Question

The stock of Business Adventures sells for $50 a share. Its likely dividend payout and end-of-year price depend on the state of the economy by the end of the year as follows: Dividend Stock Price Boom $3.00 $60 Normal economy 1.20 58 Recession 0.75 49 a. Calculate the expected holding-period return and standard deviation of the holding-period return. All three scenarios are equally likely. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

Answer:

Holding period return = 14.49%, Standard Deviation = 11.08 approx

Explanation:

Eco Scenario    Dividend     Stock Price  HPR    Prob     Expected HPR

Boom                         3                 60         26        0.33        8.58

Normal                       1.2               58        18.4       0.33       6.072

Recession                  0.75            49        (0.5)      0.33       (0.165)

              Expected HPR                                                       14.49%

Calculation Of Standard Deviation

                                      (A)                     (B)           (A) - (B)  

$P_{1}$          $P_{0}$       $D_{1}$       Given return   Exp return       d          p           $p.d^{2}$

60        50      3            26                     14.49         11.51       0.33      43.718    

58        50      1.2          18.4                   14.49         3.91       0.33      5.045

49        50      0.75      (0.5)                    14.49        14.99     0.33       74.15

                                                                                         Total $p.d^{2}$ =  122.91

wherein, d = deviation

               p = probability

               Standard Deviation = $\sqrt{Total\ p.d^{2} }$  = $\sqrt{122.91}$ = 11.08  

Working Note:

Holding period return = $\frac{P_{1}\ -\ P_{0} \ +\ D_{1} }{P_{0} }$

Boom = $\frac{60\ -\ 50 \ +\ 3 }{50 }$   = 26%

Similarly, for normal = $\frac{58\ -\ 50 \ +\ 1.2 }{50 }$  = 18.4%

Recession = $\frac{49\ -\ 50 \ +\ 0.75 }{50}$  = (0.5)%

figure in bracket indicates negative return