Chapter 16, Problem 30PS

a)

Summary Introduction

To identify: The marginal investors that determine the prices of the stocks.

Explanation of Solution

The marginal investors who determine the prices of the stocks are institutions.

b)

Summary Introduction

To determine: The prices of the low-, medium-, and high-payout stocks.

Explanation of Solution

Computation of price of the low-, medium-, and high-payout stocks is as follows:

$\begin{array}{c}{\text{Price of low-payout stock, p}}_0=\frac{\text{D}}{\text{After-tax return rate}}\\ =\frac{\$20}{0.12}\\ =\$166.67\end{array}$

$\begin{array}{c}{\text{Price of medium-payout stock, p}}_0=\frac{\text{D}}{\text{After-tax return rate}}\\ =\frac{\$10}{0.12}\\ =\$83.33\end{array}$

$\begin{array}{c}{\text{Price of high-payout stock, p}}_0=\frac{\text{D}}{\text{After-tax return rate}}\\ =\frac{\$30}{0.12}\\ =\$250\end{array}$

Therefore, the price of low-, medium-, and high-payout stock is $166.67, $83.333, and $250 respectively.

c)

Summary Introduction

To determine: The after-tax returns of the three types of stock for each investor group.

Explanation of Solution

The institution after-tax rate of return is 12% for each type of stock and the individual’s after-tax returns are as follows:

$\begin{array}{c}\text{For low-payout stock, r}\text{=}\frac{\left[\left(0.50\times \text{D}\right)+\left(0.85\times \text{capital gains}\right)\right]}{{\text{P}}_0}\\ =\frac{\left[\left(0.50\times \$5\right)+\left(0.85\times \$15\right)\right]}{\$166.67}\\ =\frac{\$15.25}{\$166.67}\\ =0.0915\text{or 9}\text{.15\%}\end{array}$ 

$\begin{array}{c}\text{For medium-payout stock, r}\text{=}\frac{\left[\left(0.50\times \text{D}\right)+\left(0.85\times \text{capital gains}\right)\right]}{{\text{P}}_0}\\ =\frac{\left[\left(0.50\times \$5\right)+\left(0.85\times \$5\right)\right]}{\$83.33}\\ =\frac{\$6.75}{\$83.33}\\ =0.0810\text{or 8}\text{.10\%}\end{array}$

$\begin{array}{c}\text{For high-payout stock, r}\text{=}\frac{\left[\left(0.50\times \text{D}\right)+\left(0.85\times \text{capital gains}\right)\right]}{{\text{P}}_0}\\ =\frac{\left[\left(0.50\times \$30\right)+\left(0.85\times \$0\right)\right]}{\$250}\\ =\frac{\$15}{\$250}\\ =0.06\text{or 6\%}\end{array}$

Therefore, the individuals after-tax rate of return of low-, medium-, and high-payout stock is 9.15%, 8.10%, and 6% respectively.

For corporations, after-tax rate of return is as follows:

$\begin{array}{c}\text{For low-payout stock, r}\text{=}\frac{\left[\left(0.95\times \text{D}\right)+\left(0.65\times \text{capital gains}\right)\right]}{{\text{P}}_0}\\ =\frac{\left[\left(0.95\times \$5\right)+\left(0.65\times \$15\right)\right]}{\$166.67}\\ =\frac{\$14.5}{\$166.67}\\ =0.087\text{or 8}\text{.7\%}\end{array}$

$\begin{array}{c}\text{For medium-payout stock, r}\text{=}\frac{\left[\left(0.95\times \text{D}\right)+\left(0.65\times \text{capital gains}\right)\right]}{{\text{P}}_0}\\ =\frac{\left[\left(0.95\times \$5\right)+\left(0.65\times \$5\right)\right]}{\$83.33}\\ =\frac{\$8}{\$83.33}\\ =0.096\text{or 9}\text{.6\%}\end{array}$

$\begin{array}{c}\text{For high-payout stock, r}\text{=}\frac{\left[\left(0.95\times \text{D}\right)+\left(0.65\times \text{capital gains}\right)\right]}{{\text{P}}_0}\\ =\frac{\left[\left(0.95\times \$30\right)+\left(0.65\times \$0\right)\right]}{\$250}\\ =\frac{\$28.5}{\$250}\\ =0.114\text{or 11}\text{.4\%}\end{array}$

Therefore, the corporations after-tax rate of return of low-, medium-, and high-payout stock is 8.70%, 9.60%, and 11.40% respectively.

d)

Summary Introduction

To determine: The dollar amounts of the three types of stock held by each investor group.

Explanation of Solution

Following table shows the dollar amounts of the three types of stock held by each investor group:

	Low payout	Medium payout	High payout
Individuals	$80 billion
Corporations			$10 billion
Institutions	$20 billion	$50 billion	$110 billion

Table no.1