Suppose a firm is expected to increase dividends by 20% in one year and by 15% in two years. After that, dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock

&9.66

Explanation:

From the question, we have:

Year 0 dividend = The last dividend = $1

Year 1 dividend = Year 0 dividend × (1 + expected increase in dividends in one year)

Year 1 dividend = $1 × (1 + 0.20) = $1 × 1.20 = $1.20

Year 2 dividend = Year 1 dividend × (1 + expected increase in dividends in two years)

Year 2 dividend = $1.20 × (1 + 0.15) = $1.20 × 1.15 = $1.38

Since, dividends will increase at a rate of 5% per year indefinitely, Year 3 dividend can be calculated as follows:

Year 3 dividend = Year 3 dividend × (1 + expected increase in dividends in three years)

Year 3 dividend = $1.38 × (1 + 0.05) = $1.38 × 1.05 = $1.449

To now calculate the price of the stock, we use the formula for the dividend discount model stated as follows:

P = Year 3 dividend ÷ (r - g) (1)

Where,

P = stock price = ?

r = required return = 20% = 0.20

g = growth rate = 5% = 0.05

Substituting the values into equation (1), we have:

P = 1.449 ÷ (0.20 - 0.05) = 1.449 ÷ 0.15 = $9.66

Therefore, the price of the stock is $9.66.

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