Chapter 9, Problem 17P

### 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

# CONSTANT GROWTH Your broker offers to sell you some shares of Bahnsen & Co. common stock that paid a dividend of $2.00 yesterday. Bahnsen’s dividend is expected to grow at 5% per year for the next 3 years. If you buy the stock, you plan to hold it for 3 years and then sell it. The appropriate discount rate is 12%. a. Find the expected dividend for each of the next 3 years; that is, calculate D1, D2, and D3. Note that D0 =$2.00. b. Given that the first dividend payment will occur 1 year from now, find the present value of the dividend stream; that is, calculate the PVs of D1, D2, and D3, and then sum these PVs. c. You expect the price of the stock 3 years from now to be $34.73; that is, you expect P ^ 3 to equal$34.73. Discounted at a 12% rate, what is the present value of this expected future stock price? In other words, calculate the PV of $34.73. d. If you plan to buy the stock, hold it for 3 years, and then sell it for$34.73, what is the most you should pay for it today? e. Use Equation 9.2 to calculate the present value of this stock. Assume that g = 5% and that it is constant. f. Is the value of this stock dependent upon how long you plan to hold it? In other words, if your planned holding period was 2 years or 5 years rather than 3 years, would this affect the value of the stock today, P ^ 0 ? Explain.

a.

Summary Introduction

To compute: The expected dividend for the next three years.

Introduction:

Constant Growth:

The change in the estimated values across different time period is depicted as the growth during that period. When that growth is uniform for each period then it is  termed as the constant growth.

Explanation

Year1:

Given,

Previous dividend is $2. Dividend growth rate is 5% each year. Formula to compute the expected dividend, D1=D0(1+g) Where, • D1 is the dividend for year1. • D0 is the previous dividend. • g is the growth rate. Substitute$2 for D0 and 5% for g

D1=$2(1+0.05)=$2.1

Year2:

Given,

Previous dividend is \$2.1.

Dividend growth rate is 5% each year.

Formula to compute the expected dividend,

D2=D1(1+g)

Where,

• D2 is the dividend for year 2.
• D1 is the previous dividend

b.

Summary Introduction

To compute: The present value of expected dividends of next three years.

c.

Summary Introduction

To compute: The present value of expected stock price after three years.

d.

Summary Introduction

To compute: The price to be paid for the stock today.

e.

Summary Introduction

To compute: The present value of the stock with constant growth rate of 5%.

f.

Summary Introduction

To identify: The change in present values based on the tenure to hold it.

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