Question

ABG Corporation has the following dividend forecasts for the next three years: Year Expected Dividend 1 $ .25 2 $ .50 3 $ 1.25 After the third year, the dividend will grow at a constant rate of 5% per year. The required return is 10%. What is the price of the stock today?

Answer 1

Price of share today = $21.302

Step-by-step explanation:

The price of a share can be calculated using the dividend valuation model

According to this model the value of share is equal to the sum of the present values of its future cash dividends discounted at the required rate of return.

If dividend is expected to grow at a given rate , the value of a share is calculated using the formula below:

Price=Do (1+g)/(k-g)

Do - dividend in the following year, K- requited rate of return , g- growth rate

Step 1 : PV of dividend from year 1 to 3

Year PV of Dividend

1 0.25 × 1.1^(-1) = 0.227

2 0.50 × 1.1^(-2) = 0.413

3 1.25 × 1.1^(-3) = 0.939

Strep 2 : PV of dividend from year 4 to infinity

PV (in year 3 terms) of dividend= 1.25 × 1.05/(0.1-0.05) = 26.25

PV in year 0 terms = 26.25 × 1.1^(-3) = 19.72

Present Value = 0.227 + 0.413 + 0.939 + 19.72 = 21.302

Price of share today = $21.302