Answer:
what is the value of a share of Gillette stock if the firm's equity cost of capital is 8.8 %?
$ 13,36
Step-by-step 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