Newman Manufacturing is considering a cash purchase of the stock of Grips Tool. During the year just​ completed, Grips earned​$3.95per share and paid cash dividends of​$2.25per share​(D0equals=$ 2.25​).​ Grips' earnings and dividends are expected to grow at25​%per year for the next 3​ years, after which they are expected to grow6​%per year to infinity. What is the maximum price per share that Newman should pay for Grips if it has a required return of11​%on investments with risk characteristics similar to those of​ Grips?

Question
Asked Nov 21, 2019
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Newman Manufacturing is considering a cash purchase of the stock of Grips Tool. During the year just​ completed, Grips earned

​$3.95

per share and paid cash dividends of

​$2.25

per share

​(D0equals=$ 2.25​).

​ Grips' earnings and dividends are expected to grow at

25​%

per year for the next 3​ years, after which they are expected to grow

6​%

per year to infinity. What is the maximum price per share that Newman should pay for Grips if it has a required return of

11​%

on investments with risk characteristics similar to those of​ Grips?  

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Expert Answer

Step 1

It is given that,

Growth rate for first three year is 25%.

Growth rate after three year is 6%.

Last paid dividend is $2.25 per share.

Required rate of return is 11%.

The below expression can be used to calculate present value for first three dividend payments:

dz
(1+f (1+i (1+)
dx(1+g) dx(1+g,)
(1+)
Present value
(1+1)
dx(1+8)
(1+i)
Here
d is last dividend.
8 is dividend growth in first three years
is required rate of return
help_outline

Image Transcriptionclose

dz (1+f (1+i (1+) dx(1+g) dx(1+g,) (1+) Present value (1+1) dx(1+8) (1+i) Here d is last dividend. 8 is dividend growth in first three years is required rate of return

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Step 2

Substitute $2.25 for d, 25% for g and 11% for i in the above formula,

$2.25x (1+25%)$2.25x (1+25%)
(1+1196)
$2.25x (1+25%)
(1+11 6)
$2.8125 $3.515625 $4.39453125
(1+119%)
Present value
1.11
1.2321
1.367631
=$2.54+$2.85+ $3.21
=$8.60
help_outline

Image Transcriptionclose

$2.25x (1+25%)$2.25x (1+25%) (1+1196) $2.25x (1+25%) (1+11 6) $2.8125 $3.515625 $4.39453125 (1+119%) Present value 1.11 1.2321 1.367631 =$2.54+$2.85+ $3.21 =$8.60

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Step 3

The below expression can be used to calculate the present value of ...

(1+ 8)
dx
ke - 82
1
Present value
(1+)
Here
d, is third dividend payment,
82 is growth rate after third year
ke is required rate of return
help_outline

Image Transcriptionclose

(1+ 8) dx ke - 82 1 Present value (1+) Here d, is third dividend payment, 82 is growth rate after third year ke is required rate of return

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