay.
Let s take a look at this example. Okay. The problem of non constant. Growth rate is only slightly more complicated.
If the dividend are not zero. So what happened if the first year. The dividend are not zero for the first several years for example. Suppose you come up with the following dividend forecast for the next three years so here s what s gonna happen year one you re gonna get a dollar and dividend here you re gonna get two dollars in dividend and here three you re gonna get two dollars and 50 cent and dividend then after the third year the different will grow at a constant rate of 5 per year once again the best way to do this is to know how to set up a time line.
So. Let me see let me set up a time line. Okay so dollar two dollars and 250. Well well they have a time line.
But let s set it up ourselves. So this is forever so year one it s gonna be they re gonna pay your one they re gonna pay a dollar year they re gonna pay two dollars year three they re gonna pay two dollars and fifty cent and from year three going forward from year three going forward what s gonna happen then they re gonna level and it s gonna g equal to 5 and d then the dividend will grow at a constant rate of 5. So starting from year three okay. So this is this is what we are giving this is what we are giving in dealing with a non constant growth.
A timeline can be helpful okay. The important thing to notice is when s the constant rate growth starts or the constant rate started at year three from here three going forward. They re gonna have a constant rate for this problem concentrate year three this means that we could use our constant growth model to determine the stock price at p three very simple we have to find what is the stock price at year three so what is p three. Because we want to find p three.
And hopefully we all know what p. 3. Is p. 3.
Equal to well equal to d. Four. Let. Me first show you the shortcut d.
4. Divided by r divided by odd minus g. What is d four well d. Four equal to d.
Three times 1 plus g. Divided by r minus g. So. What is let s let s find what s the stock price as of p.
What is d 3 d. 3. Is 2 dollars and 50 cent times 1 plus. G the growth rate for this.
Example is 5. 5 times 105. Divided by the required rate of return for this company is what s the required rate of. Return the required rate of.
Return is 10 so point. 1. Minus 005 so what is. 25 times 105.
So this is d 4. So the d. 4 equals to two dollars and sixty two cent two dollars and sixty two cents. This is d 4.
Divided by point one minus point zero five equal to point zero. Five so two point six two divided by 005. That s equal to fifty two dollars and fifty cent. So this is the price at p 3.
This is the price. Here this is the price of the stock p3 is 5250. Now well guess. What yes we can go ahead.
Now and do exactly what we did in the prior session and basically discount p3 to the present value basically go ahead and discount the p3 to the present value. But that s that s not the only thing we re gonna be getting in this problem. In this problem were also that the company is also receiving in year three two dollars and fifty cent in here to two dollars and in year. One one dollar.
So we did in the prior and in the prior example. We did not have those dividend that i have i m highlighting in red right now the dollar of the two dollars and the 250 all what we have is once we find the price and i believe you know i i remove that sheet. What we did is we discounted the price so to find the price today p0 part of it it s gonna be p3 discounted at 1 r raised to the third power of course. But also what s gonna happen in addition to thee.
Which is this is let s do this so. P0 equal. 250 250. Divided by 1.
Plus. Or the rate of. Return. Is.
10 percent 1. Plus. 01. Raised to the third power.
But also we re gonna be receiving in addition to the price of the stock in year 3. What we re gonna be getting is the dividend. Remember we re gonna be receiving dividend. Let me put.
The formula here. We re gonna be receiving d3. And that s gonna be discounted because remember we re getting that cash so we re gonna discount the cash at 1 r to the power we re going to be getting d 1 r raised to the second power and we re going to be getting dividend 1 1 r raised to the first power so basically just let s fill out the formula d. 3.
We re gonna be getting 2 dollars. And 50 cents. That s gonna be discounted and 1 point. 1 raised to the third power d.
We re gonna be receiving two dollars and d 1. Point. 1 raised to the second power and the first year. We are receiving a dollar 1 point 1 raised to the first power now we have to do is find the present value of all these components of the.
Stock so. 5250. Motors. That s first one point 1 y.
To the x equal to. 3. That s 1. So 52 point.
5. Divided by 1 point. 3 3. 1.
2. Dollars. And 50. Cent.
Divided by 1 point..
3 3. 1. 2. At one point.
1 raised to the second power 1 point 2 1. And obviously 1 divided by 1 point 2 1. Again. We re gonna have to do the calculation.
You know you can go ahead. And do the math. I believe we have the answer in the textbook. Let s find out what the stock price is so if we do all these calculations.
Well. The price should be 43 dollars in 88 cents. So if you go through the calculations. So it should be 43 dollars.
And and so the price is 43 dollars in 88 cent. So this is the price of the stock. So basically we did is it s it s big also it s a two stage process first we find the price as of p. 3.
Then we discounted the the dividend that were not constant. What are the non constant dividend. The dollar was a nun constant the 2 and the 250 those were the nine constants. So we discounted all the constant dividend and all the constant dividend by themselves are worth fifty two dollars and 50 cent.
Then you can find the what these non constant equal to if you want to separate the price. Okay. So this is the this part here is the non constant component of the price. And this is the constant component of the price okay so we could break it down into two component that the constant component and the non constant component let s work example 5 4.
Which is another similar example okay so chain reaction has been growing at a phenomenal rate of 30 percent. Because of its rapid explosion and explosive sales. There are rapid expansion in explosive sales. Yes of course when the company start they might grow at a really abnormal great very high rate in the situation.
30. Percent. You believe that this growth rate would last for three three more years and then we ll drop the 10 percent. So it s gonna be 30 percent 30 percent 30 percent on it on a timeline.
It s gonna be the growth rate is thirty percent thirty percent thirty percent. Then it s gonna level at ten percent. So what s the total value of the stock total dividend. Just paid were five million and the required rate of return is twenty percent.
So what are we saying here so they paid today five million in dividend and the required rate of return equal to ten percent. Let s have what we let s have what we let s put what we have on a side. So. All.
The required rate of return is 20 percent g equal. To well g basically one two and three it s gonna be thirty percent. So the growth rate for year one year two for year one year two and year three equal to thirty percent then year three going forward g. It s gonna be level at ten percent.
So let s find the dividend. So first you re going to be receiving dividend in year one right so what s your dividend in year one they re telling us it s five million so total dividend just paid were five million okay just fade it just fade means today it s five million now so it s gonna be one year one year two year three then forever. So what is the dividend in year one well the dividend in year one okay so what s d1. What is d1 d1 equal to d 0.
Times 1 plus g d0 today is 5 million times 1. Plus. G. 1.
Point 3 times. 13 so if we take 5 million times. 13 so this is gonna be 65 million this is the dividend that we receive what is d2 d2 equal to d1 times 1 plus. G what is d1 d1 is we already find out d1.
Is 65 million so i m gonna take. 65 million times 13. And that s gonna equal to eight point four five million eight point four five million then what s d3. What is d 3 d.
3 equal to d2 times 1 plus g. And hopefully you re getting this basically as you work more. And more you re gonna get better at the suit s eight point four five eight point four five times. One point three and that s equal to ten point nine eight ten point nine eight then what s gonna happen going from ten point nine eight going from after year three dividend.
It s gonna grow at 10 forever. So basically we have to do exactly with it in the prior problem find p3 find the constant growth rate value of the stock then discount. The non constant dividend. Which is p3 p2 and p1.
So let s do this. So. What is p. 3.
To p 3. Equal. To d. 3.
Times. 1 plus g. Divided by r minus g. So what is p 3.
What s the what is the price f. The stock at p 3 equal to d 4. Divided by r minus g. What is d 4 d.
4. Is d 3 times 1 plus g divided by r minus g. What is d 3. Now we know d 3 d.
3. Is ten point nine eight million ten point nine eight million ten point nine eight nine eight five times. One plus. The growth rate for this for the constant growth rate is 10 times.
One point one all divided by r. Minus. G. R.
Minus. G. Is 20 minus 10 percent 20 minus. 10.
Which is 20 minus. 10. Is 10 percent. So when we calculate this so.
The p. 3. The value of the company is 120 million 120 point eight three one twenty point eight three the price. The value of the company.
Which is the value of the stock p. 3. Is 120 point eight three five million now. But that s not the only thing.
We re gonna get also we re gonna get in here. Three remember nine point ten point nine million in year. Two eight point five eight point four five and in year. One six point one five.
What do we have to do we have to discount those non constant dividend to the present value okay so now we have to do is discount. D. 1 d. 2.
And d. 3. At the required rate of return which is 20. We have to discount them six point five divided by one point.
Two eight point four five divided by one point. Two ten point nine eight divided by one point nine two plus. We have to discount the price of the stock. So this is the component that s constant growth and we have to discount it we find the price we have to discount it and this and the one i highlight and yellow or i m gonna box in another yellow and red is the non non constant dividend.
So all in all the company s stock worth eighty seven point five eight million. But this is the total value because they re not giving you for sure they re giving you the total value of the stock today so the total value is eighty seven point five if there s 20 million shares outstanding all we have to do to find the price per share take the value of the company divided by all the shares. Which is 20 million. So the price per share is 4 dollars and 38 cent 4.
Dollars and 38 cents. And hopefully this example i hope that it helped you little more a little bit more than we were two examples in understanding how to solve a problem when we have at some point. An abnormal growth or a different growth rate. And that growth rate will will level off at some point.
Which. Which is a constant growth rate. Again. The more exercises.
You work the better off you get at this. But remember in those type of situation look at it as two different problems. One you have a constant growth problem and the other one you have those not non constant dividend. That you have to discount to the present value using the required rate of return.
If you have any questions by all means email. Me or see. ” ..
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