Question

Q5: A stock has just paid a dividend of 10. Dividends are expected to grow with 10% a year for the next 2 years. After that the company is expecting a constant growth of 2% a year. The required return on the stock is 10%. Determine today's stock price. (10 marks)

Answer 1

Compute the dividend at the end of year 2, using the equation as shown below:

Dividend = Just paid dividend*(1 + Growth rate)^Time

                = $10*(1 + 0.10)²

                = $12.10

Hence, the dividend at the end of year 2 will be $12.10.

Compute the stock price at the end of year 2, using the equation as shown below:

Stock price = Year 2 dividend*(1 + Growth rate)/ (Required rate – Growth rate)

                   = $12.10*(1 + 0.02)/ (10% - 2%)

                   = $12.342/ 8%

                   = $154.275

Hence, the stock price after 2 years will be $154.275.

Compute the dividend at the end of year 1, using the equation as shown below:

Dividend = Just paid dividend*(1 + Growth rate)^Time

                = $10*(1 + 0.10)¹

                = $11

Hence, the dividend at the end of year 1 will be $11.

Compute the current stock price, using Ms-excel as shown below:

3 A B C D E Stock Price 4 Year Particulars Amount PVIF Present Value 51 Dividend 11 =POWER(1/1.1,B5) =D5*E5 6 2 Dividend 12.1 =POWER(1/1.1,36) =D6*E6 Stock Price 154.275 =POWER(1/1.1,B7) =D7*E7 | Stock price =SUM(F5:F7)

The result of the above excel table is as follows:

3 B C D E F Stock Price Year Particulars Amount PVIF Present Value 1 Dividend $11.000 0.909090909 $ 10.00 2 Dividend $ 12.100 0.826446281 $10.00 2 Stock Price $ 154.275 0.826446281 $ 127.50 Stock price $ 147.50

Hence, the current stock price is $147.50.