Question

Suppose that a firm’s recent earnings per share and dividend per share are $3.30 and $2.30, respectively. Both are expected to grow at 9 percent. However, the firm’s current P/E ratio of 32 seems high for this growth rate. The P/E ratio is expected to fall to 28 within five years. Compute the dividends over the next five years. Compute the value of this stock in five years. Calculate the present value of these cash flows using an 11 percent discount rate.

Answer 1

Dividends over the next five years

Years	Dividend per share
First year [$2.30 x 1.09]	$2.507
Second year [$2.507 x 1.09]	$2.733
Third year [$2.733 x 1.09]	$2.979
Fourth year [$2.979 x 1.09]	$3.247
Fifth year [$3.247 x 1.09]	$3.539

Value of this stock in five years

EPS for the year 5 = Current Year EPS x (1 + Growth Rate)⁵

= $3.30 x (1 + 0.09) ⁵

= $3.30 x 1.53862

= $5.077 per share

P/E Ratio after 5 years = 28 Times

Therefore, the Value of this stock in five years

= EPS in Year 5 x P/E Ratio after 5 years

= $5.077 per share x 28 Times

= $142.17 per share

“Value of this stock in five years = $142.17 per share”

Present value of these cash flows using a 11 percent discount rate

Year	Annual Cash Flow ($)	Present Value factor at 11%	Present Value of Cash Flow ($)
1	2.507	0.90090	2.26
2	2.733	0.81162	2.22
3	2.979	0.73119	2.18
4	3.247	0.65873	2.14
5	3.539	0.59345	2.10
5	142.17	0.59345	84.37
TOTAL			95.26

“The Present value of these cash flows using a 11 percent discount rate = $95.26 per share”

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.