Dividend Growth and Capital Asset Pricing Model

Rrellij7914y ago

Hello John

I have a couple of questions on examples about the dividend growth model and capital asset pricing model from the bpp 2012 study text.

The first question is if the dividends in 20X1 were $150,000 and $262,350 in year 20X5 representing 4 years growth, what is the average growth rate?

$262,350/$150,000 = 1.749

1+g = 4(square root 1.749) = 1.15

I am not able to get 1.15 on my calculator which is scientific, I am obviously doing something wrong. Is the number of years 4 squared * square root of 1.749?

My second question on the CAPM is solving the Rf side of the equation:

Investors have an expected rate of return of 8% from ORDs in Algol, which have a beta of 1.2. The expected returns to the market are 7%

What will be the expected rate of return from ORDs in Rigel, which have a beta of 1.8.?

Algol: E(ri) = Rf+b(E(Rm)-Rf)

8=Rf+1.2(7-Rf)
8=Rf+8.4-1.2 Rf
0.2 Rf = 0.4
Rf=2

Rigel: E(ri) = 2+(7-2)1.8
=11%

Could you please explain to me how the beta of 2 was calculate? I know this is something I have to go back and brush up on as it is a long time since I done equations using algebra.

Thank you.

John

John MoffatTutor14y ago#1

The easiest way of getting the 4th root (on any calculator) is to simply take the square root twice :)
If you enter 1.749 and then square root twice, you will get 1.15.

For the second one, I don't know whether you have made a typing error in your last paragraph, or what - however the beta is not 2, it is Rf that is 2.

You have typed the workings for Algol, which is where Rf is calculated as 2.
I assume you are happy with the first line - just putting the numbers we know into the equation.
In the second line, they have multiplied each item in the brackets by 1.2 (so 1.2 x 7 = 8.4, and 1.2 x Rf = 1.2Rf
In the third line, the have rearrange, but subtracting 8 from both sides (so on the right side 8.4 - 8 = 0.4), and by subtracting Rf and adding 1.2Rf to both sides (so on the left side is 1.2Rf - Rf which equals 0.2 Rf
In the fourth line, they have divided both sides by 0.2, which gives Rf = 2.

Rrellij7914y ago#2

Yes you are right I did make a typo with the beta.

Thank you very much for your reply and help it has cleared that up for me :)

John MoffatTutor14y ago#3

I am glad it has cleared it up :)

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