Chapter 14, Problem 15QP

a)

Summary Introduction

To determine: The fall in the value of the 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 the 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 be entitled to the next dividend payment. Instead, 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 15QP

The amount the 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 the value of share price, if $T_P=T_G=0$:

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

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

b)

Summary Introduction

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

Answer to Problem 15QP

The fall in the value of the share price is 0.85 times 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 the value of the share price, if $T_P$ is 15 and $T_G$ is 0.

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

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

c)

Summary Introduction

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

Introduction:

The two dates before the record date is termed as the 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 be entitled to the next dividend payment. Instead, 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 15QP

The fall in the value of the share price is 1.21428 times 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

$T_P$ is 15 and $T_G$ is 30.

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

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

d)

Summary Introduction

To determine: The ex-dividend share price.

Introduction:

The two dates before the record date is termed as the 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 be entitled to the next dividend payment. Instead, 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 15QP

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

Explanation of Solution

Given information:

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

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

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

e)

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 payouts. 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.