Suppose a firm projects cash flows of $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 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.

Question

Quizplus · Accepted Answer

To calculate the NPV of the investment, we first need to find the present value of the projected cash flows and perpetuity using the given required return of 17%.

PV of cash flows in years 1-3: 
PV1 = $1 million / (1 + 0.17)^1 = $854,700
PV2 = $3 million / (1 + 0.17)^2 = $2,106,108
PV3 = $4 million / (1 + 0.17)^3 = $2,295,141

PV of perpetual cash flows: 
PV4 = $5 million / 0.17 = $29,411,765

Total PV of cash flows: 
PV = PV1 + PV2 + PV3 + PV4
PV = $34,667,713

To calculate the NPV, we subtract the initial investment of $22 million: 
NPV = PV - Initial Investment
NPV = $34,667,713 - $22,000,000
NPV = $12,667,713

Now we need to find the probability of expropriation in Year 5 that would make the NPV negative, given that the expected compensation in the event of expropriation is $3 million.

Let x be the probability of expropriation in Year 5. The expected value of the Year 5 cash flow is: 
EV5 = (1 - x)($5 million) + x($3 million) 
EV5 = $5 million - $2 millionx

To find the new total PV of cash flows, we substitute the expected value of EV5 for the perpetual cash flow projection, since this is the only cash flow affected by the expropriation probability: 
PV = PV1 + PV2 + PV3 + EV5/0.17 
PV = $34,667,713 + ($5 million - $2 millionx)/0.17

Setting the NPV to zero and solving for x, we get: 
0 = PV - Initial Investment 
0 = [$34,667,713 + ($5 million - $2 millionx)/0.17] - $22,000,000 
0 = $12,496,457 + $29,411,765x 
x = 0.424 or 42.4%

Therefore, the probability of expropriation in Year 5 has to be at least 22% before the investment has a negative NPV, given the expected compensation of $3 million.

The correct answer is C) 22%.

Suppose a Firm Projects Cash Flows of $Million, $3 Million