COMMON STOCKS â€“ RATE OF RETURN AND EPS PRICING MODEL:Earnings per Share (EPS) Pricing Model

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Financial Management MGT201

Lesson 18

COMMON STOCKS RATE OF RETURN AND EPS PRICING MODEL

Learning Objectives:

After going through this lecture, you would be able to have an understanding of the following topics

· Common Stocks Rate of Return

· EPS Pricing Model

In this lecture, we will continue our discussion on share price valuation and we discuss the common

stock valuation in case of long term or perpetual investment.

First, we review what we have studied in the previous lecture. We have discussed 2 approaches of

perpetual common stock valuation.

1. Zero growth :

In this we assume zero growth in dividends and our formula is

Po*=DIV1 / rCE (Po* is being estimated).

2. Constant growth rate:

In this we assume that dividend is growing at constant growth rate (inflationary rate).we

can also use accounting data to calculate `g'.

g= plowback ratio x ROE.

In this particular case of constant growth model the formula for estimation of fair price is

Po*= DI V1/ (rCE -g)

Now, we have studied about estimating the fair price of the common shares under a very long

term investment but it is equally important to know the Required rate of Return (ROR).

In capital budgeting criterion, we have mentioned that we have to look both NPV as well as IRR.NPV is

the price or value of the asset or security and IRR is the measure of the rate of return of a particular asset

or project. So, we have to compute both NPV and IRR. Similarly, for the case of direct claim securities

like share we can use the same equation and we can rearrange them for the required rate of return which

is equal to rCE

The Estimated Required Rate of Return for Investment in Common Equity (rCE) can be

calculated by re-arranging the same equation:

Dividends Pricing Models:

Zero Growth:

Po*=DIV1 / rCE (Po* is being estimated)

rCE*= DIV1 / Po (rCE* is being estimated)

Similarly,

Constant Growth: Po*= DI V1/ (rCE -g)

rCE*= ( DIV 1 / Po) +

Div Yield

Cap.Gain Yield

This particular formula the way it is mentioned above is known as Gordon's formula and we

use this formula to calculate the required rate of return.

Gordon's Formula: Estimated Fair Present Price (or Present Value) of Share calculated using

Forecasted Future Cash Flows of Dividend Payouts to Shareholders and their growth

rCE*= (DIV 1 / Po) + g

In this the first part

(DIV 1 / Po) is the dividend yield

g is the Capital gain yield.

The reason we use these terms is that basically (DIV 1 / Po) is the fraction of the present price

which represents by the dividends.

g the capital gain yields is simply the lumped measure of expected increase in dividend that you expect

in the dividend over the life of the asset.

Now, if you see the formulas of stock valuation that we have discussed up till now. These

formulas have used forecasted dividends and that is why we called these formula dividend yield

approach to find the price. We have use dividends as a direct measure of cash flows that a stock holder

receives from the security.

We mentioned that we will calculate value of an asset or security based on cash flows it will

generates in the future. Any working asset can be valued based on its future cash flows.

So we began valuing shares based on dividend income that a share holder's receives. There is

another approach for valuing shares.

Financial Management MGT201

Earnings per Share (EPS) Pricing Model:

In this our perspective is not the direct cash flows generated by the shares rather we value the

shares based on cash flows that are generated by the company whose share we are taking. In other

words, Estimated Fair Present Price of Share calculated based on Forecasted Future Cash Flows of

Company's Earnings and growth from Ploughed Back Reinvestments (from Retained Earnings). We can

do that because it is mentioned earlier that for direct claim securities like bond and stocks the value of

security can be calculated from the cash flows of underlying assets. For share the underlying assets are

the assets of the company and the cash flows generated by the assets of the company.

COMMON STOCK PRICING APPROACHES

DIVIDEND PRICING

E.P.S PRICING

Stock (Paper, Direct Claim

Real Assets & Future

Security) issued by Company

Investments in Projects of

ABC

Company ABC

Forecasted Earnings & Sales

Forecasted Dividends

Revenue (Cash Flows generated by

(Cash Flows generated by

real business operations)

Stocks)

Present Value of Company

Present Value of a Stock

ABC (with certain number of

of Company ABC

Common Shares Outstanding)

That is the logic behind the EPS approach. Now, let's see the EPS approach to calculate the price of the

share.

EPS Approach:

In EPS approach, we estimate the price of common stock under very long term investment.

EPS Stock Price Estimation Formula

PV = Po* = EPS 1 / rCE + PVGO

= Estimated Present Fair Price,

EPS 1 = Forecasted Earnings per Share in the next year (i.e. Year 1),

rCE = Required Rate of Return on Investment in Common Stock Equity.

PVGO = Present Value of Growth Opportunities. It means the Present Value of Potential

Growth in Business from Reinvestments in New Positive NPV Projects and Investments. PVGO is

perpetuity formula.

The formula is

PVGO = NPV 1 / (rCE - g) = [-Io + (C/rCE)] / (rCE -g)

In this PVGO Model: Constant Growth "g". It is the growth in NPV of new Reinvestment Projects (or

Investment).g= plowback x ROE

Perpetual Net Cash Flows (C) from each Project (or reinvestment).

Io = Value of Reinvestment (Not paid to share holders)

= Pb x EPS

Where Pb= Plough back = 1 Payout ratio

Payout ration = (DIV/EPS) and

EPS Earnings per Share= (NI - DIV) / # Shares of Common Stock Outstanding

Where NI = Net Income from P/L Statement and DIV = Dividend, RE1= REo+ NI1+ DIV1

ROE = Net income /# Shares of Common Stock Outstanding.

Now when we look at the detailed method of calculating the NPV you will see that

Financial Management MGT201

NPV 1 = [-Io + (C/rCE)] / (rCE -g)

If we compare it with the traditional NPV formula

-Io = Value of initial investment

(C/rCE) = present value formula for perpetuities where you assume that you are generating the net cash

inflow of C every year.

C = Forecasted Net Cash Inflow from Reinvestment = Io x ROE

Where ROE = Return on Equity = NI / Book Equity of Common Stock Outstanding

In the EPS approach, in calculating the fair price of the common stock our conceptual logic was

we calculate the value of the piece of paper based upon the cash flows the real company generated. We

do this because the value of direct claim securities can be calculated form the underlying assets.

In EPS approach, we talk abut the company and the cash flows that the company generates but in the

case of dividends approach , we are talking about the cash flows directly generated from the piece of

paper(i.e. dividends).

The PVGO in EPS approach formula is different from `g'.

`g' it is the growth rate in dividends

PVGO is potential growth in the value of the business from the future investments in new projects. The

basic model we used to estimate this present value of the company which is coming from investment in

the future projects with +ve NPV is that we assume that the company saves their part of the net income

in the form of retained earning every year. So, in this particular model we are assuming that these

retained earning is invested in projects that will yield +ve NPV each year and the cash flows are

constant. It also assumes that NPV from investment that a company makes in new projects grows at

constant growth rate `g' perpetually.

Example:

The Common Stock of Company ABC is trading in the Islamabad Stock Exchange at a market

price of Rs 105. You are considering investing in it so you study the company's Annual Report,

Financial Statements, and make some forecasts. The Data is as follows:

Forecasted Dividend Next Year = Rs 10

Expected Dividend Growth = 10% pa

Forecasted Earnings per Share = Rs 12

Your Required Return on Investment in ABC Common Stock = 20% pa.

Compute the Estimated Present Fair Price of Company ABC's Common Stock.

Dividend Pricing (Gordon's) Approach:

PV = Po* = DIV1 / (rCE - g)

= 10 / (20%-10%) = 10/0.10

= Rs 100 (Estimated Fair Price is less than Market Price of Rs 110 so share is

overvalued in the Market)

Earnings Per Share (EPS) Pricing Model

PV = Po* = EPS 1/ rCE + PVGO

EPS 1 / rCE = 12 / 0.20 = Rs 60

PVGO = NPV1 / (rCE -g) = [-Io+(c/ rCE)] / (rCE -g)

= [-(PbxEPS) + (IoxROE/ rCE)] / (rCE -g)

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

= [-2 + 6] / 0.10 = Rs 40

Pb = 1 - Payout = 1 - DIV / EPS = 1 - 10/12 = 1/6

g = Pb x ROE = 10% = 1/10 So ROE = 6/10

PV = Rs 60 + Rs 40 = Rs 100 (Same as Dividend Approach).

EPS Approach shows that 40% (i.e. Rs 40 out of Rs 100) of the Value is Growth Based (i.e. PVGO)

Growth Stock:

It is growth share where the value of the share is determined by the potential of this company to

grow its business as oppose to company which have low growth rate.

Particularly, for IT internet companies where we expect a high rate of growth for he business the PVGO

term is large percent of the price of the share.

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