Question

A new project at a firm’s foreign subsidiary initially costs $20 million. The company is forecasting cash flows of $2 million, $3.5 million, and $4 million for years 1, 2, and 3, respectively. From here on, the firm forecasts a constant $5 million indefinitely. If the required return on this investment is 17%, how large does the probability of expropriation in year 3 have to be before the investment has a negative NPV? If expropriation occurs, it will occur before the year’s cash flow; however, expected compensation at the end of year 3 in the event of expropriation is $0.

Answer 1

As the project gives $5 million cashflow indefinitely starting from Year 4, we can calculate the present value at Year 3. Present value at Year 3 can be calculated by the formula, D/r, where D is the indefinite payments and r is the rate of return, which gives 5/0.17= $29.41M. Given that at Year 3, we will have cashflow of $4M. So total cashflow at Year 3 will be $33.41M.

Consider the following table,

Time Period	Year1	Year2	Year3
Cash flows	2	3.5	33.41
Discounting Factor to T0	1.17	1.17^2	1.17^3
Present value at T0	1.71	2.56	20.86

Lets say x be the probability of expropriation at Year3. So expected present value of cashflows of Year 3 would be (1-x)*20.86. So, NPV would be -20+1.71+2.56+(1-x)*20.86. This would be zero when x=24.57%.

So, for NPV to be negative, probability of expropriation in Year 3 should be larger than 24.57%.