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A common stock has just payed a dividend of $2.32/share. The dividend is expected to grow...

A common stock has just payed a dividend of $2.32/share. The dividend is expected to grow by 16% for the coming 28 years. After that, the growth rate in dividend is expected to be 4.28% per year in perpetuity. The RRR on the stock is 12.82%. What is the value of the stock today?

Solutions

Expert Solution

The Value of the stock today is the Present Value of Future Cash flows (ie, Present value of future dividend payments plus Present value of Stock price in year 28)

Dividend in Year 28 (D28)

Dividend in Year 28 (D28) = D1 x (1 + g)n

= $2.32 x (1 + 0.16)28

= $2.32 x 63.800445

= $148.0170 per share

Price of the Stock in Year 28 (P28)

Price of the Stock in Year 28 (P28) = D28(1 + g) / (RRR – g)

= $148.0170(1 + 0.0428) / (0.1282 – 0.0428)

= $154.3522 / 0.0854

= $1,807.40

The Value of the stock today

As per Dividend Discount Model, the price of the stock today Present Value of the future dividend payments and the present value the Price of the Stock in Year 28

Year

Cash flow ($)

Present Value Factor at 12.82%

Present Value ($)

1

2.6912 [D0 x 116%]

0.88637

2.39

2

3.1218 [D1 x 116%]

0.78565

2.45

3

3.6213 [D2 x 116%]

0.69637

2.52

4

4.2007 [D3 x 116%]

0.61724

2.59

5

4.8728 [D4 x 116%]

0.54710

2.67

6

5.6524 [D5 x 116%]

0.48493

2.74

7

6.5568 [D6 x 116%]

0.42983

2.82

8

7.6059 [D7 x 116%]

0.38099

2.90

9

8.8229 [D8 x 116%]

0.33770

2.98

10

10.2345 [D9 x 116%]

0.29932

3.06

11

11.8721 [D10 x 116%]

0.26531

3.15

12

13.7716 [D11 x 116%]

0.23516

3.24

13

15.9750 [D12 x 116%]

0.20844

3.33

14

18.5310 [D13 x 116%]

0.18475

3.42

15

21.4960 [D14 x 116%]

0.16376

3.52

16

24.9354 [D15 x 116%]

0.14515

3.62

17

28.9250 [D16 x 116%]

0.12866

3.72

18

33.5530 [D17 x 116%]

0.11404

3.83

19

38.9215 [D18 x 116%]

0.10108

3.93

20

45.1490 [D19 x 116%]

0.08959

4.05

21

52.3728 [D20 x 116%]

0.07941

4.16

22

60.7524 [D21 x 116%]

0.07039

4.28

23

70.4728 [D22 x 116%]

0.06239

4.40

24

81.7485 [D23 x 116%]

0.05530

4.52

25

94.8282 [D24 x 116%]

0.04902

4.65

26

110.0008 [D25 x 116%]

0.04345

4.78

27

127.6009 [D26 x 116%]

0.03851

4.91

28

148.0170 [D27 x 116%]

0.03413

5.05

28

1,807.40

0.03413

61.69

TOTAL

161.37

“Therefore, the value of the stock today will be 161.37 per share”

NOTE

The Formula for calculating the Present Value Factor is [1/(1 + r)n], Where “r” is the Discount/Interest Rate and “n” is the number of years.

jeff jeffy answered 8 months ago
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