Question

Suppose that a firm’s recent earnings per share and dividend per share are $2.85 and $2.00, respectively. Both are expected to grow at 12 percent. However, the firm’s current P/E ratio of 21 seems high for this growth rate. The P/E ratio is expected to fall to 17 within five years.

Compute the dividends over the next five years

DIVIDENDS	YEARS
FIRST YEAR
SECOND YEAR
THIRD YEAR
FOURTH YEAR
FIFTH YEAR

Compute the value of this stock price in five years.

Calculate the present value of these cash flows using a 14 percent discount rate.

Answer 1

Dividend over the next 5 years

Year	Dividend per share ($)
First year [$2.00 x 112%]	2.240
Second year [$2.240 x 112%]	2.509
Third year [$2.509 x 112%]	2.810
Fourth year [$2.810 x 112%]	3.147
Fifth year [$3.147 x 112%]	3.525

Value of the Stock in 5 Years

Recent EPS = $2.85 per share

Growth Rate (g) = 12.00% per year

EPS after 5 years = EPS x (1 + g) ⁿ

= $2.85 x (1 + 0.12)⁵

= $2.85 x 1.76234

= $5.02267 per share

P/E ratio after 5 years = 17 Times

Therefore, the Value of the stock after 5 years = EPS x P/E Ratio

= $5.02267 per share x 17 Times

= $85.39 per share

The Present Value of the Cash flows using 14% Discount Rate

As per Dividend Discount Model, the Value of the Stock is the aggregate of the Present Value of the future dividend payments and the present value the stock price for the year 5

Year	Cash flow ($)	Present Value Factor (PVF) at 14.00%	Present Value of cash flows ($) [Cash flows x PVF]
1	2.240	0.87719	1.96
2	2.509	0.76947	1.93
3	2.810	0.67497	1.90
4	3.147	0.59208	1.86
5	3.525	0.51937	1.83
5	85.385	0.51937	44.35
TOTAL			53.83

Therefore, the Present Value of the Cash flows using 14% discount rate is $53.83

NOTE

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.