Download Impact of Dividend Policy on Value

XVI. THE FINANCING DECISION BY FIRMS: IMPACT OF DIVIDEND POLICY
ON VALUE
In Section IX, the choice of capital structure part of the firm's financing decision was
examined to determine if this choice has a significant effect on the market value of the firm. In a
parallel fashion, we examine here the impact of dividend policy on the market value of the firm.
That is, we address the question, "Does dividend policy ‘matter’?" As with the analysis of the
capital structure issue in Section IX, this question is well posed only if it is qualified to reflect
what are the "givens" of the environment. As in Section IX, we ask this question in the context
of a given or prespecified investment policy. That is, given that the firm has already set its
investment plan in real assets, can alternative choices among dividend policies change the market
value of the firm? In this framework, (as will be shown using the basic cash flow accounting
identity), asking the question in this context is equivalent to asking whether or not it matters that
the firm finances its investments by internally-generated funds or by raising the necessary money
externally in the capital markets (or through financial intermediaries).
Using the notation of Sections VI and XIV, an investment policy or plan corresponds to a
specific set of cash flows over time, {X(t)}, and investments over time {I(t)}. From the valuation
formulas (XIV.20) or (XIV.21), a seemingly obvious answer is that "of course, dividend policy
affects the value of the firm." From the valuation formula (XIV.32b), however, an equally
obvious answer is that "given that the distribution for {X(t)} and {I(t)} is fixed, V(0) cannot
change by changing the payout stream, and hence, dividend policy does not affect the value of
the firm." In fact, neither answer is universally correct. Thus, the second answer is correct
provided that the cost of capital, {k(t)}, does not depend on dividend policy. But, it remains to
be determined under what conditions this lack of dependence will obtain.
Before exploring this issue, we briefly digress to list some factors which appear to
influence dividend policy:
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Finance Theory
Factors influencing dividend policy:
(1)
legal restrictions
(6)
profit rates
(2)
cash position
(7)
access to capital markets
(tradeability of equity)
(3)
need to repay debt
(8)
control of the firm
(4)
restrictions in debt contracts
(9)
tax position of shareholders
(5)
rate of asset expansion
(10)
corporate tax liabilities
Observed stability of dividend policy with respect to earnings or cash flows.
Modigliani-Miller Theorem on Dividend Policy
First proof that "dividends do not matter"
Assume an environment in which short sales are allowed with full use of the proceeds. Suppose
there are two firms with identical investment policies, i.e.,
~
~
~
~
X1 (t) ≡ X 2 (t) and I 1 (t) ≡ I 2 (t)
Suppose that the dividend policies of the two firms for time t > T are identical, but their
dividend policies differ from
t ≤ T .
Suppose that their values today are different. By
convention, V 2 (0) > V1 (0) . For simplicity, assume that n1(0) = n2(0) . Where n1 and n2 are the
number of shares issued by the two firms.
Consider the following portfolio strategy:
At time zero, buy λ% of firm #1 and sell short λ% of firm #2. Since V2(0) > V1(0), my total
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position is at this point:
(a)
cash = λ[V2(0) – V1(0)] > 0
(b)
long λn1(0) shares of firm #1
(c)
short λn2(0) shares of firm #2
Suppose that the portfolio policy is pursued of always maintaining a long position in firm #1
equal to λ% of its value and a short position in firm #2 equal to λ% of its value.
Let N1(t) = number of shares of firm #1 which you are long at time t.
Let N2(t) = number of shares of firm #2 which you are short at time t.
Then N1(0) = λn1(0) and N2(0) = λn2(0) and
(XVI.1a)
N 1(t + 1) = N 1(t ) + λ m1(t + 1), and
(XVI.1b)
N 2(t + 1) = N 2(t ) + λ m 2(t + 1)
Where m1 and m2 are the changes in n1 and n2 .
Let C(t) = total cash flow from this portfolio strategy at time t. Then:
C (0) = λ n 2(0) S 2(0) - λ n1(0) S 1(0)
= λ[V 2(0) - V 1(0)] > 0
Where S1 and S2 are the share prices for firms #1 and #2.
Assume that C(0) is invested in riskless-in-terms-of-default, T-period discount bonds with yield
to maturity of R(T). For t > 0 and t < T–1 , we have that
(XVI.2)
C (t + 1) = N 1(t )d 1(t + 1) - N 2(t )d 2(t + 1) + λ m 2(t + 1) S 2(t + 1) - λ m1(t + 1) S 1(t + 1)
Where d1 and d 2 are the dividends per share.
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Finance Theory
From the strategy design described in (XVI.1), we have that:
(XVI.3a)
N 1(t )d 1(t + 1) = λ D1(t + 1)
(XVI.3b)
N 2(t )d 2(t + 1) = λ D 2(t + 1)
Where D1 and D2 are the total dividends paid by the two firms respectively.
Substituting from (XVI.3) to (XVI.2), we have that:
(XVI.4)
C (t + 1) = λ D1(t + 1) - λ D 2(t + 1)+λ m 2(t + 1) S 2(t + 1)-λ m1(t + 1) S 1(t + 1)
= λ{[ D1(t + 1) - m1(t + 1) S 1(t + 1)]-[ D 2(t + 1) - m 2(t + 1) S 2(t + 1)]}
From the cash flow accounting identity (VI.12), we have that:
(XVI.5a)
D1(t + 1) - m1(t + 1) S 1(t + 1)
≡ X 1(t + 1) - I 1(t + 1)
≡ Y 1(t + 1)
(XVI.5b)
D 2 (t + 1) - m2 (t + 1) S2 (t + 1) ≡ X 2 (t + 1) - I2 (t + 1) ≡ Y 2 (t + 1) ,
and by hypothesis of a fixed investment policy, Y 1(t + 1) ≡ Y 2(t + 1) for all t. Therefore,
substituting into (XVI.4), we have that:
C (t + 1) = 0 for 0 < t < T -1
(XVI.6)
If the positions are liquidated at time T, then we have that:
(XVI.7)
C (T ) = λ{[ D1(T ) - m1(T ) S 1(T )] - [ D 2(T ) - m 2(T ) S 2(T )]}
+λV1(T)
sale of
shares long
-λV2(T)
purchase of
shares short
T
+ C(0)[1+R(T)]
cash and interest on
maturity of bonds.
By assumption, after date T, the dividend policies of the two firms are identical. So after the
dividend payments at time T, it must be that the two firms have identical market values, i.e.,
V1(t) = V2(t) for t ≥ T . In particular, V1(T) = V2(T) . From this and (XVI.5), we have that:
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Robert C. Merton
(XVI.8)
C (T ) = C (0)[1 + R(T )]T
= λ[V 2(0) - V 1(0)][1 + R(T )]T >0 if V 2(0) > V 1(0)
Therefore, by investing no money at any time during the interim, the investor can earn C(T) at
time T . Therefore, to avoid arbitrage, C(T) ≡ 0 or:
V 2(0) = V 1(0)
(XVI.9)
Therefore, the values of the two firms must be equal and dividend policy "does not matter."
Second proof that "dividends do not matter":
Assume that: 1. Imputed Rationality: If, in forming expectations, each individual investor
assumes that every other trader in the market (A) is rational in the sense of preferring more
wealth to less, independent of the form an increment in wealth may take, and (B) imputes
rationality to all other investors. (2) Symmetric Market Rationality (SMR): Market as a whole
satisfies SMR, if every trader is both rational in behavior and imputes rationality to the market.
We do not assume that short sales can be made with the full use of the proceeds. Consider two
firms as in the "first proof." Suppose that at time t = T–1 there is an investor who is considering
buying λ% of firm #2 for $λV2(T–1). Suppose instead he bought λ% of firm #1 and did the
following: at time T, he will receive λD1(T) in dividends. Suppose he sells (ex-dividend)
$λ[D2(T) – D1(T)] of his stock for cash if D2(T) ≥ D1(T), or if D1(T) > D2(T) , then he buys
$λ[D1(T) – D2(T)] of the stock of firm #1. At this point, he will then have ${λD1(T) + λ[D2(T)
– D1(T)]} = $λD2(T) in cash and ${λ[V1(T) – m1(T)S1(T)] + λ[D1(T) – D2(T)]} worth of firm
#1's stock. From (XVI.5), we have that D1(T) – m1(T)S1(T) = D2(T) – m2(T)S2(T). So, –
λ[m1(T)S1(T) – D1(T) + D2(T)] = – λm2(T)S2(T). Therefore, our investor would have:
$ λD2(T) , in cash, and
$ λ[V1(T) – m2(T)S2(T)] = $ λ[V2(T) – m2(T)S2(T)] , in stock,
because V1(T) = V2(T) .
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But, this is exactly the amount of cash and stock which he would have had if he bought λ% of
firm #2. If V1(T–1) < V2(T–1), then every investor (who prefers more to less) would be better
off to buy firm #1 instead of firm #2.
Hence, unless V1(T–1) = V2(T–1), there will be a
dominance of one of the firms over the other. If one firm dominates the other, who would buy
the dominated firm, or who would hold it? Clearly, no one. Hence, V1(T–1) = V2(T–1) .
Suppose at some date τ, V1(τ) = V2(τ) , then, by the same argument (with "τ" replacing "T"),
we have that V1(τ–1) = V2(τ–1). Proceeding inductively, we have that V1(0) = V2(0). Both
proofs neglect transactions costs and personal taxes. We now explore what effect these might
have.
Dividend Policy & Market Imperfections: It appears that reductions in current dividends per
share (for fixed investment policy) may increase stockholders' wealth.
(i)
because substantial underwriting costs are incurred in issuing stock, shareholders should
prefer a reduction in dividends to a stock issue.
(ii)
because capital gains are taxed at a lower rate than dividends and only at the time of their
realization through sale.
Informational Content of Dividends
Since the practice is that dividend payments are smoothed to conform to managers'
estimates of average earnings, the announcement of an increase in dividend payments implies
that management has raised its estimate of average future earnings. If unanticipated through
other means, such an announcement would be expected to affect the stock price.
Generally,
(i)
Managers are reluctant to cut the dividend rate for fear that this would be
interpreted as a sign of poor earning prospects.
(ii)
Dividends are increased only when management is reasonably confident that
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Robert C. Merton
the increase can be maintained.
(iii)
⎛ Dividends ⎞
⎟⎟ fluctuate because dividends are more stable than
⎝ Earnings ⎠
Payout ratios ⎜⎜
earnings. But, a firm's target payout ratio is normally stable over time.
(iv)
Target payout ratios vary widely from company to company. A typical ratio
is .50 - .60 .
Example: The Constant-Growth Case: Growth Stocks
Review Section VI, pp. 6-20 and 6-21.
Consider the constant growth examined there:
We have from (VI.18) that:
V (0) =
(XVI.10)
(1- δ )π (0)
r - r *δ
*
where r δ = rate of growth of earnings
and δ = fraction of profits allocated to new investment.
From (XIV.27), we have that:
(XVI.11)
V (0) =
D(1)
r-g
where g is the rate of growth of dividends per share. From the accounting identity, D(t) –
m(t)S(t) = X(t) – I(t). If I(t) = δX(t) , then D(t) – m(t)S(t) = [1–δ]X(t). Let δr = fraction of
current earnings retained (i.e., D(t) = [1–δr]X(t). Let δe = the amount of external financing
required expressed as a fraction of current earnings. It follows that [1–δr]X(t) – δeX(t) = [1δ]X(t) or δe = δ – δr.
X (1) = π (0), so, D(1) = [1 - δ r ] π (0).
From (XVI.10) and (XVI.11), we have that
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Finance Theory
(XVI.12)
(1- δ )π (0)
r - r δ
*
= V (0) =
[1- δ r ]π (0)
r - g
or
(XVI.12')
g=
δ r * (1- δ r )
r
- δe
(1- δ )
1- δ
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Robert C. Merton
Note: Unless δe = 0 (i.e., no external financing), the rate of growth of dividends, g , is less
*
than the rate of growth of profits, δ r . Further, even if the firm pays out all of its current earnings in
dividends, i.e., δr = 0 , dividends and price per share will grow over time, i.e., g =
δ (r * - r )
.
(1- δ )
Example: three firms all with π (0) = $100 and identical investment policies:
Firm
I
II
III
π (0)
$100
$100
$100
r
.10
.10
.10
r*
.20
.20
.20
δ
.40
.40
.40
δr
.40
0
.20
δe
0
.40
.20
V(0)
$3,000
$3,000
$3,000
I(1)
$40
$40
$40
n(0)
1,000
1,000
1,000
S(0)
$3.00
$3.00
$3.00
Firm I: Finances all its investment internally through retained earnings, i.e., δr = δ = .40 and
δe = 0 .
From (XVI.10),
(1- δ )π (0)
(.6)(100)
60
=
=
= $3,000
*
.10-.4(.2) .02
r -δ r
I (1) = δ X (1) = .4($100) = $40.
V (0) =
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Finance Theory
Since this firm does no external financing, D(1) = dividends = X(1) – I(1) = $100 – 40 = $60, by
the accounting identity. Dividends per share, d (1) =
have
60
D(1)
=
= $.06 per share. We
n(0)
1, 000
X (t ) = X (t -1) + r * I (t -1) = π (0)[1 + r *δ ]t -1.
that
Hence,
X (2) = X (1)[1 + r *δ ] = 100(1.08) = $108. Therefore, the value of the firm next period will
be:
X (2)(1- δ )
$108(1-.4)
=
= $3, 240 . Since no new shares are issued, n(1) = n(0) =
r - rδ
.10 -.4 x .2
V (1) =
1,000 shares. So, the price per share will be $3.24. The total rate of return to the stockholder will
be:
d(1) + S(1) - S(0) .06 + 3.24 - 3.00
=
= 10% = r .
S(0)
3.00
The rate of growth of dividends, g, from (XVI.12'), will be
(1- δ r )
V (1) - V (0)
δ r
- e = δ r * .08 = 8% = rate of growth of the firm
V (0)
(1- δ )
1- δ
S (1) - S (0)
= rate of growth of price per share
.
S (0)
g = δr*
Firm II: Finances all new investment by issuing new shares and pays out all earnings as
dividends. As has been demonstrated previously, since the investment policy is the same for all
three firms, X(1), X(2), V(0), V(1), and S(0) will be the same for all firms, and they depend on
the profitability of current assets and future investment opportunities which are independent of
dividend policy. Hence, V(1) = $3240 for this firm, but at that point, the firm will not belong
completely to the shares outstanding at time zero. Namely, it must issue m(1) new shares at
price S(1) to finance investment I(1). I.e., m(1)S(1) = I(1) = $40, V(1) = n(0)S(1) + m(1)S(1) or
S (1) =
V (1) - m(1) S (1)
=
n(0)
3240-40
or S(1) = $3.20 and m(1) = 12.5. The return to the
1000
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Robert C. Merton
shareholders is
and d (1) =
.10+3.20-3.00
d (1) + S (1) - S (0)
=
= 10% = r since D(1) = X(1) = $100
S (0)
3.00
100
D(1)
=
= .10 . Note that the larger dividend of Firm II is offset by a smaller capital
n(0) 1000
gain.
The rate of growth of dividends, g, from (XVI.12') is
g=
δ r * (1- δ r ) δ er
(.4)(.2)(1-0) .4(.1)
S (1) - S (0)
=
= 0.0667 = rate of growth of price per share =
.
S (0)
1- δ
1- δ
.6
.6
Note: The growth of dividends is smaller than for Firm I.
Firm III: Uses a mix of one-half internal and one-half external financing. Hence, m(1)S(1) =
.5I(1) = $20 and again,
S (1)
D(1)
d (1)
g =
=
V (1) - m(1) S (1)
3240-20
=
= $3.22 per share
n(0)
1000
= X (1) - I (1) + m(1) S (1) = 100 - 40 + 20 = $80 and
D(1)
d (1) S (1) - S (0)
.08+3.22-3.00
=
= $0.08 and
=
= 10% = r
n(0)
S (0)
3.00
(1- δ r ) δ er
(.8)(.8) (.2)(.1)
δr*
=
= .07334
(1- δ ) 1- δ
.6
.6
S (1) - S (0)
= rate of growth stock price .
S (0)
=
Note: r = 10% =
d (1)
+ g = current dividend yield + growth .
S (0)
On Corporate Earnings and Investor Returns
What is the relationship between total dollar returns to shareholders in a particular period
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Finance Theory
(i.e., dividends plus capital gains) and total dollar earnings of the firm, X(t)? If G(t) = capital
gains to shareholders between period t – 1 and t, then D(t) + G(t) = (1–δr)X(t) + gV(t–1) ,
because (1–δr)X(t) is the amount of earnings not retained, and g, the rate of growth of
dividends, is equal to the rate of growth of price per share. We have that V (t -1) =
and from (XVI.12'), that g =
X (t )
δ r *(1- δ r )(1- δ )
(r - r *δ )(1- δ )
-
δ er (1- δ ) }
(r - r *δ )(1- δ )
{r (1- δ r ) - δ r * (1- δ r ) + δ r * (1- δ r ) - δ er }
r-r δ
rX (t )
=
{1- δ r - δ e} =
r - r *δ
*
r - r *δ
δ r * (1- δ r )
r
- δ e . Hence,
(1- δ )
(1- δ )
D(t ) + G (t ) = X (t ){(1- δ r ) +
=
(1- δ ) X (t )
rX (t )
[1- δ ] since δ = δ r + δ e .
r - r *δ
So,
D(t ) + G (t )
X (t )
=
r (1- δ )
r - r *δ
= 1 for r * = r
> 1 for r * > r for 0 < δ <1
for 0 < δ < 1
< 1 for r * < r
X (1) π (0)
r - r *δ
D(1)
=
=
, and from (XVI.11),
= r - g.
Note: From (XVI.10),
V (0) V (0)
1- δ
V (0)
So, in general, neither the earnings-to-price nor the dividends-to-price ratio is an unbiased
estimate of the cost of capital, r.
Does dividend policy "matter"? Empirical Evidence Graham & Dodd (early work)
As the result of a cross-sectional fit of companies, they found the following relationship:
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Robert C. Merton
P = m[ D +
E
]
3
where
E = earnings; D = dividends; change in retained earnings = ∆RE;
P = price of stock; m = constant.
Because E = D + ∆RE , we also have
P =
m
[4 D + ∆RE ] .
3
The weighted average is important and the dividends have a large weight. Implied policy: make
the dividend as large as possible. The equation was "derived" by looking at the data (although it
did not do well for growth stocks, e.g., IBM). Regression or "fit" was done as follows:
Implication: Other things equal, the higher the payout ratio, the higher the price.
Is there any problem with this analysis?
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Finance Theory
Suppose: P = price is a function of future earnings and managements choose dividends as a
function of future earnings. Does it follow that because P plotted against D gives a good fit,
one can raise price by increasing the dividend payout if the anticipated future earnings stream
remains the same? I.e., is the Graham-Dodd result a causal relationship?
Suppose: the price-earnings ratio properly computed, using long-run "smooth" earnings (i.e.,
π (0) and the "target" payout ratio, D /π (0) , are independent of each other). At a point in time, some
firms' earnings will be transitorily lower than their long-run average. Realizing the transitory
nature of the lower earnings, management does not "cut" the dividend which is based on "longrun" earnings trend. Hence,
D / E > D /π (0) . Similarly, the market, recognizing that price is
dependent on "long-run" earnings, will not bid down the price. Hence, P / E > P /π (0). At the same
time, some firms' earnings will be transitorily higher than their long-run average. For the same
reasons, management does not raise the dividend nor does the market bid up the price. Hence
D / E < D /π (0) and P / E < π (0) .
In a cross-section, the strong positive fit between D/E and P/E could merely reflect
transitory earnings coupled with managements having a target payout based on long-run
"smoothed" earnings.
Because of their concern over the information effect of dividends, management may well
"smooth" dividend payments to match their long-run expectations about the earnings of the firm.
Suppose: (as seems to be the case empirically), that dividend payout policy and the risk (as, for
example, measured by beta) of a firm's underlying assets are not independent. I.e., that high (or
low) dividend payout policies are not randomly distributed across firms. Moreover (as seems to
be the case), suppose that low-risk firms tend to also have high payout policies. Then in a crosssection of firms, one would expect to find that high-payout ratios would be associated with high
price-earnings ratios. Yet, such a finding does not imply that a firm can raise its PE ratio by
increasing its payout ratio if it maintains the same risk level for its assets.
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Robert C. Merton
Black-Scholes Dividend Paper
As was discussed in the beginning of this section, the only way that dividend policy can
affect the value of the firm (given, a fixed investment policy) is if alternative choices for dividend
policy affects the required expected return on the firm (i.e., the {k% (t )}) . In their dividend paper,
Black and Scholes provide a test of the hypothesis that alternative dividend policies differentially affect
required expected returns. To overcome the inherent difficulties with simple cross-sectional analysis,
their test is a combined time-series and cross-sectional analysis. Moreover, their test attempts to correct
for the different risks inherent in a cross-section of stocks. In constructing the test procedure, they begin
with a (generalized) Capital Asset Pricing Model specification for expected returns on securities:
(XVI.13)
E ( Z j ) = γ 0 + [E ( Z M ) - γ 0]β j + γ 1[δ j - δ M ] / δ M
where δj = current dividend yield on security j; δM = current dividend yield on the market; γ0 =
expected return on a "zero-beta" portfolio; and γ1 is the "expected return" on the dividend factor.
Possibilities:
(i)
The classical security market line relationship of the CAPM would predict γ0 =
R, the riskless rate γ1 = 0 .
Thus, if they could not reject γ0 = R and γ1 = 0 , we cannot reject the CAPM and
we cannot reject the hypothesis that dividend policy "does not matter."
(ii)
If γ1 ≠ 0 , then the data suggest that dividend policy does differentially affect
returns. Further, if γ1 > 0 , then this would imply that investors prefer lowdividend yielding stocks. If γ1 < 0 , then this would imply that investors prefer
high-dividend yielding stocks.
Their findings were that while they could reject the hypothesis that γ0 = R, they could not reject
the hypothesis that γ1 = 0 .
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Finance Theory
Their results seem somewhat surprising in the light of our proof that dividend policy does
not matter in the absence of transactions costs and personal taxes. Since both exist in the real
world, one's prior might be that γ1 > 0 . I.e., investors prefer low-dividend yielding stocks.
The Black-Scholes explanation of this result is as follows: because payout policies are
not randomly distributed across the firms and risk classes, to achieve dividend yields that are
significantly different from the market's, the investor must hold a less-than-well-diversified
portfolio. Thus, to achieve a higher (or lower) dividend-yielding portfolio, one must pay a price
in the form of increased variance. Because dividend-yield is only a small fraction of the total
return on the market and the maximum tax-saving is even smaller, it does not pay to adjust one's
portfolio to avoid dividends. Moreover, unless a taxpayer is in the maximum tax bracket, he
does not know if he would prefer high or low-dividend paying portfolios unless he knows the
"spread" between pre-tax yields. Hence, they conclude that for stock portfolios (in the world as it
is) investors neglect tax differentials between dividends and capital gains.
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