Payout Policy - Part 1: Dividend Irrelevance Theory
Payout policy and its effect on a firm valuation - a review of Gordon's perspective ; Miller and Modigliani dividend irrelevance theory.
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Introduction
The magnitude of cash that firms return to their shareholders and the form of disbursement is an important capital allocation decision known as Payout Policy, and it is associated with positive excess Total Shareholders Returns (TSRs)1. Dividends were previously the predominant method for cash payout to investors, but share repurchases have gained importance in recent decades. In 1999, aggregate cash returned to investors in the form of stock buyback exceeded dividends distribution for the first time in US corporate history2.
An enduring topic in financial literature is how payout affects firm valuation. Many people believe that dividends are good since managers typically have asymmetric information about the prospects of their companies and could use cash distribution as a signaling effect of true worth to the market. Similarly, if contracts between owners and managers are not fully enforceable, dividends could be used by equity holders to discipline the management. Others point out that dividends attract more tax and note that it is better for corporations to repurchase shares. At the center, a middle-of-the-road party asserts that as long as a firm’s investment policy is fixed, payout decisions are irrelevant.
In this series on Payout Policy, I present a synthesis of theories that have been developed in academic literature to examine the behavior of firms with respect to cash distribution to shareholders. The 1961 research paper of Miller and Modigliani (MM) on the irrelevance of dividend payments on firm valuation in a frictionless world and perfect capital markets was the seminal contribution to the payout policy debate. Subsequent theoretical efforts have focused on the potential impact of payout on equity value in an imperfect environment.
In this introductory article, I summarized MM’s irrelevance theory and used a fictitious company to prove their framework. The prevalent belief on payout policy in the era that preceded MM’s publication was also examined.
Before MM’s Theory, There was Myers Gordon
Pre-1961, the pervasive school of thought among economists was that the value of a firm is an increasing function of dividends paid to shareholders3. The conclusion was derived from an extension of the dividend discount method (DDM) for evaluating a firm valuation. The mathematical expression that relates a firm value to its stream of dividend payments is presented below
Where Vo is the value of the firm at time t = 0, DIVt is the indefinite stream of dividend payments at the end of period t (1, 2, 3…∞) and r is the investors’ cost of capital also known as the discount rate that is applied to the stream of dividends to find their present value at t = 0.
Gordon, a prominent American economist was arguably the poster boy for researchers and theorists who believed that dividend policy affects a firm valuation. He opined that if a firm delay paying out dividends and instead increase its retention rate to grow the assets base, investors’ cost of capital will increase due to risk aversion and uncertainty associated with future dividend receipts4. It was argued that this dividend policy will reduce the value of a firm despite the expected increase in DIVt that will be available in future periods from reinvestments.
To prove how dividend policy affects a firm value, Gordon considered a corporation whose change in the distribution of dividends has no effect on its share price. The hypothetical firm earns E[0] at t = 0 and decides to pay it all out to shareholders. It is assumed that the firm doesn't reinvest in new assets so E[0] is the net profit that will be produced in perpetuity and disbursed to equity owners. The share price Po of the firm is evaluated as follows
[Eqn 2] is a restated form of the ‘enterprise valuation expression’ presented in [Eqn 1], used to derive the price of a share; Instead of computing the market cap of the company with [Eqn 1], [Eqn 2] was presented to obtain how much a single share will be sold. Hence, e[0] is the earning that accrues to a share, also known as earnings per share (EPS), and it is calculated by the division of Eo with the total outstanding shares.
Now, if the management decides at t = 0 that it will reinvest its earnings just once at the end of t = 1 and if the expected rate of return on the investment is r, then a share will be eligible to earn an extra re[0] in perpetuity after period t = 1. In this scenario, the price of a share could be computed as follows
Under an assumption that investors are indifferent to the new dividends regime, then discount rate r in [Eqn 2] and [Eqn 3] are equal and the mathematical simplification of the right-hand side of [Eqn 2] and [Eqn 3] produce the same result. Therefore, it can be concluded that the change in the dividend policy of the firm has not affected its valuation.
Gordon advanced his proof by highlighting that with the risk averseness of investors, it is unlikely that r in [ Eqn 2] and [Eqn 3] will be the same. It was argued that given the riskiness of a company, there is an increase in uncertainty attached to cash receipts that are expected to be obtained in the future. So, discount rate r ought to increase with time t. Put simply, the discount rate at time t is greater than the discount rate in a previous period t – 1 {r(t) > r(t-1)}. Therefore, [Eqn 2] and [Eqn 3] can be rewritten as follows
In valuation formulas, a uniform cost of capital r is typically used across all periods t to discount cash flows. Consequently, we can view r in [Eqn 2] as the average of r[1],r[2]…r[t] in [Eqn 4] weighted by the corresponding cash receipts. It is evident that replacing the differing discount rates in [Eqn 4] with the mean r will yield the same share price as [Eqn 2].
In the same vein, we could also compute a mean discount rate r* from [Eqn 5] that can be substituted for the varying discount rates in the expression. Importantly, we would expect that the rate will be greater than the average cost of capital r obtained from [4]. This is because the mean rate r* in [5] will be evaluated at discount rates t = 2 to ∞. Furthermore, the rates are weighted by higher numerators re[0] due to the reinvestment at t = 1. By using a single rate r* in [Eqn 5], the share price P*[0] will be less than the price P[0] obtained from [Eqn 2] or [Eqn 4].
In summary, Gordon deduced that lowering near dividends and raising distant dividends alter the weights of r[t] and increase their averages. This affects share price and buttresses the argument that dividend policy is important to valuation.
MM’s Irrelevance Framework
In response to the position held by economists that dividend policy affects a firm valuation, MM developed a rigorous analytical framework that shows that what really matters is the investment policy. They proved that as long as a firm’s investment strategy is fixed, cash flow from assets is the determinant of valuation instead of how it is packaged for distribution to shareholders.
MM made the following assumptions to derive their model5:
Perfect markets – No differential taxes between dividends and capital gain, no transaction costs in issuing new securities, no brokerage fees and all investors have costless information about a firm’s value.
Rational behavior – Investors are value-optimizers so more wealth is preferred.
Perfect certainty – Investors know the investment policy of every firm and there is complete assurance of expected profits.
MM started their derivation from the discount dividend expression for evaluating the value of a firm
DIVt represents the total dividend receipts that will be distributed to shareholders from t = 1 to H. H is a terminal period and V[H] is the market value at t = H.
Sidenote 1: Terminal period can be viewed as a time in the future when the value of an asset is evaluated. For example, if a real estate investor decides to purchase a rental property and sell it after a year, they will earn rental income for the 12 months they own the asset; the rental income is synonymous with dividend payments obtained from running a business. Furthermore, the investor will receive additional revenue from the sales of the asset. The end of year 1 is the terminal period and the dollar amount the building will sell for is akin to the market value of a business at a point in the future.
Sidenote 2: [Eqn 6] is equivalent to [Eqn 1]. The market value at period H in [Eqn 6] is the sum of discounted dividends from H to infinity and if we look far into the future, the second term on the right hand side of the expression - (V[H]/(1 + r)^H) - can be reduced to 0. This is because as H approaches ∞, the discount value of V[H] at t = 0 tends towards 0 and the upper limit of the summation symbol (sigma) can be replaced with ∞. This is an acceptable assumption when evaluating the value of a ‘going concern’ which is expected to produce cash flows forever.
For ease of illustration, the value of the firm could be evaluated over a single period t = 1. Therefore, DIVt and V[H] can be replaced with DIV(1) and V(1) respectively. Substituting the variables into [Eqn 6] transmutes the expression into [Eqn 7] as presented below
In a nutshell, V(0) is the value of the firm at t = 0 (today). DIV(1) is the dividends that will be paid to the firm’s equity owners and V(1) represents the corporation’s market value at t = 1 (a year from now).
From MM’s third assumption, if the firm investment policy is fixed, then investors know what the business will earn as net profit X(1) and the portion of the earnings I(1) that will be retained for reinvestment at t = 1. The residual amount from net income is the dividend DIV(1) that will be paid to the firm’s shareholders. Mathematically, DIV(1) is related to X(1) and I(1) as follows
Now, if the management of the corporation decides to pay more than the residual amount at t = 1 because they learned from a financial expert that dividend policy influences valuation, they would have 2 options to raise the extra fund. They could either sell some of their assets but that is not permitted under the assumption of a fixed investment strategy. If the firm doesn’t use leverage, the other alternative is to seek external capital and issue shares to new shareholders. In this scenario, [Eqn 8] can be modified as follows
Where n(1) is the number of new shares that must be sold at t = 1 and P(1) is the ex-dividend price of the shares in the same period.
The implication of issuing new shares and increasing the dividend amount DIV(1) at t = 1 is that the enterprise value of the firm V(1) that ought to be fully owned by existing shareholders must be reduced by the same amount of capital that will be raised from new investors. In other words, the market value V(1) is fixed but existing and new shareholders will have a claim to the future cash flows that will be produced by the firm’s asset. The promise to receive future dividends is what new investors pay for.
The mathematical split of the market value V(1) between existing and new shareholders at t = 1 is presented below
On the right-hand side (RHS) of [Eqn 10], the expression in the single quote is the portion of the market value V(1) for existing shareholders’ and the unquoted addend is the chunk that will belong to the new equity owners.
We can now compute what the firm will be worth to existing shareholders at t = 0 if management decides to proceed with paying more residual cash than it can typically afford under a fixed investment regime at t = 1. To do this, we must substitute [Eqn 9] into [Eqn 7]. Furthermore, the market value in [Eqn 7] must be replaced by the expression that represents the percentage existing shareholders will own after new shares are issued
[Eqn 11] can be simplified to
DIV(1) doesn’t appear in the argument of [12] and since X(1), I(1) and V(1) are all independent of the dividend payments at t = 1, MM submitted that the value of the firm is unaffected by the dividend policy and the financial engineering of the firm won’t increase its value. In summary, it was proven that valuation is dependent on real considerations - earnings obtained from invested capital.
Sidenote 3: V(1), the value of the firm in year 1 is the present value of future dividends in year 2, year 3 etc. But with a fixed investment policy, the value can also be expressed as V(1) = {X(2) – I(2) + V(2)}/(1 + r). The same logic can be extended to obtain the expression for V(2), V(3); and so on as far as we care to look into the future. This buttresses MM’s conclusion that the payout policy doesn’t affect total returns to shareholders.
Proof of the Dividend Irrelevance Theorem
A hypothetical company with made-up financial metrics is now used to expound the proof of MM’s dividend irrelevance framework.
Let’s assume that Click & Shop (C&S) is an equity-financed firm in a steady state which means there are no available future investment opportunities with a return that will exceed discount rate r. Therefore, C&S can produce $90K in net profit perpetually and this will be distributed to shareholders.
Furthermore, let’s assume that the firm has 9,000 outstanding shares and 9% cost of capital r. Then, the fair value of a share can be computed as follows
[Eqn 13] is a restated form of [Eqn 7] and it presents the value of a single share instead of the enterprise value of C&S. $10 is the dividend per share DPS(1) and it represents the payout the owner of a single share is entitled to receive. It is obtained by dividing the dividend payments ($90K) at t = 1 by the total number of shares (9,000). $111.11 is the terminal share price P(1) at t = 1 and it is computed by taking the sum of discounted dividends that will accrue to a share from t = 2 to ∞. Since a share will earn $10 perpetually {DPS(2) = DPS(3) …. DPS(∞) = $10}, P(1) is then calculated by dividing d(2) by r. That is $10/0.09 which gives $111.11.
The market value at t = 0 and t = 1 can be derived by simply multiplying P(0) and P(1) by the total number of shares. V(0) = V(1) = $1M
Sidenote 4: The shorthand formula that is used to evaluate the value of the share P(1) at the terminal period t = 1 works only when a constant future cash stream is expected in perpetuity.
Scenario 1 – C&S will pay $180K in total dividend at t = 1
If the management of C&S announces at t = 0 to change its dividend policy by increasing the total dividend paid at t = 1 to $180K, in a rational world with no imperfection, investors will not value the share of the firm at a premium. Therefore P(0) will still be $111.11 and the reason for this indifference is explained in this section.
By deciding to pay out $180K at t = 1, DPS(1) will now be $20. That is $180k divided by total shares (9,000).
For the firm to pay $90K more than its assets can produce, the management will have to raise the extra $90K from new investors and that will be done by issuing shares at t = 1. V(1), the market value of the firm at t = 1 is $1M and that won’t change as long as the investment policy remains fixed. Since new investors will be purchasing a claim to a portion of the market value of the entity at t = 1, the amount that is left for existing equity owners must be reduced by $90K raised from new equity owners. Therefore, the ex-dividend market value is $910K and if that is divided by the number of shares owned by existing shareholders 9,000, we obtain terminal price P(1) = $101.11.
Since our cost of capital is unchanged, we have all the variables to obtain P(0) and it can be calculated as follows
P(0) from [Eqn 13] and [Eqn 14] are the same despite the additional $10 dividend that is expected to be paid to existing shareholders at t = 1. When investors purchase a share, they expect to earn a return from dividends and what they will receive from selling a share. In a perfect world, they will be indifferent about how their earnings are distributed between the 2 sources of income as long as the total value is fixed. In [Eqn 13], the total income DPS(1) and P(1) in the numerator is $121.11. In [Eqn 14], the value is also fixed. This explains why the share price at P(0) is the same.
Scenario 2 – C&S will buy back its shares at t = 1
MM derived their theory when dividend payment was the predominant form of payout to shareholders. Nonetheless, their model is extensible to encompass shares repurchase. So, if our hypothetical company C&S announced at t = 0 that it would buy back its stock instead of paying dividends at t = 1, the share price P(0) can be re-evaluated and according to the irrelevance theorem, it should be the same as in [Eqn 13] and [Eqn 14]. The rationale is explained below.
If C&S is not paying dividends at t = 1, then the market value V(1) will be the sum of retained profit ($90K) and the terminal value of the business ($1M). Consequently, the share price P(1) at t = 1 can be derived by dividing V(1) by the total outstanding shares (9,000). That is $1.09M/9,000 = $121.11. Consequently, P(0) can be evaluated as follows
The dividend is noticeably absent since the firm is not paying any under the scenario under analysis. However, price appreciation is higher to neutralize the zero-dividend yield and the sum of values in the numerator was the same as in [Eqn 13] and [Eqn 14].
The effect of the buyback is a reduction in the total number of outstanding shares. C&S will be able to buy approximately 734 shares at P(1) = $121.11. The investors that decide to sell their shares at t = 1 and the retained shareholders will discount the expected P(1) by 9% at t = 0 which will yield $111.11.
Looking Ahead
The irrelevance theory was developed under assumptions of certainty and perfect market conditions. Still, the real world has imperfections such as preferential taxation of capital gain over dividend income and issuance cost when selling new securities. Subsequently, researchers in financial economics have extensively studied how relaxing the assumptions under irrelevance deduction could affect valuation.
In the following article under the Payout Policy series, attention is focused on tax, the propensity of firms to distribute cash via dividend despite its taxation disadvantages and the effect on the market value of a corporation. It is essential to have an understanding of the degree to which investor taxes are embedded into security prices, which in turn affect the cost of capital, investment spending and return on investment6.
Stay tuned!
Mauboussin, M.J and Callahan, D, ‘Capital Allocation: Results, Analysis and Assessment’, 2022.
Damodaran, A. ‘Applied Corporate Finance’, 4th Edition, 2014.
Michaely, R and Allen, F, Payout Policy, 2001.
Gordon, M.J, ‘Optimal Investment and Financing Policy’, 1963.
Miller, M.H and Modigliani, F, ‘Dividend Policy, Growth and Valuation of Shares’, 1961.
Ibid