1. Securities Analysis
Company Analysis

2. Constant Growth DDM
D1
V0 =
k−g
 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

3. 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
D1
V0 =
k−g

4. 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
D1 3.81(1 + 0.05) 4.00
P0 = = = = 57.14
k−g 0.12 − 0.05 0.12 − 0.05

5. 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
D2 4.00(1 + 0.05) 4.20
P=
1 = = = 60.00
k−g 0.12 − 0.05 0.12 − 0.05
60.00 − 57.14
= 5%
57.14

6. Generalize
D2 D1 (1 + g ) D1
P1 = = = (1 + g ) = P0 (1 + g )
k−g k−g k−g
 In the case of constant growth, the rate of price
appreciation in any year will be equal to the constant
growth rate

7. Constant Growth HPR
 For a stock whose price = intrinsic value, the
expected HPR is
D1 P1 − P0 D1
E (r ) = DividendYield + CapitalGainsYield = + = +g
P0 P0 P0
 The market capitalization rate can be
calculated from this equation
 If the stock is selling at intrinsic value then
E(r)=k, so D1
k= + g = DividendYield + g
P0

8. 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
D1 3.81(1 + 0.06 ) 4.04
P0 = = = = 67.31
k−g 0.12 − 0.06 0.12 − 0.06
 But the expected return E(r) stays at 12%
D1 4.04
E (r ) = +g= + 0.06 = 12%
P0 67.31
 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

9. 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

10. 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

11. 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
D1 4.00
E (r ) = +g= + 0.04 = 12.00%
V0 50.00
D1 4.00
E (r ) = +g= + 0.04 = 12.33%
P0 48.00

12. Convergence of Price and
Value – Assumption 2
 If the gap disappears by end of the year
 In this case P1=V1=Rs.52
D1 P1 − P0 4 52 − 48
E (r ) = + = + = 16.67%
P0 P0 48 48
 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%

13. 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

14. 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%

15. Prices and Investment
Opportunities
 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

16. 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
Re investedEarnings Re investedEarnings TotalEarnings
g= = × = b × ROE
BV TotalEarnings BV

17. Prices and Investment Opportunities
 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
D1 E1 5
NoGrowthValue = = = = 40
k − g k 0.125

18. 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

19. Prices and Investment Opportunities
 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

20. 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

21. 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
E1 P0 1  PVGO 
P0 = + PVGO = 1 + 
k E1 k 
 E1 / k 


22. If PVGO = 0
 Inthis case P0=E1/k and the stock is valued as
a non-growing perpetuity of E1
 The PE ratio will be 1/k
P0 1  PVGO 
= 1 +
 
E1 k  E1 / k 


23. 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
P0 1  PVGO 
= 1 +
 
E1 k  E1 / k 


24. Alternative PE formula
D1 E1 (1 − b )
P0 = =
k − g k − ( ROE × b )
P0 1− b
=
E1 k − ( ROE × b )
 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

25. PE Behavior
P0 1− b
=
E1 k − ( ROE × b )
 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

26. 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

27. 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
P0 1 − b
=
E1 k − g

28. 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

29. 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

30. 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

31. The End