In 6 years, the P/E ratio is expected to be 25 and the payout ratio to be 80%. What is the current stock price when using the P/E ratio

Complete Question:

A stock just paid an annual dividend of $7.7. The dividend is expected to grow by 5% per year for the next 6 years. In 6 years, the P/E ratio is expected to be 25 and the payout ratio to be 80%.

The required rate of return is 8%.

What should be the current stock price?

$245.10

Explanation:

As we know that:

P/E = Market Price of Stock / Earning Per Share

Here

P/E is 25 time

Earning Per Share is $12.9 per share (Step1)

By putting values, we have:

25 Times = Market Price of Stock / $15.6 per share

25 Times  *  $12.9 per share   = Market Price of Stock

Market Price of Stock = $322.5 per share

Present value computation for first 6 years:

Yrs   Future Cash flow      Discount Factor    Present Value

1       $7.7 *(1.05)^1                     0.926                      7.49

2      $7.7 *(1.05)^2                    0.857                       7.28

3      $7.7 *(1.05)^3                     0.794                      7.08

4      $7.7 *(1.05)^4                     0.735                      6.88

5      $7.7 *(1.05)^5                     0.681                       6.69

6      $7.7 *(1.05)^6  + $322.5   0.630                     209.68

Present value of stock                                          $245.10

Step1: Find Earning Per Share

As we know that:

Earning Per Share = Dividend / Payout Ratio

Here

Dividend after 6 years = $7.7 (1 + 5%)^6 = $10.32 per share

Payout Ratio = 80% = 0.8

By putting values, we have:

EPS = $10.32 / 0.8 = $12.9 per share

answer; dogs;