Question

A venture capitalist, willing to invest $1,000,000 , has three investments to choose from. The first investment, a software company, has a 20% chance of returning $5,000,000 profit, a 50% chance of returning $1,000,000 profit, and a 30% chance of losing the $1,000,000 dollars. The second investment, a hardware company, has a 15% chance of returning $5,000,000 profit, a 35% chance of returning $4,000,000 profit, and a 50% chance of losing the $1,000,000 dollars. The third investment, a biotech company, has a 25% chance of returning $5,000,000 profit, a 5% chance of returning $3,000,000 profit, and a 70% chance of losing the $1,000,000 dollars. Find the expected value for each investment.

Answer 1

Answer:

Expected Values : 1st Investment = 1200000 ; 2nd Investment = 2000000 ; 3rd Investment = 7000000

Explanation:

Expected Value = Sum of  [(X Value) x (X Probability)]

E[X] = Σ [X.{P(X)}]  

1st Investment

X = 20% , 50% , 30%  ; P(X) = +5000000 , +10000000 , -  10000000

E(X) = 0.2 (5000000) + 0.5 (1000000) + 0.3 (-1000000)

= 1000000+ 500000 - 300000 = 1200000

2nd Investment

X =15% , 35% , 50% ; P(X) = +5000000 , +4000000 , -1000000

E(X) = 0.15 (5000000) + 0.35 (5000000) + 0.5 (-1000000)

= 750000 + 1750000 - 500000 = 2000000

3rd Investment

X = 0.25 , 0.05 , 0.70 ; P(X) = 5000000 , 3000000 , -1000000

E(X) = 0.25 (5000000) + 0.05 (3000000) + 0.70 (-1000000)

= 1250000 + 150000 - 700000 = 700000