Question

Company X is expected to pay a dividend of $8.93 a year from now. This dividend is expected to grow at 15.3% for the next two years and at 9.97% forever after. The return that investors expect on X is 19.22%. Its payout ratio is 0.42

(a) What is X's stock price?

(b) What is X's P/E ratio?

(c) What will be the P/E ratio of X in one year from now?

Answer 1

This question requires application of dividend discount model, which can be mathematically represented for this question as:

where V3 is the terminal value which can be calculated as below:

D1 = $8.93

D2 = $8.93 * (1 + 15.3%) = $10.2963

D3 = $10.2963 * (1 + 15.3%) = $11.8716

D4 = $11.8716 * (1 + 9.97%) = $13.0552

V3 = $141.1375

V0 = 7.4903 + 7.2441 + 7.0059 + 83.2904

V0 = 105.0308

V0 = $105.03 (Answer a)

Based on infoprmation in question, payout ratio = 0.43

Dividend payout ratio = Dividend per share paid/Net Income per share

0.42 = 8.93/Net Income per share

Net Income per share = $21.2619

P/E Ratio = 105.0308/21.2619 = 4.94 (Answer b)

c) Now in order to calculate P/E ratio one year from now, we first need to calculate expected price one year from now.

V1 = 8.6364 + 8.3524 + 99.2989

V1 = 116.2877

Net Income per share = 10.2963/0.42 = $24.5150

P/E Ratio = 4.74