Primary P/E calculation method



  Preliminary remarks on rates of return

For the 5-year projected EPS (earnings per share), we use, like most analysts and investors
do, numbers in nominal prices (= including the projected inflation).

Now we have to find the adequate rate of return that the investor would normally apply to
those earnings, taking into account the financial and monetary environment

=> We will derive it from the bonds market interest rates, from which we take

the historical rates and the current rates.

In their expectations, market traders, as well as the general public, confuse often nominal
prices and incomes and those called "real" (= inflation-adjusted). Some economists call that

"the monetary illusion".

  First step, the rate cocktail

To take into account that monetary illusion we start by mixing a "cocktail" of interest rates.

This mix dilutes somewhat the biases of each one and takes into account historical realities.

=> In a first step, we calculate thus the average of three interest rates
      of 10 years State bonds

Current gross (1) nominal (3) market rate.

for ex. 3,5%, or  0,035

1) Current gross (1) real (2) market rate.

for ex. 1,5%, or  0,015

2) Historical gross (1) real (2) market rate

3%, or  0,030

3) Historical gross (1) nominal (3) market rate

5%, or  0,060

 Total  1) + 2) +3) =  0,095     Average 0,095 / 3 = 

0,0 32

or 3,2%

(1)     = before tax  (2)    =  inflation-adjusted  (3) = non inflation-adjusted

=> Let us make it simple, the trick is to:

*     Add  0,08 (thus 8 points) to the current real rate
=> 0,015 + 0,08 = 0,095 (or 1,5 % + 8 % = 9,5 %),

*     Then divide this total (real rate + 0,08), by three => 0,032

  Second step : cocktail extract, and projected economic P/E

The above result expresses the bonds rate of return.

As stocks are not bonds, that rate must be adjusted to apply it to EPS so as to calculate
a P/E :

*     For that, we could increase it, by multiplying it:

  • By, let us say, 1,2 or 1,5, to include the structural stock market risk
    , although stocks protect better from inflation than bonds.

  • And again by 2, as we apply it to EPS and not to cash dividends.
    The EPS is not
    a direct income for shareholders. In general, only
    the half is paid in dividends (average pay-out ratio: 50 %).

*  Also, we should take into account that our formula uses gross rates, while there are tax
situation differences among investors, and between stocks and bonds.

To take this whole "sauce" into account is quite complicated. Let us abandon pure logic and
stick to facts, this is the scientific method. Let us be guided by the average pricing prices
used by markets.

Altogether, to mimic market benchmarks, we multiply by two the arithmetic average of the
rates in the cocktail (thus doubling the expected dividend return).

To divide by three - to transform the total of rates into an average rate - then multiply
by two
, to adapt the return to stocks, is :

=> to divide the total of the three rates by 1,5, thus:

Let us take the above rates addition:

Real rate + 0,08

= 0,095

The division by 1,5 gives an expected
return of:

(Real rate + 0,08) / 1,5

= 0,095 / 1,5
= 0,063

The projected "economic" P/E is the
reverse of the expected rate:

1 / (expected return)

= 1 / 0,063
= 15,9

  Third step: moving back to the present, the primary P/E

The projected economic P/E in five years, that we just calculated, is a determinant of the
 end of period  EEV in five years.

But what we want to know, is the today EEV.

For that purpose, we need the, not the projected P/E coefficient, but the coefficient to apply
today to earnings projected five years later

We call this ratio, shown in the table of the economic value page, the "primary P/E "

To calculate it, we just need to discount the projected economic P/E in 5 years seen

The discount rate we use is the current gross rate for 10 years State bonds.

Here, we don't make differences about rates of inflation, of taxes, of risk premia, if not we
would drown in complications

In our above example, if we suppose a 3,5 % nominal rate, the primary P/E applicable
on the EPS projected 5 years later is:

We start with the projected

"economic" P/E seen above:

1 / (Current  gross real rate. + 0,08)

 1 / 0,063
= 15,9

The primary P/E is this projected
P/E, but discounted

15,9 / (1,035 x 1,035 x 1,035
         x 1,035 x 1,035) 

15,9 / 1,19
= 13,4

  Just a note : choice of currency

To be consistent with this model, in this age of transnational companies and global investors, the i
nterest / inflation rates used as reference are those of the same currency in which the projections
of earnings or dividends are made

The main stock exchange where the shares are listed, give an indication of what currency the main
investors use.

  For theoreticians

The primary P/E used by this heuristic method might seem

either too low, or too high, in theory.

Is that important?

=> See the page on this theoretical debate


 This page last update: 05/06/13 
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