DIFFICULT (applied) 17.20 Suppose a firm projects cash flows of $2.5 million, $3
ID: 2658197 • Letter: D
Question
DIFFICULT (applied) 17.20 Suppose a firm projects cash flows of $2.5 million, $3 million, and $4 million for years 1, 2, and 3, respectively, on an initial investment in Ecuador of $22 million. The firm projects a perpetuity of $5 million in years 4 and beyond. If the required return on this investment is 17%, how large does the probability of expropriation in year 5 have to be before the investment has a negative NPV? Expected compensation in the event of expropriation is $3 million. a) 31% b) 42%Explanation / Answer
Base case NPV ( in $ millions) = -22 + 2.5/(1+17%) + 3/(1+17%)2 + 4/(1+17%)3 + (5/17%)/(1+17%)3 = 3.19
In case of expropriation in year 5, we will have the following cash flows:
Year 4 = 5 million
Year 5 = [{x% * 5 + (1-x%) * 3} + (x% * 5)/17%] / (1+17%)5 ; where x is the probability of continuing on as is basis.
NPV = -22 + 2.5/(1+17%) + 3/(1+17%)2 + 4/(1+17%)3 + 5/(1+17%)4 + [{x% * 5 + (1-x%) * 3} + x% * 5/17%] / (1+17%)5 ;
Putting NPV = 0, and solving for x, we get x = 77.74%. Then the probability of expropriation for zero NPV = 22.26% or rouded 22%
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