Chapter 17, Problem 14QP

Dividends and Taxes [LO2] As discussed in the text, in the absence of market imperfections and tax effects, we would expect the share price to decline by the amount of the dividend payment when the stock goes ex dividend. Once we consider the role of taxes, however, this is not necessarily true. One model has been proposed that incorporates tax effects into determining the ex-dividend price:⁹

  $(P_0-P_X)/D=(1-T_P)/(1-T_G)$

where P₀ is the price just before the stock goes ex, P_X is the ex-dividend share price, D is the amount of the dividend per share, T_P is the relevant marginal personal tax rate on dividends, and T_G is the effective marginal tax rate on capital gains.

a. If T_P = T_G = 0, how much will the share price fall when the stock goes ex?

b. If T_P = 15 percent and T_G = 0, how much will the share price fall?

c. If T_P = 15 percent and T_G = 30 percent, how much will the share price fall?

d. Suppose the only owners of stock are corporations. Recall that corporations get at least a 70 percent exemption from taxation on the dividend income they receive, but they do not get such an exemption on capital gains. If the corporation’s income and capital gains tax rates are both 35 percent, what does this model predict the ex-dividend share price will be?

Summary Introduction

To determine: The fall in the value of share price when the stock goes ex-dividend, if $T_P=T_G=0$

Introduction:

The two dates before the record date is termed as ex-dividend date. If the shareholder purchases the stocks on or before the ex-dividend date, then he is entitled to get the dividend payment; and if the shareholder purchases on or after the ex-dividend date, then he will not entitled to the next dividend payment rather the seller gets the payment.

The stocks will get the ex-dividend position if the person gets the dividends from the company.

Answer to Problem 14QP

The amount share price falls by the amount of dividend.

Explanation of Solution

Given information:

The model to determine the ex-dividend price is $\left(\frac{P_O-P_X}{D}\right)=\left(\frac{1-T_P}{1-T_G}\right)$

Where,

$P_o$ is the price just before the stock goes ex

$P_X$ is the ex-dividend share price

D is the dividend per share

$T_P$ is the marginal personal tax rate on dividends

$T_G$ is the marginal tax rate on capital gains

Determine the fall in value of share price, if $T_P=T_G=0$:

$\begin{array}{l}\left(\frac{P_o-P_X}{D}\right)=\left(\frac{1-T_P}{1-T_G}\right)\\ P_o-P_X=D\left(\frac{1-0}{1-0}\right)\\ P_o-P_X=D\end{array}$

Hence, the share value will fall by the amount of dividend D.

Summary Introduction

To determine: The quantum fall in the share price, if $T_P$ are 15 and $T_G$ is 0.

Answer to Problem 14QP

The fall in value of the share price is 0.85 times of D.

Explanation of Solution

Given information:

The model to determine the ex-dividend price is $\left(\frac{P_O-P_X}{D}\right)=\left(\frac{1-T_P}{1-T_G}\right)$

Where,

$P_o$ is the price just before the stock goes ex

$P_X$ is the ex-dividend share price

D is the dividend per share

$T_P$ is the marginal personal tax rate on dividends

$T_G$ is the marginal tax rate on capital gains

Determine the fall in value of the share price, if $T_P$ are 15 and $T_G$ is 0.

$\begin{array}{l}\left(\frac{P_o-P_X}{D}\right)=\left(\frac{1-T_P}{1-T_G}\right)\\ P_o-P_X=D\left(\frac{1-0.15}{1-0}\right)\\ P_o-P_X=D\left(\frac{0.85}{1-0}\right)\\ P_o-P_X=0.85D\end{array}$

Hence, the fall in value of the share price is 0.85 times of D.

Summary Introduction

To determine: The quantum of fall in the share price, if $T_P$ are 15 and $T_G$ is 30

Answer to Problem 14QP

The fall in value of share price is 1.21428 times of D.

Explanation of Solution

Given information:

The model to determine the ex-dividend price is $\left(\frac{P_O-P_X}{D}\right)=\left(\frac{1-T_P}{1-T_G}\right)$

Where,

$P_o$ is the price just before the stock goes ex

$P_X$ is the ex-dividend share price

D is the dividend per share

$T_P$ is the marginal personal tax rate on dividends

$T_G$ is the marginal tax rate on capital gains

Determine the fall in value of share price, if $T_P$ are 15 and $T_G$ is 30.

$\begin{array}{l}\left(\frac{P_o-P_X}{D}\right)=\left(\frac{1-T_P}{1-T_G}\right)\\ P_o-P_X=D\left(\frac{1-0.15}{1-0.30}\right)\\ P_o-P_X=D\left(\frac{0.85}{0.70}\right)\\ P_o-P_X=1.21428D\end{array}$

Hence, the fall in value of share price is 1.21428 times of D.

Summary Introduction

To determine: The ex-dividend share price.

Answer to Problem 14QP

The ex-dividend share price will be 1.3769 times of D.

Explanation of Solution

Given information:

The corporation gets 70% exemption from the dividend income and is taxable on capital gains. The income and capital gains tax rates of corporation are 35%.

The model to determine the ex-dividend price is $\left(\frac{P_O-P_X}{D}\right)=\left(\frac{1-T_P}{1-T_G}\right)$

Where,

$P_o$ is the price just before the stock goes ex

$P_X$ is the ex-dividend share price

D is the dividend per share

$T_P$ is the marginal personal tax rate on dividends

$T_G$ is the marginal tax rate on capital gains

Determine the ex-dividend price using the above mentioned model:

$\begin{array}{l}\left(\frac{P_o-P_X}{D}\right)=\left(\frac{1-T_P}{1-T_G}\right)\\ P_o-P_X=D\left(\frac{1-0.35\left(0.30\right)}{1-0.35}\right)\\ P_o-P_X=D\left(\frac{0.895}{0.65}\right)\\ P_o-P_X=1.3769D\end{array}$

Hence, the ex-dividend share price will be 1.3769 times of D.

Summary Introduction

To discuss: The impacts of the given models on tax considerations and policy of the dividend.

Explanation of Solution

Every company will focus on a particular group of shareholders, according to their dividend distribution. If a company pays low dividend payouts, then it will concentrate on shareholders who prefer low dividend payout. If the company pays high dividend payouts, then it will attract shareholders who prefer high payouts. This effect is known as clientele effect.

Thus, this model determines various groups of investors that vary on the tax rates on ordinary income and capital gain. Different investors will have different tax implications.