Chapter 5, Problem 3Q

### Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250

Chapter
Section

### Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250
Textbook Problem

# If a firm’s earnings per share grew from $1 to$2 over a 10-year period, the total growth would be 100%, but the annual growth rate would be less than 10%. True or false? Explain. (Hint: If you aren’t sure, plug in some numbers and check it out.)

Summary Introduction

To explain: Whether the statement is true or false and the reason for it.

Introduction:

Annual growth rate: An annual growth rate refers to that rate which represents the average change in the value of the investment. It is determined for a year. This growth rate is a tool to measure the trends of investment and is commonly used by the investors and users.

Explanation

Given,

The earnings per share grew from $1 to$2.

The time period is 10 years.

The total growth rate is 100%.

The annual growth rate is less than 10%

Calculation of the total growth rate:

The formula to calculate the total growth rate is:

TotalāGrowthāRate=(EndingāBalanceāBeginningāBalanceBeginningāBalanceĆ100)

Substitute ending balance as $2 and beginning balance as$1 in the above formula,

TotalāGrowthāRate=($2ā$1\$1Ć100)=100%

The total growth rate is 100%

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