Question

Miller Corporation's next dividend is expected to be $7. Dividend growth is estimated at 22%, 20%, 10% and then expected to stabilize to 3%. The required rate of return is 10%.

a.    Calculate the dividend in the first, second, third, fourth and fifth years. Show all your work. (1 point)

b.    Using your answers in a), calculate what price would you be willing to pay for this stock today. Show all your work. (2 points)

Answer 1

a. Dividend in first year is as follows:

= Next dividend i.e. $ 7

Dividend in second year is as follows:

= $ 7 x 1.22

= $ 8.54

Dividend in third year is as follows:

= $ 8.54 x 1.20

= $ 10.248

Dividend in forth year is as follows:

= $ 10.248 x 1.10

= $ 11.2728

Dividend in fifth year is as follows:

= $ 11.2728 x 1.03

= $ 11.610984

b. The price is as follows:

= Dividend in year 1 / (1 + required rate of return)¹ + Dividend in year 2 / (1 + required rate of return)² + Dividend in year 3 / (1 + required rate of return)³ + Dividend in year 4 / (1 + required rate of return)⁴ + 1 / (1 + required rate of return)⁴ x [ (Dividend in year 5 / (required rate of return - growth rate) ]

= $ 7 / 1.10 + $ 8.54 / 1.10² + $ 10.248 / 1.10³ +$ 11.2728 / 1.10⁴ + 1 / 1.10⁴ x [ $ 11.610984 / (0.10 - 0.03) ]

= $ 7 / 1.10 + $ 8.54 / 1.10² + $ 10.248 / 1.10³ +$ 11.2728 / 1.10⁴ + $ 165.8712 / 1.10⁴

= $ 7 / 1.10 + $ 8.54 / 1.10² + $ 10.248 / 1.10³ + $ 177.144 / 1.10⁴   

= $ 142.11