The following solution assumes the following assumptions:
1) In either Scenario 1 or 2, the initial investment of $20 million is made at the start of investment year; therefore, in Scenario 1, the investment is made at t=0; where as in Scenario 2, the investment is made at the start of t=0+1, or t=1.
2) The cash inflows under both scenarios begin in the year following the initial investment. Further, it is assumed that these cash flows are linear in nature and occur evenly throughout the year (as opposed to at the end of the year which is not a reasonable assumption for earnings). This is relevant b/c the appropriate discount in the period of the cash flow must be to the power 1/2, and not 1 as 1 assumes cash flow occurs at the end of the period.
In the case of Scenario 1, the investment is made at t=0 in Year 1 and the first cash flows occur during year 2 and occur evenly throughout the year.
3) There is no terminal value to the cash flows, that is, cash flows cease in the 3rd year. Further, there is no residual value attributed to the initial $20 million investment.
4) There is no opportunity cost to waiting on year, that is, there is no competing investment opportunity to consider and there is no return on the dormant capital during the year in which the market survey is completed.
Solution Calculations
Scenario 1Year 1Year 2Year 3Year 4Year 5
Invested Capital $ (20.0) $ (20.0)
Cash Flows
Well Received50% $ 10.0 $ 5.0 $ 5.0 $ 5.0
Poorly Received50% $ 5.0 $ 2.5 $ 2.5 $ 2.5
Net Cash Flows $ (20.0) $ 7.5 $ 7.5 $ 7.5
PV10% $ (20.0)$6.50 $5.91 $5.37
NPV - t=0 $ (2.2)
Scenario 2
Invested Capital $ (20.0) $ - $ (20.0)
Cash Flows
Well Received100% $ 10.0 $ - $ 10.0 $ 10.0 $ 10.0
Poorly Received0% $ 5.0 $ - - - -
Net Cash Flows $ - $ (20.0) $ 10.0 $ 10.0 $ 10.0
PV10% $ - $ (18.2) $ 7.9 $ 7.2 $ 6.5
NPV - t=0 $ 3.4
Implied IRR - t=023%
Variance6.25
Std 2.50
Mean 7.50
Coefficient of Variation0.333333
Solution Recommendation
Scenario 2 is the recommended course of action. The probably adjusted cash flows under scenario 1 results in a negative NPV, that is the project IRR is less that the required hurdle rate (WACC @ 10%).
Given that Scenario 1 is negative, the company would only proceed with the project in the case that the marketing study indicated that the new cell phone would be well received by the market and as a result the probability adjusted cash flows would be $10 million annually.
let me know if that works for you