The current price of a certain non-dividend-paying stock is $120.00. The future 2 pri ce is characterized by the following probability distribution: EVENT PROBABILITY FUTURE PRICE P RETURN R
A 0.18 $180 ?
B 0.09 $108 ?
C 0.3 $90 ?
D 0.25 $81 ?
E ? $225
Calculate [i] the expected future price, [ii] the return in each of the five events, and [iii] Calculate l the expected return. Recall that for a stock which does not pay dividends, return is just ain divided by the initial price. Expected return can be calculated in two ways:
[a]: You could calculate the return to be realized in each of the five events, and then calculate the expected value of the return, or,
[b]: You could calculate the expected price first, and then use the possible fact that:
E(R) = E(P)/Po - 1

Non-Dividend-Paying Stock

i) Calculation of the expected future price:

EVENT   PROBABILITY   FUTURE PRICE P   RETURN R

A                 0.18                      $180                   $32.40

B                 0.09                     $108                     $9.72

C                 0.3                        $90                   $27.00

D                0.25                       $81                   $20.25

E                 0.18                    $225                   $40.50

Total           1.0                 $129.87                 $129.87

Future price = the expected returns = $129.87

ii) Calculation of the return in each of the five events:

EVENT   PROBABILITY   FUTURE PRICE P   RETURN R

A                 0.18                      $180                   $32.40

B                 0.09                     $108                     $9.72

C                 0.3                        $90                   $27.00

D                0.25                       $81                   $20.25

E                 0.18                    $225                   $40.50

iii) Calculation of the expected return:

EVENT   PROBABILITY   FUTURE PRICE P   RETURN R

A                 0.18                      $180                   $32.40

B                 0.09                     $108                     $9.72

C                 0.3                        $90                   $27.00

D                0.25                       $81                   $20.25

E                 0.18                    $225                   $40.50

Total           1.0                                                 $129.87

Explanation:

a) Data & Calculations:

EVENT   PROBABILITY   FUTURE PRICE P   RETURN R

A                 0.18                      $180                      ?

B                0.09                      $108                      ?

C                 0.3                        $90                      ?

D                0.25                       $81                      ?

E                  ?                        $225

If stock A does not pay dividend, it will attract capital appreciation which compensates for the unpaid dividends since the company has increased assets over liabilities.  When the assets grow more than the liabilities from the reinvestment of the profits, the net value of the business which is the equity increases.  This capital growth belongs to the stockholders and  is distributable to them in the form of the future price of the stock, which appreciates with the capital growth.