Question

It announces that it plans to pay dividends of $1 per share exactly three years from now and $2 per share exactly four years from now. From year 5 onwards, dividends are expected to grow at a constant rate of 10% per year. The company pays no dividends in years one and two. The risk-free rate is 5%, the company's beta is 1.5 and the expected return on the market is 11%. Calculate the price of this stock at time period 4, P4

Answer 1

The Question is incomplete.

The complete question is as follows:

It announces that it plans to pay dividends of $1 per share exactly three years from now and $2 per share exactly four years from now. From year 5 onwards, dividends are expected to grow at a constant rate of 10% per year. The company pays no dividends in years one and two. The risk-free rate is 5%, the company's beta is 1.5 and the expected return on the market is 11%. Calculate the price of this stock today

Answer:

Price of stock =  $34.42

Explanation:

The Dividend Valuation Model is a technique used to value the worth of an asset. According to this model, the worth of an asset is the sum of the present values of its future cash flows discounted at the required rate of return.

Required rate of return

Using the CAPM , the rate of return on equity can be determined as follows:

E(r)= Rf +β(Rm-Rf)

E(r) =? , Rf- 5%, Rm- 11%, β- 1.5

Ke = 5% + 1.5× (11-5)%

   = 14%

Present value of Dividends(PV)

Year                                                      PV

3                       $1.00, × (1.14^(-3) =   0.6749

4                        $2.00× 1.14^(-4) =  1.18416

5 and beyond

This will be done in two (2) steps as follows:

PV in year 4 = (2 × 1.10) /(0.14-0.1) = 55

PV in year 0 = 55× 1.14^(-4) = 32.56

Price of stock

=  0.6749  +  1.18416 + 32.56

=  $34.423