company analysis/valuation

Securities Analysis

Company Analysis

Constant Growth DDM

Valid only when g < k If dividends are expected to grow forever at a rate equal to or

faster than k, value will be undefined If the derived estimate of g is greater than k, then g must be

unsustainable in the long run In this case a multistage DDM must be used

gk

DV

1

0

Implications of Constant Growth DDM

Value will be greater Larger the expected dividend per share Lower the market capitalization rate, k Higher the expected growth rate of dividends Stock price is expected to grow at the same rate as dividends

gk

DV

1

0

Price Growth = Dividend Growth

According to the formula price is proportional to dividends

Say D0=3.81, k=12% and g = 5% If the stock is trading at intrinsic value its price can

be calculated as

14.57

05.012.0

00.4

05.012.0

05.0181.310

gk

DP

Price Growth = Dividend Growth

Since price is proportional to dividends, price must increase at the same rate as dividends

The price next year can be calculated as

00.60

05.012.0

20.4

05.012.0

05.0100.421

gk

DP

%514.57

14.5700.60

Generalize

In the case of constant growth, the rate of price appreciation in any year will be equal to the constant growth rate

gPggk

D

gk

gD

gk

DP

111

0112

1

Constant Growth HPR

For a stock whose price = intrinsic value, the expected HPR is

The market capitalization rate can be calculated from this equation

If the stock is selling at intrinsic value then E(r)=k, so

gP

D

P

PP

P

DnsYieldCapitalGaieldDividendYirE

0

1

0

01

0

1)(

geldDividendYigP

Dk

0

1

Constant Growth Model Say the company gets a major contract which enables it to

increase dividend growth to 6% The new price of the stock will be

But the expected return E(r) stays at 12%

Once the news is reflected in the price, the expected return will be consistent with the risk of the stock

Since the risk remains unchanged, the expected return should not change

31.67

06.012.0

04.4

06.012.0

06.0181.310

gk

DP

%1206.031.67

04.4)(

0

1 gP

DrE

Convergence of Price and Value

Suppose for ABC stock CMP P0 = Rs.48 Intrinsic Value V0= Rs.50 Growth = 4%

Then Undervaluation = Rs.2 The expected rate of price appreciation

depends on Whether the discrepancy will disappear And, if so, when

Convergence of Price and Value – Assumption 1

One common assumption is that the discrepancy will never disappear

So price will continue to grow at g forever This means that the discrepancy between intrinsic

value and price will grow at the same rate

Now Next Year

V0 = Rs.50 V1 = Rs.50 x 1.04 = Rs.52.00

P0 = Rs.48 P1 = Rs.48 x 1.04 = Rs.49.92

V0-P0 = Rs.2 V1-P1 = Rs.2 x 1.04 = Rs.2.08

Convergence of Price and Value – Assumption 1 Under this assumption expected HPR will exceed the required rate This is because dividend yield is higher than it would be if price =

value The excess return is earned each year and the price never catches

up with value The investor gets a dividend that exceeds the required return by 33

bps

%33.1204.000.48

00.4)(

0

1 gP

DrE

%00.1204.000.50

00.4)(

0

1 gV

DrE

Convergence of Price and Value – Assumption 2

If the gap disappears by end of the year In this case P1=V1=Rs.52

Complete catch up produces a much larger HPR Most analysts assume that price will approach value

over several years So, expected 1 year HPR lies somewhere between

12.33% and 16.67%

%67.1648

4852

48

4)(

0

01

0

1

P

PP

P

DrE

Prices and Investment Opportunities Consider two companies A and G Each has expected EPS of Rs.5 Both could payout all of these earnings as dividends

maintaining a perpetual dividend flow of Rs.5 per share

If the market capitalization rate is 12.5% both companies will be valued at D1/k = 5/0.125 = Rs.40

Neither will grow in value since all earnings are paid out and there is no reinvestment

Earnings and dividends will not grow Here earnings are considered to be net of funds

required to maintain productive capacity

Prices and Investment Opportunities

Suppose G engages in projects that generate an ROI of 15% which is greater than k=12.5%

It would be wise for G to plowback some of its earnings

Otherwise its shareholders would have to invest dividends in other opportunities at the fair market rate of only 12.5%

Say G decreases payout ratio to 40% and increases retention ratio to 60%


The dividend will now be Rs.2 (40% of Rs.5) instead of Rs.5 Should the price fall because of the decrease in dividend? Although dividends may initially fall, subsequent growth in assets

will generate future dividend growth The price will rise The growth rate in dividends will be g = ROE x b = 0.15*0.60 =

0.09 If the stock price is equal to intrinsic value, it should sell at

P0 = D1/(k-g) = 2/(0.125-0.09) = Rs.57.14

If the company had followed a no growth policy by paying out all earnings its price would have been P0 = D1/(k-g) = 5/(0.125-0) = Rs.40.00

General Formula for Growth

The growth rate in dividends is g = ROE x b If ROE is fixed, earnings which is equal to ROE x BV, will

grow at the same rate as BV The growth rate of BV is Reinvested Earnings/BV So

ROEbBV

ngsTotalEarni

ngsTotalEarni

rningsinvestedEa

BV

rningsinvestedEag

ReRe


The price increase shows that planned investments provide an expected return greater than the required rate

The investment opportunities have positive NPV and firm value rises by this amount

This NPV is called the Present Value of Growth Opportunities (PVGO)

Price = No Growth Value + PVGO P0 = E1/k + PVGO 57.14 = 40 +17.14 The No Growth Value is the value when g=0 in which case

D1=E1 and

40125.0

511

k

E

gk

DlueNoGrowthVa

ROE must be greater than k

Say the ROE = 12.5% = k Suppose the company fixed b = 0.60 then g = ROE x b =

0.125x0.60=0.075 Stock price stays at P = D1/(k-g) = 2/(0.125-0.075) = Rs.40

Here PVGO = P0 – E1/k=40-40=0 The NPV of investment opportunities is zero Growth enhances company value only if ROE > k


Growth is not the same as growth opportunities This is why firms with good cash flow but limited

investment prospects are called Cash Cows If such firms try to increase retention ratio, they will

become takeover targets New management can buy shares at the current

price, and increase firm value by simply changing investment policy

Life cycles and Multi Stage Growth Models

The constant growth model is based on the simplifying assumption that dividend growth will be constant forever

Practically, the firms pass though life cycles with different dividend profiles

In early years, there are growth opportunities and reinvestment is high and payout is low

In later years, attractive investment opportunities are difficult to find and payout ratios rise

The dividend increases, but later dividend grows at a slower rate because of few growth opportunities

Price Earnings Ratio

Consider the case of C and G again G reinvests 60% of EPS at an ROE of 15% whereas

C pays out all EPS as dividend C has a PE of 40/5=8.0 but G has a PE of

57.14/5=11.4 Therefore PE ratio serves as an indicator of growth

opportunities

PVGOk

EP 1

0

kE

PVGO

kE

P

/1

1

11

0

If PVGO = 0

In this case P0=E1/k and the stock is valued as a non-growing perpetuity of E1

The PE ratio will be 1/k

kE

PVGO

kE

P

/1

1

11

0

PVGO > 0 As PVGO becomes an increasingly dominant contributor to price,

the PE ratio rises The ratio of PVGO to E/k is interpreted as the ratio of PVGO to

the no growth value of the firm When future growth opportunities dominate value, the PE rises PE ratio differentials indicate growth opportunities If the analyst is more optimistic than the market about these

growth opportunities he will recommend a buy

kE

PVGO

kE

P

/1

1

11

0

Alternative PE formula

PE ratio increases with ROE since high ROE opportunities give the firm good growth opportunities

PE ratio increases for higher plowback as long as ROE > k since value rises if the firm plows back more when there are good growth opportunities

bROEk

bE

gk

DP

111

0

bROEk

b

E

P

1

1

0

PE Behavior

Higher the plowback, higher the growth, but Higher plowback does not necessarily mean a higher PE Higher plowback increases PE only if investments offer an

expected return higher than market capitalization rate Otherwise, higher plowback hurts investors since that means

that more money is sunk into projects with inadequate return

bROEk

b

E

P

1

1

0

PEG Ratio

PE ratios are commonly taken as proxies for expected growth

A rule of thumb is that growth rate should be roughly equal to PE ratio

The PEG = PE/g should be approximately 1.0 Therefore if

PEG < 1.0 underpriced PEG = 1.0 fairly priced PEG > 1.0 overpriced

PE and stock risk

Ceterus paribus riskier stocks will have lower PE This is because riskier stocks will have higher k However, many small startup firms have high PE

because of growth expectations This is why the ceterus paribus clause is important

gk

b

E

P

1

1

0

Pitfalls in PE The denominator is accounting earnings which are influenced by

accounting rules on depreciation and inventory When there is high inflation historic cost depreciation and

inventory will tend to overstate earnings Generally PE ratios are lower in periods of high inflation because

of low earnings quality Also earnings management will impact the PE ratio The concept of DDM is based on economic earnings and not

accounting earnings Economic earnings is the maximum flow of income that cold be

paid out without depleting productive capacity Lastly, constant models assume that earnings grow along a

smooth trend line but actual earnings are volatile over the business cycle

Pitfalls of PE

PE ratios reported in the press are the ratio of price to past earnings whereas the concept of PE is the ratio of price to future earnings

PE can be high even if current earnings are depressed if the market expects that long term earnings are unaffected

Therefore there is no way of saying whether PE ratio is currently high or low without considering long term earnings prospects

Other uses of PE

PE ratios can be used to forecast prices at a horizon date

The procedure involves forecasting EPS at horizon date and then multiplying the EPS by the estimated PE

This value can be substituted into the last term of a DDM model for finding the value of the stock

The End

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