Question

1) Suppose a firm projects a $5 million perpetuity from an investment of $20 million in Spain. If the required return on this investment is 20 %, how large does the probability of expropriation in year 4 have to be before the investment has a negative NPV? Assume that all cash inflows occur at the end of the year and that the expropriation, if it occurs, will occur just before the year 4 cash inflow or not at all. There is no compensation in the event of expropriation

Answer 1

Let x be the probability of expropriation
NPV=-20+5/1.2+5/1.2^2+5/1.2^3+(x*0+(1-x)*5/20%)/1.2^4

-20+5/1.2+5/1.2^2+5/1.2^3+(x*0+(1-x)*5/20%)/1.2^4>=0
=>x=0.21472

So, probability of expropriation is 0.21472