Assume Gillette Corporation will pay an annual dividend of $ 0.61 one year from now. Analysts expect this dividend to grow at 12.9 % per year thereafter until the 6th year. Thereafter, growth will level off at 1.7 % per year. According to the dividend-discount model, what is the value of a share of Gillette stock if the firm's equity cost of capital is 8.8 % ?

what is the value of a share of Gillette stock if the firm's equity cost of capital is 8.8 % ?

$ 13,36

Explanation:

First it's necessary to find the present value of the annual dividend paid during the next 6 years, which is calculate by the formula of the Present Value.

PV = Dt / (1+r) ^t, it means that each Dividend at the year "t" will be value with the rate r calculated a this same moment "t".

Will pay an annual dividend of $ 0.61 one year from now. Analysts expect this dividend to grow at 12.9 % per year thereafter until the 6th year.

Year 1

0,61 = Div

1,09 = (1+0,88) ^1

0,56 = Div/1,09

Year 2

0,69 = Div Year 1 (0,61) * 1,129, because increase at 12,9% by year

1,18 = (1+0,88) ^2

0,58 = Div/1,18

Year 3

0,78 = Div Year 2 (0,69) * 1,129, because increase at 12,9% by year

1,29 = (1+0,88) ^3

0,60 = Div/1,18

Year 4

0,88 = Div Year 3 (0,78) * 1,129, because increase at 12,9% by year

1,24 = (1+0,88) ^4

0,63 = Div/1,24

Year 5

0,99 = Div Year 4 (0,88) * 1,129, because increase at 12,9% by year

1,52 = (1+0,88) ^5

0,65 = Div/1,52

Year 6

1,12 = Div Year 5 (0,99) * 1,129, because increase at 12,9% by year

1,66 = (1+0,88) ^6

0,67 = Div/1,66

PV of 6 Years = 0,56 + 0,58 + 0,60 + 0,63 + 0,65 + 0,67 = $3,70

Thereafter, growth will level off at 1.7 % per year.

To this second part the model indicates that de dividend is calculated by = Dividend / (Rate-Growth), which means that if a dividend grows forever, we applied the perpetuity formula where dividend growth it's applied as negative to the discount rate.

Year 6

1,14 = Div Year 6 (1,12) * 1,017, thereafter will growth at 1,7% by year.

7,1% = (8,8%-1-7%) Discount rate less growth of dividend.

16,03 = Div/0,071 = In this case we use the rate not the 1+rate.

This value it's calculated at the moment of Year 7, we need to apply the Present Value to calculate the actual value, which is:

16,03 = Perpetuity calculated before until year 6.

1,66 = Discount Rate applied this year.

9,66 = Present Value of the Dividen which grows forever at 1,7%

TOTAL Value of Share = PV of 6 Years + PV Perpetuity =

$3,70 + $9,66=$13,36