Question

A $25 stock has the following probability distribution with associated outcomes after 1 year:

Probability	10%	20%	40%	20%	10%
Outcome	$10	$20	$25	$30	$45

What is the expected value of the stock price at the end of year 1? If the prevailing interest rate is 4%, is this a good investment? (Why?)

Answer 1

Solution :- i). Expected value for stock at end of Year 1 = 0.10 * 10 + 0.20 * 20 + 0.40 * 25 + 0.20 * 30 + 0.10 * 45

= 1 + 4 + 10 + 6 + 4.50

= $ 25.50

Conclusion :- Expected value for stock at the end of Year 1 = $ 25.50 (approx).

ii). Current stock price = Expected stock value at the end of Year 1 / (1 + interest rate)^{Time period in years}

= 25.50 / (1 + 0.04)¹

= 25.50 / (1.04)¹

= 25.50 / 1.04

= $ 24.52 (approx).

Based on current value of stock amounting to $ 24.52 only as against the stock worth of $ 25, The investment can not be considered as good one.