Download assumptions of gordon model

FINANCIAL MANAGEMENT (PART – 16)
DIVIDEND POLICY-II
1. INTRODUCTION
Dear Students,
Welcome to the lecture series on Financial Management. Today in this
lecture we shall cover the topic Dividend Policy. Under dividend policy,
we shall learn about various dividend decisions which affect the value of
the firm. So our topic of discussion today is dividend decisions and the
value of firm. Under dividend decisions there are two schools of thought
which suggest that whether the dividend policy affect the market price of
shares or not. So there are certain scholars who are of the view that the
dividend policy does affect the market price of the shares and there are
other set of people who suggest that it is not at all relevant to determine
the market value of share.
So we have already discussed one of the models in our previous lectures.
Let us recap them. There are two thoughts of school one suggest relevant
theory and other suggest irrelevant theory. By relevant theory we mean
market price is affected and by irrelevant theory we mean that market
price of shares is not affected by the payment of dividend. The relevant
theory is given by Walter and Gordon while irrelevant theory is suggested
by Modigliani Miller model.
So we have already discussed the Walter’s theory in our previous lecture.
Today we will concentrate on Gordon Model of dividend decision and
other one is Modigliani Miler Approach. So MM Model and Gordon model
we have to learn in detail
2. THEORIES OF RELEVANCE – GORDON MODEL
Myron Gordon has suggests that dividend policy affects the market value
of the share. That is the valuation gets affected as the dividend payment
is increased or decrease so payout ratio and retention ratio plays a vital
role to analyze or to evaluate the market price of the shares. Let us see
what the Gordon model suggest?
Now students we will learn in detail what the Gordon model suggest?
Gordon Model suggests that investors are risk averse and they put their
preference more on current dividend rather than capital gains so there is
a direct relationship between dividend policy and market price of the
share.
He has built his assumptions on the premises that the future dividends or
the capital gains are risky and uncertain proposition that is why there is
the nexus between current dividend and market price of the share.
Hence dividend policy has become relevant. He has based this model on
the assumption that the bird in the hand argument is more appropriate as
the current dividends are given preference under Gordon Model. Now
what happens that dividends are more predictable than capital gains
because the company cannot dictate the market price of the share but
they can control the dividend the payout ratio and retention ratio can be
controlled by the management? These are the basis guidelines on which
the Gordon Model is based.
ASSUMPTIONS OF GORDON MODEL
The assumptions are almost same as that of the Walter Model. So let us
analysis what are the assumptions of Walter Model?
1. The firm only uses retained earnings for financing its investments. It is
all equity based firm and there are no debts and debenture.
2. In the firm r and k remain unchanged.
3. The firm has perpetual life. It is going assumption will be on long-term
basis.
4. There are no corporate taxes
5. The retention ratio is constant after once firm decided it.
There are certain additional assumptions in Gordon Model besides those
we have already learnt and we have taken those assumptions from
Walter’s model. Both the model share some common assumptions but
there are certain additional assumptions which we need to keep in mind
when we learn the Gordon model.
1. G is the growth rate and it is the product of b and r. Where b denotes
retention ratio and r denotes rate of return on investment. So our growth
rate will be the product of retention rate and return on investment.
2. Besides being constant Ke is greater than g that means the cost of
capital is greater than the growth. (ke>G). Where this assumption fails,
the Gordon Model’s calculation fails. The implication is that where g is
greater than ke we cannot work on the Gordon Model.
So these are the assumptions which we need to keep in mind while
considering the Gordon model to evaluate the market price of the share
where there is relevance in the dividend policy as well as the market
price of the share.
3. GORDON MODEL – FORMULA AND ANALYSIS
Now we will learn the formula for Gordon Model
P=
𝐸(1−𝑏)
𝐾𝑒−𝑏𝑟
or
𝐷1
𝐾𝑒−𝑔
where
P= Price of the share in the market
E= Earnings per share
b= retention ratio/ 1- payout ratio
1-b= Percentage of earnings distributed as dividends
R= rate of return
Ke= cost of capital
br= Growth rate
These both the formula will give us same result. The presentation of
formula is different.
4. ANALYSIS OF GORDON MODEL WHERE r>Ke
Now we will learn the Gordon model’s calculation with the help of an
example where we will analyze the data of three companies known as
Growth limited, normal limited and Declining Limited. First of all we have
to analyze the situation of growing company. Growing company is a
company where rate of return is greater than cost of capital?
The only difference among these three companies is that of r that is rate
of return so we will analyze the situation at different payout that is at
40%, 60% and 90% that how the change in the payouts will result in the
change in the market price of the shares. The earnings and cost of capital
will remain same for all the cases. The earnings will be Rs.10/- per share
and the cost of capital (ke) will be 10% which is denoted by .10 and we
will calculate g as g= b*r. b will be calculated as 1-payout.
In the first case we have the payout as 40% so b will come as 60% because
1- payout will give us the retention ratio as 60%
In the second case the payout is 60% so b will be 40%
And in the last case the payout is 90% so b will be 10%
So 60%, 40% and 10% will be the retention ratios meaning thereby if we
have Rs.10 with us in the first case we are retaining Rs.6 and paying Rs 4
as dividend. In the second case out of Rs.10 we are paying Rs. 6 and
retaining Rs.4 and in the last case we are paying dividend as high as 90%
that is we are paying Rs.9 as dividend out of Rs.10 and retaining only
Rs.1.Payout and retention ratio shall be equal to 100%
What is the implication of this payout, retention in the case of Growth,
normal and declining limiting? In Growth limited r will be greater than ke
so we will assume r to be 15% that is 0.15. r is greater than ke so it is
growing firm.
Then we will calculate the g for each type of payout which is being
computed in the table below:
Growth Limited
Where r>ke, r= 0.15, ke= .10 E= Rs.10
Calculation of Market price as per Gordon Model
Payout 40%
Retention
60%
G= b*r
(b) Retention (b) 40%
P= E(1-b)/ ke-g
P=
G=
Payout 60%
10(1−0.6)
0.10−0.09
0.6*.15= 0.09
P=
400
G=
0.4*0.15=
4
0.001
= Rs.
P= E(1-b)/ ke-g
Payout 90%
Retention (b) 10%
0.06
P=
P=
10(1−0.4)
0.10−0.06
6
0.04
= Rs. 150
P=
G=
0.10*.15=0.015
10(1−0.1)
0.10−0.015
P=
106
9
0.085
= Rs.
Conclusion:
Where the payout ratio is low and retention ratio is high we are getting
the market price to be highest. As the payout ratio is increasing the
market price is decreasing from Rs.400/- it has gone as low as Rs.106. It
is because of the high payout ratio.
In a growth firm, we can say that the retention ratio should be high in
order to have the higher market price of the share
We can conclude that the higher the retention ratio better will be the
market price of the share so the company will have better investment
opportunities than the shareholders.
This is the first part of the calculations under Gordon Model which we
have analysis right now.
5. ANALYSIS OF GORDON MODEL WHERE r=Ke
We are going to analysis the Normal Limited. Normal limited is a company
where rate of return is equal to cost of capital here both r and ke are
equal to 10% under this scenario we have to pay out the market value of
the share and we will find out what shall be the impact of higher payout
ratio or the lower payout ratio. Whether retention should be there or
payout should be there in order to maximize the wealth of the
shareholders.
So let us start off our computation with the same formula
P=
𝐸(1−𝑏)
𝐾𝑒−𝑔
This is the formula we are going to use in all the three situation where
payout ratio is 40%, 60% and 90%. So what we need to do is first of all we
need to calculate P for 40% payout then for 60% and then for 90%
Calculation of Market price as per Gordon Model
Payout 40%
Payout 60%
Retention (b) 60% Retention (b) 40%
P= E(1-b)/ ke-g
G= b*r
P=
Payout 90%
Retention (b) 10%
P= E(1-b)/ ke-g
10(1−0.6)
0.10−0.06
G=
0.6*.10= 0.06
P=
4
0.04
= Rs. 100
P=
G= 0.4*0.10=
0.04
P=
G=
0.10*.10=0.01
10(1−0.4)
0.10−0.04
6
0.06
= Rs. 100
P=
P=
10(1−0.1)
0.10−0.01
9
0.09
= Rs. 100
Conclusion: in all the three payouts the market price is coming as Rs.100.
We can conclude that where the normal limited sort of company is there
that is where rate of return and cost of capital are equal the change in
the payout ratio or the dividend are not going to affect the market price
of the share. It is an indifferent point. The market price of the share will
remain same irrespective of the retention ratio or payout ratio.
6. ANALYSIS OF GORDON MODEL WHERE r<Ke
Now we are going to analyze the third scenario which is called the
declining firm or declining company. By declining we mean that the rate
of return is lower than cost of capital. Here our cost of capital is 10% in
the question and in the declining firm the rate of return will be lower
than cost of capital so we assume it to be 8%.Now we have to find out the
prices under different scernios where payout is 40%, 60% and 90%. We can
analysis the computation in the table prepared below having details of
calculation of growth rate as well as the price of the shares of the
company.
Calculation of Market price as per Gordon Model
Payout 40%
Retention
60%
G= b*r
G=
Payout 60%
(b) Retention (b) 40%
P= E(1-b)/ ke-g
P=
Payout 90%
Retention (b) 10%
P= E(1-b)/ ke-g
10(1−0.6)
0.10−0.048
0.6*.08= 0.048
P=
G= 0.4*0.08=
0.032
4
0.052
= Rs. 77
P=
P=
10(1−0.4)
0.10−0.032
6
0.068
= Rs. 88
P=
G=
0.10*.08=0.008
P=
10(1−0.1)
0.10−0.008
9
= Rs. 98
0.092
Conclusion : Analyzing this table we can conclude that as the payout ratio
is increasing so is the market price is increasing in the case of declining
firm that is if r is less than ke higher the payout ratio , higher the market
price of the share meaning thereby the investors have better investment
opportunities than the company.
So we can conclude that:
In the case of growth limited where r>ke, higher the retention ratio,
higher is the market price of the share.
In the case of normal limited where r=ke, whether the payout ratio is
higher or lower it is not going to affect the market price of the share and
it will remain unchanged.
In the case of declining firm, where r< ke, higher the payout ratio, less
the retention ratio, the market price of the share will be higher.
So accordingly we have to analysis the dividend policy.
7. SUMMARY
With this we have completed the calculation part of the Gordon Model.
Today we have learnt in our lecture the relevant theory and irrelevant
theory aspect that is the two sets of theories given under dividend policy
whether the market price of the share is affected by the dividend or not.
So the relevant theory has been propounded by two scholars first is
Walter and another is Gordon. So under this lecture, Gordon’s
assumption, the underlying scenario of the Gordon’s model and the
calculation aspect has been covered.
Thank You!!