If Target Corp. (TGT) recently earned a profit of $6.07 earnings per share and has a P/E ratio of 16.5. The dividend has been growing at a 10 percent rate over the past few years. If this growth continues, what would be the stock price in five years if the P/E ratio remained unchanged? What would the price be if the P/E ratio increased to 18 in five years?

a)P_5 = $161.3

b) P'_5 = $176

Step-by-step explanation:

Given:

- The earnings per share today Eo = $6.07

- The P/E ratio = 16.5

- The growth rate of dividend R = 10 %

Find:

a) What would be the stock price in five years if the P/E ratio remained unchanged?

b) What would the price be if the P/E ratio increased to 18 in five years?

Solution:

- The factor of increase per year of dividend can be determined:

                          1  > 100

                          x   > 110

                          x = 110*1 / 100 = 1.1

- The value of earnings/ share in n number of years time is given by:

                          E_n = Eo*x^n

                          E_5 = $6.07*1.1^5

                          E_5 = $9.7757957

- The Price of the stock is expressed by the ratio:

                          P_n / E_n = 16.5

                          P_5 = 16.5*E_5

                          P_5 = 16.5*$9.7757957

                          P_5 = $161.3

- If the P/E ratio decreases to 18 in 5 years then stock price while earnings increased at rate of 10% is:

                          P'_5 = 18*$9.7757957

                          P'_5 = $176

m∠a is 90°

m∠b is 40°