# Neutrality of a dividend imputation system under the Modigliani-Miller proposition.

JEL G10 * G30 * M21In "The Cost of Capital, Corporation Finance, and the Theory of Investment" (American Economic Review, June 1958, 48(3), pp. 261-97) and "Corporate Income Taxes and the Cost of Capital: A Correction" (American Economic Review, June 1963, 58(3), pp. 433-43), Modigliani and Miller (M&M 1958, 1963) demonstrated that the value of a firm consists of the present value of uncertain future income and the present value of certain income, and that the tax shield will increase the value of a firm in the presence of tax deductibility of the interest payments on debt. However, often criticized is the double taxation of income received by the stockholders from the firm. In a classical taxation system, the double taxation happens because the income is taxed at a firm's level first and then at a stockholder's level when the income is delivered to them. Some countries, such as Australia, Canada, and the UK, have removed the double taxation and adopted a dividend imputation system where the amount of tax charged at the firm's level will be credited back to the stockholders when they receive cash dividends. The most representative one is the system in which a firm is taxed at the corporate tax rate and such taxes are notionally pooled as franking credits. When cash dividends are paid, an amount equal to the cash dividends times the corporate tax rate will be given back to the stockholders as a tax credit.

Some early papers discussing the effect of a dividend imputation system misled the audience and gave an impression that imputation would lower the cost of capital and thereby increase the value of the firm or eliminate use of debt. Most misunderstanding of the effect of a dividend imputation system appears to stem from the incorrect assertion that all taxes paid by the firm will be fully credited back to the stockholders. This does not happen in reality. Under a dividend imputation system, tax credits are only available in proportion to the amount of cash dividends paid to the stockholder.

The neutrality can be demonstrated with a slight modification on the original M&M model. A random variable X can be expressed in the form [bar.X][Z.sup.i], where [bar.X] is the expected value of X, and the random variable [Z.sup.i] = X/[bar.X] has the same value for all firms belonging to the risk class [z.sup.i] and has a distribution [f.sub.z]([Z.sup.i]). The investors demand a certain amount of cash payments, C, either through interest payments or cash dividends, C = E + R-E, where (R-E) is the tax deductable interest payment and E is the non-tax deductable cash dividends. R is the interest payment the firm pays on its debt incurred. Let [delta] ,0 [greater than or equal to] [delta] [greater than or equal to] 1, be the proportion of franking credit. The stockholders receive E(1 + [delta]t) through a dividend imputation system. The effective cash receipt is E(1 + [delta]t) +R-E = C +[delta]tE. The original M&M (1963) is now expressed as;

[X.sup.r.sub.imp] = [(1 - t)(X - R + E) - E] + C + [delta]tE = (1 - t)-[bar.X][Z.sup.i] + tR - (1 - [delta])tE (1).

For [delta]= 0, (1) is reduced to [X.sup.r.sub.imp] = (1 - t)X + t(R - E) = (1 - t)X + tR because [delta]= 0 implies E = 0, and yields exactly the same result obtained by the original M&M (1963) under a classical system for which [delta]= 1, [X.sup.r.sub.imp] = (1 -t)X + tR. Thus, the after tax-return is the same regardless of the means of cash payments. The value of the firm under a dividend imputation system can be expressed as:

[V.sub.L] = (1 - t)/[p.sup.i] + tR/r - (1 - [delta]) tE/r = [V.sub.u] + [tD.sub.L] - (1 - [delta]) tK (2).

This differs from the original M&M (1963) Eq. (3) by the term, (1-[delta]) tK, that signifies the effect of a cash dividend payment under a classical and dividend imputation system. For [delta]=1, the above equations yield the identical result obtained by the original M&M (1963). Thus, in conclusion, under a dividend imputation system, fully franked cash dividends have no effect on the value of the firm and hence dividend policies are irrelevant in determining the value of the firm.

Published online: 21 April 2009

T. Watanabe ([mail])

University of Southern Queensland, Toowoomba, QLD, Australia

e-mail: watanabe@usq.edu.au

T. Watanabe

State University of New York at Binghamton, Binghamton, NY, USA

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Title Annotation: | ANTHOLOGY |
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Author: | Watanabe, Taiji |

Publication: | Atlantic Economic Journal |

Geographic Code: | 8AUST |

Date: | Sep 1, 2009 |

Words: | 771 |

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