Question

Davidson, Inc. is experiencing a period of rapid growth. Davidson will pay a dividend of $1.25 a share in one year from today. Dividends are expected to grow at 25% in the second year and at 20% in the third year. However, as a result of competition, dividends are expected to grow at a constant rate of 5% (per year) thereafter. The equity cost of capital is 15%. (12 points)

a) What are the dividends over the next four years? b) Compute the value (today) of a share of the stock.

Please show all work

Answer 1

a. Dividend in year 1 is $ 1.25

Dividend in year 2 will be as follows:

= $ 1.25 x 1.25

= $ 1.5625

Dividend in year 3 will be as follows:

= $ 1.25 x 1.25 x 1.20

= $ 1.875

Dividend in year 4 will be as follows:

= $ 1.25 x 1.25 x 1.20 x 1.05

= $ 1.96875

b. The price is computed as shown below:

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

= $ 1.25 / 1.15 + $ 1.5625 / 1.15² + $ 1.875 / 1.15³ + 1 / 1.15³ x [ $ 1.96875 / (0.15 - 0.05) ]

= $ 1.25 / 1.15 + $ 1.5625 / 1.15² + $ 21.5625 / 1.15³

= $ 16.45 Approximately

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