Question

A financial firm is considering two investment opportunities. A real estate investment would require a $3 million investment, and the experts at the firm predict that there is a 70% chance that the investment will yield $7 million in gross revenue, a 20% chance that it will yield $4 million in gross revenue, and a 10% chance that it will yield $0 in gross revenue. A stocks and bonds investment would require a $4 million investment, and the firm’s experts predict that there is a 50% chance that this investment would yield gross revenue of $12 million, a 30% chance that it would "break-even" ($4 million in gross revenue), and a 20% chance that it would yield $0 in gross revenue.
Find the expected value for each of these two investment opportunities.

Answer 1

Answer:

Expected value of real estate = $2.7 million  

Expected value of stock and bonds = $4.2 million  

Explanation:

Data provided in the question:

Investment required = $3 million

Chances of $7 million yield = 70%

Chances of $4 million yield = 20%

Chances of $0 yield = 10%

Investment required in stocks and bond = $4 million

Chance that this investment in stocks and bond yield gross revenue of $12 million = 50%

Chances of break-even i.e $4 million = 30%

Chances of $0 in stocks = 20%

Now,

Expected value of real estate

= [ $(7 - 3) × 0.70 ) ] + [ $(4 - 3) × 0.20 ] - [ $3 × 0.10 ]

= $2.7 million  

Expected value of stock and bonds

= [ $(12 - 3) × 0.50 ) ] + [ $(4 - 3) × 0.30 ] + [ ( 0 - $3)  × 0.20 ]

= $4.5 million + $0.3 million - $0.6 million

= $4.2 million