Chapter 13, Problem 18PS

Summary Introduction

(a)

To determine:

Price and P/E ratio at which the firm would sell.

Introduction:

P/E ratio defines the relationship between EPS and market price of share of a company. It is also known as price multiple or earning multiple. It is calculated simply by dividing market price of share by EPS.

Answer to Problem 18PS

The Market Price will be $23.33.

The P/E ratio will be $11.67

Explanation of Solution

Given Information:

Projected ROE = 20%

Plowback ratio = 0.30

E1= $2 per share

Rate of return on the stock = 12%

  $\begin{array}{l}\text{=> g = ROE × b}\hfill \\ \text{=> g = 0}\text{.20 × 0}\text{.30}\hfill \\ \text{=> g = 6\%}\hfill \\ {\text{=> D}}_{\text{1}}\text{= \$2 }\left(\text{1 - b}\right)\hfill \\ {\text{=> D}}_{\text{1}}\text{= \$2 }\left(\text{1 - 0}\text{.30}\right)\hfill \\ {\text{=> D}}_{\text{1}}\text{= \$1}\text{.40}\hfill \\ {\text{=> P}}_{\text{0}}\text{= }\frac{{\text{D}}_{\text{1}}}{\left(\text{k - g}\right)}\hfill \\ {\text{=> P}}_{\text{0}}\text{= }\frac{\text{\$1}\text{.40}}{\left(\text{0}\text{.12 - 0}\text{.06}\right)}\hfill \\ {\text{=> P}}_{\text{0}}\text{= \$23}\text{.33}\hfill \\ \text{=> P/E ratio= }\frac{\text{\$23}\text{.33}}{\text{\$2}}\hfill \\ \text{=> P/E ratio= 11}\text{.67}\hfill \end{array}$

Summary Introduction

(b)

To determine:

The present value of growth opportunity

Introduction:

Present Value of Growth Opportunity describes the element of stock price that states to the expectations of investors of growth in earnings.

Answer to Problem 18PS

The PVGO will be $6.66

Explanation of Solution

Given Information:

The Market Price = $23.33.

The P/E ratio = $11.67

Projected ROE = 20%

Plowback ratio = 0.30

E1= $2 per share

Rate of return on the stock = 12%

PVGO will be calculated as under:

  $\begin{array}{l}{\text{=> PVGO = P}}_{\text{0}}\text{- }\left\{{\text{E}}_{\text{0}}\text{/ k}\right\}\hfill \\ \text{=> PVGO = \$23}\text{.33- }\left\{\text{\$2 / 0}\text{.12}\right\}\hfill \\ \text{=> PVGO = \$6}\text{.66}\hfill \end{array}$

Summary Introduction

(c)

To determine:

The P/E ratio and the present value of growth opportunities if the firm planned to reinvest only 20% of its earning.

Introduction:

P/E ratio defines the relationship between EPS and market price of share of a company. It is also known as price multiple or earning multiple. It is calculated simply by dividing market price of share by EPS.

Present Value of Growth Opportunity describes the element of stock price that states to the expectations of investors of growth in earnings.

Answer to Problem 18PS

The P/E ratio will be 10

The PVGO will be $ 3.33

Explanation of Solution

Given Information:

The Market Price = $23.33.

The P/E ratio = $11.67

Projected ROE = 20%

Reinvestment ratio =20%

E1= $2 per share

Rate of return on the stock = 12%

  $\begin{array}{l}{\text{=> D}}_{\text{1}}\text{= \$2 }\left(\text{1 - b}\right)\hfill \\ {\text{=> D}}_{\text{1}}\text{= \$2 }\left(\text{1 - 0}\text{.20}\right)\hfill \\ {\text{=> D}}_{\text{1}}\text{= \$1}\text{.60}\hfill \\ {\text{=> P}}_{\text{0}}\text{= }\frac{{\text{D}}_{\text{1}}}{\left(\text{k - g}\right)}\hfill \\ {\text{=> P}}_{\text{0}}\text{= }\frac{\text{\$1}\text{.60}}{\left(\text{0}\text{.12 - 0}\text{.04}\right)}\hfill \\ {\text{=> P}}_{\text{0}}\text{= \$20}\text{.00}\hfill \\ \text{=> P/E ratio= }\frac{\text{\$20}\text{.00}}{\text{\$2}}\hfill \\ \text{=> P/E ratio= 10}\hfill \\ {\text{=> PVGO = P}}_{\text{0}}\text{- }\left\{{\text{E}}_{\text{0}}\text{/ k}\right\}\hfill \\ \text{=> PVGO = \$20}\text{.00- }\left\{\text{\$2 / 0}\text{.12}\right\}\hfill \\ \text{=> PVGO = \$3}\text{.33}\hfill \end{array}$