Question

Suppose that a firm’s recent earnings per share and dividend per share are $2.75 and $1.80, respectively. Both are expected to grow at 10 percent. However, the firm’s current P/E ratio of 19 seems high for this growth rate. The P/E ratio is expected to fall to 15 within five years.

Compute the dividends over the next five years. (Do not round intermediate calculations. Round your answers to 3 decimal places.)

  

Compute the value of this stock price in five years. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  

Calculate the present value of these cash flows using a 12 percent discount rate. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

(a)-Dividend over the next 5 years

Year	Dividend per share
First year [$1.80 x 110%]	$1.980
Second year [$1.980 x 110%]	$2.178
Third year [$2.178 x 110%]	$2.396
Fourth year [$2.396 x 110%]	$2.635
Fifth year [$2.635 x 110%]	$2.899

(b)-Value of the Stock in 5 Years

Recent EPS = $2.75 per share

Growth Rate (g) = 10% per year

EPS after 5 years = EPS x (1 + g) ⁿ

= $2.75 x (1 + 0.10) ⁵

= $2.75 x 1.61051

= $4.4289 per share

P/E ratio after 5 years = 15 Times

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

= $4.4289 x 15 Times

= $66.43 per share

“The value of this stock in five years = $66.43”

(c)-The Present Value of the Cash flows using 12% 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 ($)	Present Value Factor at 10%	Stock price ($)
1	1.980	0.89286	1.77
2	2.178	0.79719	1.74
3	2.396	0.71178	1.71
4	2.635	0.63552	1.67
5	2.899	0.56743	1.64
5	66.43	0.56743	37.70
TOTAL			46.23

The Present Value of the Cash flows using 12% Discount Rate = $46.23”

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.