The last dividend paid by Abbot Labs was $1.00. Abbot's growth rate is expected to be a constant 8% for three years, after which the growth rate is expected to be 10%. Investors require a return of 16% on stocks like Abbot. What should the price of Abbot's stock be?

Question

Quizplus · Accepted Answer

Using the Dividend Discount Model, we can calculate the price of Abbot's stock as follows:

P = D1 / (r - g)

where:
D1 = next year's dividend = D0 * (1 + g) = $1.08
r = required rate of return = 16%
g = growth rate in year 1-3 = 8%
g2 = growth rate in year 4 onwards = 10%

We can calculate the dividends and price for each year:

Year 1: D1 = $1.08
Year 2: D2 = $1.08 * (1 + 8%) = $1.1664
Year 3: D3 = $1.1664 * (1 + 8%) = $1.25971
Year 4: D4 = $1.25971 * (1 + 10%) = $1.38568

Using the above formula and the dividend values, we can calculate the price of Abbot's stock:

P = D1 / (r - g) + D2 / ( (r - g) * (1 + r - g)^1) + D3 / ( (r - g) * (1 + r - g)^2) + D4 / ( (r - g) * (1 + r - g)^3)

P = $1.08 / (16% - 8%) + $1.1664 / ( (16% - 8%) * (1 + 16% - 8%)^1) + $1.25971 / ( (16% - 8%) * (1 + 16% - 8%)^2) + $1.38568 / ( (16% - 10%) * (1 + 16% - 10%)^3)

P = $17.40

Therefore, the price of Abbot's stock should be $17.40. The correct answer is D.

The Last Dividend Paid by Abbot Labs Was $1