What would an investor be willing to pay for common stock in a firm that is expe

Question

What would an investor be willing to pay for common stock in a firm that is expected to pay an annual dividend that will grow at 10 percent over the next 2 years, then grow at 5 percent for 3 years and then stop growing (i.e., will grow at zero percent) from then on? The firm just paid its dividend of $2.00. Thus, if an investor buys this stock, they will not receive the dividend that was just paid. The next dividend will be paid in one year. The required rate of return is an effective annual rate of 10%

                                                                              PV= of ___ annuity that starts a

                  Time            DIV                      PV at t = 0     

                    0                  

                    1              

2

3

4

           

5

6

7

8

9

10

PV =

2

3

4

           

5

6

7

8

9

10

PV =

Explanation / Answer

We need to determine the present value of dividends expected to be recieved in the next years in order to calculate the value of common stock. The value of stock will be calculated with use of following formula:

Value of Stock = D1/(1+Required Return)^1 + D2/(1+Required Return)^2 + D3/(1+Required Return)^3 + D4/(1+Required Return)^4 + D5/(1+Required Return)^5

___________

Solution:

To solve, we have to calculate the dividend per year. The details of dividend per year are as follows:

D1 = 2*(1+10%)^1

D2 = 2*(1+10%)^2

D3 = 2*(1+10%)^2*(1+5%)^1

D4 = 2*(1+10%)^2*(1+5%)^2

D5 = 2*(1+10%)^2*(1+5%)^3

Using these values in the above formula, we get,

Value of Stock (Present Value) = 2*(1+10%)^1/(1+10%)^1 + 2*(1+10%)^2/(1+10%)^2 + 2*(1+10%)^2*(1+5%)^1/(1+10%)^3 + 2*(1+10%)^2*(1+5%)^2/(1+10%)^4 + 2*(1+10%)^2*(1+5%)^3/(1+10%)^5 = $9.47 (answer)

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