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“There my name is david elia. And i m going to give you a very very quick video today looking at the dividend growth model and also the net present of growth opportunities model now both of those are used to value equities and in previous videos have spent quite a lot of time explaining both the double den growth model and also the net present value of growth opportunities model in this video. I m going to bring them together and show you that they are equivalent. One is more difficult than the other.
But this is an important thing. Because a lot of finance is all about consistency and you know there s no point having one module that gives you a definite result from another model so in these two approaches that have given and we re going to be looking at why they are consistent. Now let s start off with a simple example. So you ve got an equity.
The earnings per share is 10 euros. Now you ve got a tension ratio of 60. So that means that you re retaining 60 of your earnings. And that means that your p note.
40 in the form of dividends. We have a discount rate of 16. And we have return and retained earnings of 20. So what that means is that from the amount t of keeping back your investing and projects that are actually giving you a higher return than what investors are looking for so investors are looking at 16.
You re getting 20. So that s a good man s goodness. A reason for a you know not paying all of your your earnings are in the form of dividends. So we re going to be using an s alight.
The dividend growth model to value this company. So a retention ratio is 60. Which means p. A ratio is 40.
So how much of the dividends is 40 percent times. The an exposure of 10 euros. Which means that our dividends are 4. Euros.
Now we want to work out the growth rate and dividends..
And you recall from a previous video. The growth rate is equal to the retention rate multiplied by the return on the retained earnings which got a little sloppy so the growth rate is equal to retention ratio. Which is 60 percent multiplied by the return on the retained earnings. Which is 20 percent.
Which gives us a growth rate into evidence of 12. So let s look at the value of this company. Then the value of the company is equal to the dividend next year. That s this point here for euros divided by the discount rate minus the growth rate.
So it s point one six minus point one. Two notice that we re not using all numbers were using decimals here. And that gives us a value of 100 euros for the equity now. We can look at where okay.
What is the value of the company without growth. If the value of the company with no growth and we have the l. Nice pushy. Remember you re not paying in you re not keeping anything back sorry you re not keeping anything back to invest.
So everything is getting paid out in the form of dividends given that that is a case. Then the dividends are equal to the earnings. So the share price is equal to they honest procedure divided by the discount. Rate there is no growth and we get 10 euros divided by 016.
Which gives us a share price of 62 euros and 50 cents. So the difference between the share price with growth and the share price without growth as the net present value of growth opportunities and that is equal to 37 euros and 50 cents. Okay so just look at that these are some key key values. The value of the the equity is equal to 100 euros and the value of the net reservoir with growth opportunities.
Using this approach is 37 euros and 50 cent s now we re now going to do the exact same. But this time use the net present value of growth opportunity modem and it s a bit more difficult i have to say that because in the previous video. We looked at case. Where you only have one investment which takes place at time 1.
But with this example you re going to be holding money back every year..
So you effectively you ve got perpetuity of investments. It s not just one investment. You re looking at this is a number of investments. So we re going to have to just do a little a few more things to make them just a little bit more complex apologize for this screed of writing.
But it s important that we do it step by step so it s exact same as sure there s no difference between what we did in the previous slide. Even what we re doing just now so the first thing we do with net present value of growth opportunities as you work out the net present value of the investment that is made from the retained earnings so let s look at date one date one you can see here that we ve got a retention ratio of 60. So that means we re retaining 60 of 10 euros. Which is equal to 6 euros.
And we know that that earns 20 per annum forever right. So. If it s going to earn 20 per annum forever. 20.
Of the sec s euros is equal to 1 euro. 20. So we can work out the net present value of that retained investment. Which is set euros plus.
The perpetuity of one euro 20 divided by the discovery that you re getting well will the investors expect. And that gives us a net present value at time one of the growth opportunities to be 1 euro and 50. No careful the net present value at time 1. Okay.
We re going to come back to that now we go to d2. Now because the earnings per share. And in the dividends of growing at 12. We know that we we calculated that here then it s a constant proportion of the the earnings.
So the devid ends are growing to a percent. The onions will grow at 12 as well so 12 of six euros is he 36 euros in 72. So that s the retained earnings date. They re going to um.
As we said. Which means the 20 of the sermon is one euro and thirty four point four cents. So we do the exact same thing. But that same is a date so what s the net present value of this investment.
We re investing sex euros in 72. We re getting one euro and thirty four point four cents. We re getting our every year forever. Source of perpetuity.
But this counting not by the discovery of sixteen percent. Which means that the net present value of the retained investment at day two as one euro and sixty. But that s net present value attempt to write so that s we re looking at the the second year. And we re going to do that again for day three just so i can take you through it in detail.
So the illness per share grows at twelve percent. The retention rate is sex this last is the same so that means the retained earnings grows by twelve percent which means that six point seven two multiplied by 1 point one two i means you re increasing the retained earnings becomes seven point five two six four never gone t. I m twenty percent on that that means that you re getting one euro and fifty cents every year forever. Because remember there s a perpetuity.
So we re going to calculate net present value at time three as the investment plus. The present value of the perpetuity that gives us a net present value. Ten three of one euro and eighty eight point two cents. So you re seeing here that if we then want to calculate well what s the value today.
What s the net present value of the growth opportunities today. Then we need to discount each of these net present values that take place in the future by the discount. Rate so you see that. Time one is one euro 50 divided by.
11. Six at. Time 2 is 1. Euro 68 divided by.
11 six squared and one point eat it too 116..
Cubed. Now you may say well okay. Where we going with the spell. If you look carefully then that is effectively over doing here is growing that s 1 euro.
50 each time by 12. So what we ve got here as we ve got a growing perpetuity similar to what we did with the deviled egg growth model do you see that so it s 150. That s growing so given is a growing perpetuity. We can use the growing perpetuity model to calculate the net present value if the growth opportunities that s 1 euro.
50 divided by the discount rate minus the growth rate and we get a net present value of growth opportunities of 37 euros and 50 so just look at that as the same formula. But that s 10 instead of the dividend. We re looking at the return or the amount the npv of the retained advancement. What s a value of the company without the dividend growth.
I m sorry without the growth opportunities then you ve got just the basically the dividend. There s no growth. So it means you re not retaining anything so the dividends are equal to them is proshare. The discovery is 16.
So we get the value of 62 euros. 50. And so the value of the equity is the net present value of the growth opportunities. Plus.
The value of the equity without any growth opportunities. Which gives us 100. Euros. So you might be asked in an exam show the equivalence of the dividend growth model and the net present value of growth opportunities model and you can just use this video to as a basis for showing for any situation to do with value in equities.
How both of these models are consistent. So i hope that you enjoyed that very quick video as important. There s not really a wall there suppose practical implications and yeah. This is just a theoretical thing we show the equivalence of these two models so hope you found that useful and ” .
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