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.

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Business

Rebekah

21 February, 12:32

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.

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Farrell · Answer 1

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