WACC - weighted average cost of capital or discount rate

[TheMotorcycleBoy]

Continuing from my last post, I'm starting to feel more enamoured by the CAPM approach i.e.

Cost of equity = R1 +β {E (R2) – R1}

Where,
E = Expected rate of return on asset,
β = Beta coefficient of assets (being analysed),
R1 = Risk free rate of return
E (R2) = Expected return from market portfolio.

(This value can be calculated by analyzing data of usually five years.)

Though I have heard the term E(R2) i.e. R2 being better stated as the just the average result from the market in which the stock market which the asset under analysis occupies (i.e. FTSE100/250 etc).

What put me off in the past was the silly use of a mysterious term, i.e. β = Beta. If they had *just* called this "volatility index" i.e. V which seems to be what it actually is, then the arrogant sod that I am would have considered this more seriously.

Formula used to calculate beta value is as follow:
β = PIM (SD1) (SDM)/SD2M

Where,
β = Beta of stock
PIM = Correlation coefficient between the returns on stock, I and the returns on market portfolio, M.
SD1 = Standard deviation of returns on assets
SDM = Standard deviation of returns on the market portfolio
SD2M = Variance of market returns

[TheMotorcycleBoy]

The next documented approach in the web resource I linked here

Bond Yield plus Risk Premium Approach:
The bond yield plus risk premium approach states that the cost on equity capital should be equal to the sum of returns on long-term bonds of an organization and risk premium given on equity shares. The risk premium is paid on equity shares because they carry high risk.

just seems a more common-or-garden way of expressing CAPM, in my naive opinion.

[TheMotorcycleBoy]

Looking at this document http://www.economicsdiscussion.net/capi ... pital/4415 again, i.e. the one I mentioned a week or so back in here.

The last method in the above document I found interesting was this one:

Gordon Model:
The Gordon model was proposed by Myron Gordon to calculate cost of equity capital.
As per this model, an investor always prefers less risky investment as compared to more risky investment.

Therefore, an organization should pay risk premium only on risky investment.
The Gordon model also suggests that an investor would always prefer more of those investments,
which would provide them current income.

The Gordon model is based on the following assumptions:
a. The rate of return on the investments of an organization is constant
b. The cost of equity capital is more than the growth rate
c. The corporation tax does not exist in the economy
d. The organization has perpetual existence
e. The growth rate of the organization is a part of retention ratio and its rate of return

According to the Gordon model, cost of capital can be calculated mathematically by using the following formula:
P = E (1 -b)/K – br

Where,
P = Price per share at the beginning of the year
E = Earnings per share at the end of the year
b = Fraction of retained earnings
K = Rate of return required by shareholders
r = Rate of return earned on investments made by the organization

However, then the lame quality of many online references becomes apparent, as the writer, as far as I can see, does not elaborate this model, or if he/she does it is done very obtusely. Furthermore the reader is left with an equation i.e. "P = " where the resultant looks like the price of a share, not of the cost of equity.

Am I to assume that the author, themselves assumes the reader will quickly rearrange the above with K on the left? that is:

K = E(1 -b)/P  +  br

Since "rate of return required by shareholders" is effectively the cost of equity. Presumably r is RoA or RoCE or some such......

I may give this a whirl on some of the companies I currently have under the microscope...

Matt

[TheMotorcycleBoy]

According to the Gordon model, cost of capital can be calculated mathematically by using the following formula:
P = E (1 -b)/K – br

Where,
P = Price per share at the beginning of the year
E = Earnings per share at the end of the year
b = Fraction of retained earnings
K = Rate of return required by shareholders
r = Rate of return earned on investments made by the organization[/pre]
However, then the lame quality of many online references becomes apparent, as the writer, as far as I can see, does not elaborate this model, or if he/she does it is done very obtusely. Furthermore the reader is left with an equation i.e. "P = " where the resultant looks like the price of a share, not of the cost of equity.

Am I to assume that the author, themselves assumes the reader will quickly rearrange the above with K on the left? that is:

K = E(1 -b)/P  +  br

Since "rate of return required by shareholders" is effectively the cost of equity. Presumably r is RoA or RoCE or some such......

I may give this a whirl on some of the companies I currently have under the microscope...

Matt

I'm now wondering a) if I rearranged the above:

P = E (1 -b)/K – br [1]

correctly? Or whether the author indeed wrote the formula correctly in the first place? That is, perhaps the author intended this:

P = E(1 - b)/(K - br) [2]

Recollection of "dimensional analysis" from my degree days, would actually imply [2] is correct, hence I rearrange it correctly - since (1 - b) and (K - br) and strictly rates, where as only P and E represent a financial currency.

Anyway I'm going to play with my rearranged formula with MSLH's 2017-2018 numbers and see what happens.

[dspp]

MB,

With respect to your underlying investigation of DCF as a tool you might want to read the pithy comment re DCF in this

https://www.starcapital.de/en/research/ ... in-charts/

(with thanks to monabri from viewtopic.php?f=55&t=14660)

(CAPE etc may also be of interest to you)

dspp

[TheMotorcycleBoy]

MB,

With respect to your underlying investigation of DCF as a tool you might want to read the pithy comment re DCF in this

https://www.starcapital.de/en/research/ ... in-charts/

(with thanks to monabri from viewtopic.php?f=55&t=14660)

(CAPE etc may also be of interest to you)

dspp

Thanks,

I had a quick skim over this. I'd like to spend more time reading up on CAPE.

Regards DCF, this is very error-prone, not only due to the setting of the discount rate, but because cash flow growth obviously can't be predicted. Best is probably to model most of the company's time on this planet at a guessimate of just following inflation (e.g. about 2.5%).

So I've been spending more time using EPV as a tool to be honest.

But since I now have spread sheets for both techniques it's fairly straight forward to run several models of both DCF and EPV at various discount and growth rates. Then compare and contrast all results and aim for "margin of safety".

What's more depressing is when I've valued stocks we bought impetuously earlier on, and discovered that maybe we should have been more cautious. But anyway, we have to learn some how, and we are in it for the long term.....

thanks
Matt

[TheMotorcycleBoy]

According to the Gordon model, cost of capital can be calculated mathematically by using the following formula:
P = E (1 -b)/K – br

Where,
P = Price per share at the beginning of the year
E = Earnings per share at the end of the year
b = Fraction of retained earnings
K = Rate of return required by shareholders
r = Rate of return earned on investments made by the organization[/pre]
However, then the lame quality of many online references becomes apparent, as the writer, as far as I can see, does not elaborate this model, or if he/she does it is done very obtusely. Furthermore the reader is left with an equation i.e. "P = " where the resultant looks like the price of a share, not of the cost of equity.

Am I to assume that the author, themselves assumes the reader will quickly rearrange the above with K on the left? that is:

K = E(1 -b)/P  +  br

Since "rate of return required by shareholders" is effectively the cost of equity. Presumably r is RoA or RoCE or some such......

I may give this a whirl on some of the companies I currently have under the microscope...

Matt

I'm now wondering a) if I rearranged the above:

P = E (1 -b)/K – br [1]

correctly? Or whether the author indeed wrote the formula correctly in the first place? That is, perhaps the author intended this:

P = E(1 - b)/(K - br) [2]

Being the obsessive sod that I am, I spent the last couple of minutes, while waiting for a test to complete, studying these formulae again.

The website I had read, I now believe, was probably correct in stating this: P = E (1 -b)/K – br as contrasted to this P = E(1 - b)/(K - br). Since if we rearrange this latter equation, solving for k (return required by shareholders, i.e. the WACC), we get a formula which would imply that the higher the company's internal rate of return (it's ROCE) than higher it's WACC - which would be ridiculous. However rearranging [1] gives us:

k = E(1 - b)/(P + br)

Hmm....

I'm still dubious of the worthiness of this as a formula, and as you all no doubt are too, the point behind calculation of WACC. But value is of course important, who wants to buy something without even a vague idea of it's worth?

[TheMotorcycleBoy]

In this clip that I've just watched (lots of tests to run this morn)

https://www.youtube.com/watch?v=-ELXrTZ_Pc0

we can see the classic Gordon DDM being used to calculate the WACC.

Comparing this with the formula I lifted from here i.e. P = E (1 -b)/K – br , it looks like the differences in the approaches are mainly the one model uses dividend and the other uses earnings * (1 - equity retention rate) - clearly interrelated concepts.

[TheMotorcycleBoy]

Just found a few more links about the cost of equity:

https://www.valuewalk.com/2014/09/calcu ... of-equity/

and also a link to a (possibly?) free Ebook

https://onlinelibrary.wiley.com/doi/pdf ... 679X.00007

(you do need to register first however)

Matt