Problem 3: The Ontario Provincial government is interested in partially funding
ID: 1108265 • Letter: P
Question
Problem 3: The Ontario Provincial government is interested in partially funding improvements to transportation in the GTA. Five projects have been proposed, but the Provincial government can only invest in one. After performing studies on the value of each proposal, the government has estimated probability distributions on the potential returns for each project. The distributions are provided in the table below; for example, the probability of a subway extension yielding a $100,000,000 return is 0.3 Subway Extension Electric Vehicles Driverless Statistics LRT Hyperloop S50,000,000 $100,000,000 $200,000,000 $400,000,000 $800,000,000 0.2 0.2 0.3 0.3 Cars 0.05 0.05 0.5 0.3 0.15 0.15 0.2 0.25 0.25 0.3 0.4 0.3 0.2 0.25 0.3 0.15 a) Determine the expected returns for each project. Which one should the government fund? b) Directly investing in the project that guarantees the most returns is risky. Plot the efficient frontier for the options. Which projects can be rejected?Explanation / Answer
Expected Return for each project = The amount of yield by a project * the probability that the project will be successful
Subway Extension = 50,000,000 (0) + 0.3 (100,000,000) + 0.4(200,000,000) + 0(800,000,000) + 0.3(400,000,000)
= 0 + 30,000,000 + 80,000,000 + 120,000,000 = 230,000,000
LRT = 50,000,000(0.2) + 0.2(100,000,000) + 0.3(200,000,000) + 0.3(400,000,000)
= 10,000,000 + 20,000,000 + 60,000,000 + 120,000,000 = 210,000,000
Driverless Cars = 0.05(50,000,000) + 0.05(100,000,000) + 0.5(200,000,000) + 0.3(400,000,000) + 0.1(800,000,000) = 2,50,0000+ 5,000,000 + 100,000,000 + 120,000,000 = 227,500,000
Electric Vehicles = 0.1(50,000,000) + 0.2(100,000,000) + 0.25(200,000,000) + 0.3(400,000,000) + 0.15(800,000,000) = 5,000,000 + 20,000,000 + 50,000,000 +120,000,000 + 120,000,000 = 315,000,000
Hyperloop = 0.15(50,000,000 + 100,000,000) + 0.2(200,000,000) + 0.25(400,000,000 + 800,000,000)
= 22,500,000 + 40,000,000 + 300,000,000 = 362,500,000
Thus, hyperloop has the highest retuen on investment.
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