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A common stock has just paid a dividend of $2.18/share. The dividend is expected to grow by 5.62% per year for 18 years.


A common stock has just paid a dividend of $2.18/share. The dividend is expected to grow by 5.62% per year for 18 years. After that the dividends will stay constant in perpetuity. The required rate of return on the stock is 16%. What should the price of the stock be today?

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Expert Solution

Computation of Price of the Stock

Answer : As per dividend discount model price of the share is present value of all future cash flow

Step 1 : Explicit Forecast period

Year

Dividend

PVIF @16%

Present Value

1

$2.30

0.862068966

$1.98

2

$2.43

0.743162901

$1.81

3

$2.57

0.640657674

$1.65

4

$2.71

0.552291098

$1.50

5

$2.87

0.476113015

$1.36

6

$3.03

0.410442255

$1.24

7

$3.20

0.35382953

$1.13

8

$3.38

0.305025457

$1.03

9

$3.57

0.26295298

$0.94

10

$3.77

0.226683603

$0.85

11

$3.98

0.1954169

$0.78

12

$4.20

0.168462844

$0.71

13

$4.44

0.14522659

$0.64

14

$4.69

0.125195336

$0.59

15

$4.95

0.107927014

$0.53

16

$5.23

0.093040529

$0.49

17

$5.52

0.080207353

$0.44

18

$5.83

0.06914427

$0.40

Total

$18.08

Step 2 : Horizon Value

Price at the end of Year 18 = D­19 / Re

                                         = 5.83 / 0.16

                                         = $ 36.44 approx

Price of the Stock Today = $ 36.44 * 0.06914427

                                        = $ 2.52 (approx)

       

Price of the Stock = Step 1 + Step 2

                          = $18.08 + $ 2.52

                         = $ 20.6 (approx.)

jeff jeffy answered 1 year ago
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