Assume Gillette Corporation will pay an annual dividend of $0.65 one year from now. Analysts expect this dividend to grow at 12% per year thereafter until the fifth year. After then, growth will level off at 2% 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%?

In order to find Gillette's value of a share we need to use the multi stage model and find what will its dividend be at the end of the 5th year

The dividend of the first 5 years can be calculated by multiplying the previous one by 1.12

Dividend 1 year from now = 0.65

Dividend 2 years from now = 0.65*1.12=0.728

Dividend 3 years from now=0.728*1.12=0.81536

Dividend 4 years from now = 0.81536*1.12 = 0.913203

Dividend 5 years from now=0.91320.*1.12 = 1.022788

After this the growth level will be 2% so we can find the 6th years dividend by multiplying 1.022788 by 1.02 and we will get 1.043243

Now we can calculate the share price will be after 5 years by using the DDM

D1 / (R-G)

D1 = 1.0432

R = 0.08

G = 0.02

1.0432/0.06 = 17.38

Now in order to find the current price we need to discount this price to find the present value we can do this by using its cost of capital as the discount rate.

17.38/1.08^5

=12.98735