**Earnings per Share (EPS) Pricing Model** is useful method of calculating value of **Common Stock** on the basis of the cash flows generated by the company whose shares are under consideration. In other models the main concept is to ascertain the value of share on the basis of the cash flows associated with it. But in Earnings per Share (EPS) Pricing Model the concept is quite different in which the estimated fair present price of share is calculated from the anticipated future cash flows of the earnings of the company & from growth of its ploughed back reinvestment (retained earnings). The reason behind this new concept is that it is clear that the value of share (direct claim security) is associated with some underlying real asset. In case of share the assets of the company & the cash flows generated by it are regarded as underlying real assets.

**Earnings Per Share Formula & Approach**

The price of common stock with infinite investment is estimated. For this purpose, following formula is used

PV = P_{o}* = EPS_{1} / r_{CE} + PVGO

Where PV or P_{o}* = Estimated present fair price

r_{CE} = The expected or required rate of return for investing in common stock

EPS1 = the anticipated earnings per share in the next year (Year 1)

PVGO = Present Value of Growth Opportunities. It means that when company invests in projects with positive NPVs there is higher return which is reinvested to enhance the growth of business and the present value of that business growth through following reinvestments from returns of positive NPV projects is referred to as PVGO.

Additionally the formula for PVGO is as under

PVGO = NPV_{1} / (r_{CE} – g) = [-I_{o}+(C / r_{CE})] / (r_{CE} – g)

In PVGO “g” is the constant growth in NPV of new reinvestment projects.

Where g = plowback x ROE

C = perpetual net cash flows from every investment (project)

I_{o} = Value of reinvestment (which is not paid to shareholders)

I_{o} = Pb x EPS

Where Pb = plough back = 1-payout ratio

And payout ratio = DIV / EPS

Earnings per Share (EPS) = (NI-DIV) / No. of outstanding share of common stock

Where NI = Net Income from Profit & Loss Statement

And DIV = Dividend

RE_{1} = RE_{o} + NI_{1} + DIV_{1}

ROE = Net Income / No. of outstanding shares of common stock

Now NPV can also be calculated as follow

NPV_{1} = [-I_{o} + (C / r_{CE})] / (r_{CE} – g)

-I_{o} = value of initial investment

(C / r_{CE}) = perpetuities present value formula where it is assumed that net cash inflow of C is generated every year

C = Anticipated net cash inflow from reinvestment = I_{o} x ROE

And ROE = return on equity = NI / Book equity of outstanding common stocks

In the calculating of the fair rice in EPS, the main idea is to ascertain value of piece of paper on the basis of the cash flows generated by the underlying real assets.

The PVGO in EPS formula is changed from “g” of dividend models, where g = growth rate in dividends

On the other hand PVGO is the value of the company from the future investments in new projects. In fact the estimated present value of the company is calculated on the basis of the emerging investments in future projects that contain positive NPVs. It is assumed that the company saves the portion of its income as retained earnings and which will further reinvested in new projects that contain positive NPV every year. In this way there are constant cash flows and the NPV of every new investment made by the company increases at constant arte “g” in a perpetual manner.

**Earnings Per Share Analysis with Example**

At **Newyork Stock Exchange** the stocks of Company XYZ are being traded at a market price of $ 105. An investor making decision for investment studies the annual reports & **financial statements** of the company & forecasted the following data.

Anticipated dividend for next year = $ 10

Forecasted earnings per share = $ 12

Expected dividend growth = 10% p.a.

The required rate of return on investment = 20% p.a.

For calculation of estimated present fair price of common stock of Company XYZ, Following formula is used

PV = P_{o}* = EPS_{1} / r_{CE} + PVGO

EPS_{1} / r_{CE} = 12 / 0.20 = $ 60

PVGO = NPV_{1} / (r_{CE} – g) = [-I_{o}+(C / r_{CE})] / (r_{CE} – g)

= [-(Pb x EPS) + (I_{o} x ROE / r_{CE})] / (r_{CE} – g)

= [ -(1/6 x 12) + (2 x 6/10 / 0.20)] / (0.20 – 0.10)

= [-2 +6] / 0.10

PVGO = $ 40

Pb = 1-payout = 1 – DIV / EPS

Pb = 1 – 10 / 12

Pb = 1/6

g = Pb x ROE (Where g = 10%)

and ROE = g / Pb = (1/10) / (1/6)

ROE = 6/10

So PV = $ 60+ $ 40 = $ 100. It is cleared from EPS that 40% value of total ($ 100) is growth based (PVGO).

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