The Expected Value of Perfect Information (EVPI) measures the value of having complete knowledge of an uncertain outcome. It is calculated by comparing the expected value (EV) of the best decision under uncertainty to the expected value of the best decision under perfect information.
To calculate the EVPI for the given decision options, follow these steps:
- Calculate the Expected Values (EV) for each decision.
The expected value of each option can be calculated using the formula:
\[ EV = (P(\text{Success}) \times \text{Payoff for Success}) + (P(\text{Moderate Success}) \times \text{Payoff for Moderate Success}) + (P(\text{Failure}) \times \text{Payoff for Failure}) \]
Given the probabilities:
- Success = 0.3
- Moderate Success = 0.3
- Failure = 0.4
Calculate the EV for each decision:
-
Sell Company: \[ EV_{\text{Sell Company}} = (0.3 \times 96) + (0.3 \times 96) + (0.4 \times 96) = 96 \]
-
Form Joint Venture: \[ EV_{\text{Joint Venture}} = (0.3 \times 210) + (0.3 \times 120) + (0.4 \times 113) = (63) + (36) + (45.2) = 144.2 \]
-
Sell Software on Own: \[ EV_{\text{Sell Software}} = (0.3 \times 420) + (0.3 \times 110) + (0.4 \times -100) = (126) + (33) + (-40) = 119 \]
-
Determine the Best Decision:
- \( EV_{\text{Sell Company}} = 96 \)
- \( EV_{\text{Joint Venture}} = 144.2 \) (best decision)
- \( EV_{\text{Sell Software}} = 119 \)
The best decision without perfect information is to Form a Joint Venture, with an expected value of 144.2.
- Calculate the Best Decision Under Perfect Information:
Under perfect information, you would choose the option based on the best outcome for each scenario:
- Success: Sell Software on Own with payoff 420
- Moderate Success: Form Joint Venture with payoff 120
- Failure: Sell Company with payoff 96
Now we calculate the EV under perfect information:
\[ EV_{\text{Perfect Info}} = (0.3 \times 420) + (0.3 \times 120) + (0.4 \times 96) = (126) + (36) + (38.4) = 200.4 \]
- Calculate EVPI:
Now we can find the EVPI:
\[ EVPI = EV_{\text{Perfect Info}} - EV_{\text{Best Under Uncertainty}} \] \[ EVPI = 200.4 - 144.2 = 56.2 \]
Final Result:
The Expected Value of Perfect Information (EVPI) is 56.2.