Suppose a city is evaluating two upgrade policies for its downtown streets: "C", a conventional upgrade, and "A", an upgrade designed to accommodate large numbers of autonomous vehicles (AVs). There are no AVs in the city now, and no one is sure whether there will ever be very many. To keep things simple, suppose that the uncertainty will be resolved in year 5 and there is a 20% chance that lots of AVs will be on the road from then on (state "AV"). On the other hand, there is an 80% chance AVs won't succeed any time soon and conventional vehicles will still be dominant (state "CV").
The net payoff from building C in year 0 is $205 M and doesn't depend on whether or not AVs appear in year 5. The expected NPV from building A in year 0 is $97 M. However, the city could wait to build until year 5 when it sees what happens with AVs. If it builds C then, the year-0 NPV is $161 M. If it builds A in year 5 when AV occurs, the year-0 NPV would be very high: $568 M. On the other hand, if it builds A in year 5 when CV occurs, the year-0 NPV is $-46 M.
Please determine: (1) the expected NPV of waiting until year 5 to build; and (2) the option value associated with waiting. Please note that the dates are given to help you picture what's going on but all NPVs are given relative to year 0 and you do NOT need to do any additional PV calculations.