Chapter 19, Problem 14QP

a.

Summary Introduction

To determine: The Current Value of Firm.

Introduction: The term dividends allude to that portion of proceeds of an organization which is circulated by the organization among its investors. It is the remuneration of the investors for investments made by them in the shares of the organization.

Answer to Problem 14QP

The Current Value of Firm is $1,625,178.57.

Explanation of Solution

Determine the current value of firm

$\begin{array}{c}CurrentValueofFirm=\left[NetIncome+\left(\frac{ExpectedValueofFirminOneYear}{1+DiscountRate}\right)\right]\\ =\left[\$85,000+\left(\frac{\$1,725,000}{1+12\%}\right)\right]\\ =\left[\$85,000+\$1,540,178.57\right]\\ =\$1,625,178.57\end{array}$

Therefore the current value of firm is $1,625,178.57

b.

Summary Introduction

To determine: The Ex-Dividend Price of the Company.

Answer to Problem 14QP

The Ex-Dividend Price of the Company is $61.61.

Explanation of Solution

Determine the current stock price

$\begin{array}{c}CurrentStock\mathrm{Pr}ice=\left[\frac{CurrentValueofFirm}{SharesOuts\tan ding}\right]\\ =\left[\frac{\$1,625,178.57}{25,000}\right]\\ =\$65.01\end{array}$

Therefore the current stock price is $65.01

 Determine the present dividend of the company

$\begin{array}{c}\mathrm{Pr}esentDividend=\left[\frac{NetIncome}{SharesOuts\tan ding}\right]\\ =\left[\frac{\$85,000}{25,000}\right]\\ =\$3.40\end{array}$

Therefore the present dividend of the company is $3.40

Determine the ex-dividend price of the company

$\begin{array}{c}Ex-Dividend\mathrm{Pr}ice=\left[CurrentStock\mathrm{Pr}ice-\mathrm{Present}Dividend\right]\\ =\left[\$65.01-\$3.40\right]\\ =\$61.61\end{array}$

Therefore the ex-dividend price of the company is $61.61

c. i.

Summary Introduction

To determine: The Reasons on low dividends depressing the stock prices.

Explanation of Solution

Determine the value of dividends

$\begin{array}{c}ValueofDividends=\left[SharesOuts\mathrm{tand}ing\times NewDividend\right]\\ =\left[25,000\times \$4.60\right]\\ =\$115,000\end{array}$

Therefore the value of  dividends is $115,000

Determine the amount raised in dollars

The organization is required to increase the funds by funding the dividend payments in dollars.

$\begin{array}{c}AmountRaise{d}_{Dollars}=\left[ValueofDividends-NetIncome\right]\\ =\left[\$115,000-\$85,000\right]\\ =\$30,000\end{array}$

Therefore the amount raised in dollars is $30,000

Determine the value of new shareholder in one year

The new shareholders value is raised only if the company sell the new equity in order to maintain the all-equity financing.

$\begin{array}{c}ValueofNewShareholder{s}_{InOneYear}=\left[AmountRaise{d}_{Dollars}\times \left(1+DiscountRate\right)\right]\\ =\left[\$30,000\times \left(1+12\%\right)\right]\\ =\$33,600\end{array}$

Therefore the value of new shareholder in one year is $33,600

Determine the value of old shareholder in one year

As a result of new shareholder value, the value of old shareholder will fall.

$\begin{array}{c}ValueofOldShareholder{s}_{InOneYear}=\left[\begin{array}{l}ExpectedValue-Valueof\\ NewShareholder{s}_{InOneYear}\end{array}\right]\\ =\left[\$1,725,000-\$33,600\right]\\ =\$\text{1,691,400}\end{array}$

Therefore the value of old shareholder in one year is $1,691,400

Determine the current value of firm

$\begin{array}{c}CurrentValueofFirm=\left[\left(\frac{ValueofOldShareholder{s}_{InOneYear}}{1+DiscountRate}\right)+ValueofDividends\right]\\ =\left[\left(\frac{\$1,691,400}{1+12\%}\right)+\$115,000\right]\\ =\left[\$1,510,178.57+\$115,000\right]\\ =\$1,625,178.57\end{array}$

Therefore the current value of firm is $1,625,178.57

The Reasons on low dividends depressing the stock prices is as follows:

• As indicated by Modigliani and Miller, the facts cannot prove that the lesser dividend is depressing the cost.
• According to the dividend policy it is considered as inappropriate, the dividend level ought not make any differences.
• Any resources not circulated as dividends add to the estimation of the firm, consequently the price of stock.
• These managers simply need to change the period of dividends.
• The estimation of the firm is unaltered by their proposition. Hence, the price of share will be remain same.
• Therefore the value of firm is similar from part a, hence the change in dividend will have no impact.

c. ii.

Summary Introduction

To determine: The Price of New Shares and the number of shares sold.

Answer to Problem 14QP

The Price of New Shares is $60.41 and the number of shares sold 497 shares.

Explanation of Solution

Determine the present value of stock

$\begin{array}{c}\mathrm{Pr}esentValueofStock=\left[\frac{ValueofOldShareholder{s}_{InOneYear}}{1+DiscountRate}\right]\\ =\left[\frac{\$1,691,400}{1+12\%}\right]\\ =\$1,510,178.57\end{array}$

Therefore the present value of stock is $1,510,178.57

Determine the price of new shares

$\begin{array}{c}\mathrm{Pr}iceofNewShares=\left[\frac{\mathrm{Pr}esentValueofStock}{SharesOuts\tan ding}\right]\\ =\left[\frac{\$1,510,178.57}{\$25,000}\right]\\ =\$60.41\end{array}$

Therefore the price of new shares is $60.41

Determine the number of shares sold

$\begin{array}{c}NumberofSharesSold=\left[\frac{AmountRaise{d}_{Dollars}}{\mathrm{Pr}iceofNewShares}\right]\\ =\left[\frac{\$30,000}{\$60.41}\right]\\ =496.63or497shares\end{array}$

Therefore the number of shares sold is 497 shares