Data for all Dixon Corp. problems are the same. Dixon Corp. just paid out a dividend of $4.50 per share of common stock.  Analysts expect the dividend to grow by 17% over the coming three years, and then grow steadily at 5% for the foreseeable future after that.  Investors require a return of 8% on this stock. Dixon stock should be selling for _____ today.

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
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Data for all Dixon Corp. problems are the same. Dixon Corp. just paid out a dividend of $4.50 per share of common stock.  Analysts expect the dividend to grow by 17% over the coming three years, and then grow steadily at 5% for the foreseeable future after that.  Investors require a return of 8% on this stock. Dixon stock should be selling for _____ today.
Expert Solution
Step 1

Price of stock is the present value of future dividend and horizon value.

price of stock = PV of future dividend +PV of horizon value

Horizon value formula:

Horizon value =Dividend at the begining of constant growth rate year×1+gr-g

where, 

g = constant growth rate

r = rate of return

 

Step 2

given,

current dividend (D0) = $4.50

Non constant growth rate = 17% for 3 years

therefore dividend for next three years can be calculated as follows:

D1=$4.5 ×1+17%= $4.5 ×1.17=$5.27D2=$4.5 ×1+17%2=$4.5×1.172=$6.16D3=$4.5 ×1+17%3=$4.5×1.173=$7.21

AFTER YEAR 3 , 

growth becomes steady for perpetuity,

g = 5%

r =8%

Dividend at the beginning of constant growth rate 5% is $7.21

substituting values in formula for horizon value:

Horizon value =Dividend at the begining of constant growth rate year×1+gr-g=7.21×1+5%8%-5%=$252.25

 

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