Question

Suppose that a firm’s recent earnings per share and dividend per share are $3.90 and $2.90, respectively. Both are expected to grow at 7 percent. However, the firm’s current P/E ratio of 20 seems high for this growth rate. The P/E ratio is expected to fall to 16 within five years.

Compute the dividends over the next five years. (Do not round intermediate calculations and round your final answers to 3 decimal places.)     Dividends Years   First year $3.10   Second year $3.32   Third year $3.55   Fourth year $3.80   Fifth year $4.07 Compute the value of this stock in five years. (Do not round intermediate calculations and round your final answer to 2 decimal places.)   Stock price $87.52

Calculate the price of this stock today, including all six cash flows at discount rate of 9 percent.

Present value

$ ?

Answer 1

(a)-Dividend over the next 5 years

Year	Dividend per share
First year [$2.90 x 107%]	$3.103
Second year [$3.103 x 107%]	$3.320
Third year [$3.320 x 107%]	$3.553
Fourth year [$3.553 x 107%]	$3.801
Fifth year [$3.801 x 107]	$4.067

(b)-Value of the Stock in 5 Years

Recent EPS = $3.90 per share

Growth Rate (g) = 7% per year

EPS after 5 years = EPS x (1 + g) ⁿ

= $3.90 x (1 + 0.07) ⁵

= $3.90 x 1.4026

= $5.47 per share

P/E ratio after 5 years = 16 Times

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

= $5.47 x 16 Times

= $87.52

“The value of this stock in five years = $87.52”

(c)-The Present Value of the Cash flows using 9% 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 ($)	PVIF at 9%	Stock price ($)
1	3.103	0.91743	2.85
2	3.320	0.84168	2.79
3	3.553	0.77218	2.74
4	3.801	0.70843	2.69
5	4.067	0.64993	2.64
5	87.52	0.64993	56.88
TOTAL			70.60

The Present Value of the Cash flows using 9% Discount Rate = $70.60”

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.