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How do you compute expected return for two projects?

Capital OneData Scientist · Technical Screen
EasyData ScientistTechnical ScreenStatistics & Math

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This question tests your ability to calculate the Expected Monetary Value (EMV) of probabilistic outcomes and apply discounting principles to evaluate competing capital investment projects.

The Investment Decision

You are a data scientist at a firm evaluating two mutually exclusive projects. You must decide whether to invest in Project A or Project B based on their expected financial performance.

Project A (Stable Asset)

Project A requires an upfront cost of $100,000. It has two possible outcomes at the end of Year 1:

  • A 70% probability of a $150,000 return.
  • A 30% probability of a $80,000 return.

Project B (Growth Opportunity)

Project B requires an upfront cost of $120,000. It has two possible outcomes at the end of Year 1:

  • A 40% probability of a $300,000 return.
  • A 60% probability of a $50,000 return.

Requirements

  1. Calculate the Expected Value (EV) of the return for both projects at the end of Year 1.
  2. Calculate the Expected Net Profit for each project by subtracting the initial investment from the Expected Value.
  3. Assume a discount rate of 10% (r = 0.10). Calculate the Expected Net Present Value (ENPV) for both projects.
  4. Based on these calculations, which project should the firm choose and why?

Constraints

  • Use the formula: ENPV = (Expected Value / (1 + r)) - Initial Investment.
  • Provide your reasoning for why ENPV is a better metric than Expected Value alone.

Hints

Hint 1

Recall that Expected Value is the sum of each outcome multiplied by its respective probability.

Hint 2

The discount rate represents the time value of money; future cash flows must be brought to their present value equivalent before subtracting the initial cost.

Hint 3

Consider how the risk profile (the variance or spread of outcomes) might influence your decision beyond just the ENPV.

Follow-up questions

  • How would your decision change if the firm was extremely risk-averse, even if Project B had a higher ENPV?
  • What would the break-even probability for the $300,000 outcome in Project B need to be to make it equivalent to Project A's ENPV?
  • How would you incorporate the possibility of a 'total loss' (0 return) into these models?