You are considering a project that you expect will produce $200 FCFF every year in perpetuity. Depending on whether the project is successful or not, however, the demand one year from today will be either low, producing $100 FCFF in perpetuity, or high, producing $300 FCFF in perpetuity. The high and low demand outcomes are equally likely and will be revealed in one year. The revealed outcome is expected to persist forever. The project cost is $1,000. The discount rate for the first year is 30% and 15% for subsequent years. The project can be dismantled and sold at the end of the first year for $700 after taxes. Should you take the project

Yes, because the expected value ($1,308) is higher than the investment ($1,000), that means the NPV is positive.

Explanation:

We have two possible scenarios:

1) the best possible scenario is $200 for year 1, and $300 in perpetuity.

to determine the present value of the project for this scenario = $200/1.3 + ($300/0.15)/1.3 = $154 + $1,538 = $1,692

2) the worst possible scenario is $200 for year 1, and $150 in perpetuity.

to determine the present value of the project for this scenario = $200/1.3 + ($150/0.15)/1.3 = $154 + $769 = $923

since both scenarios are equally possible, then the expected value of the project should be = ($1,692 x 50%) + ($923 x 50%) = $846 + $462 = $1,308

Since the expected value of the project is higher than the investment, we should carry it out.