Suppose you have the opportunity to invest in a second-hand machine for $100M, and you are unsure of its quality. There is a 75 percent chance it will be high quality, and a 25 percent chance it will be low quality.
If it is high quality, its production will yield you $180M with 60 percent probability, and $140M with 40 percent probability.
If it is low quality, its production will yield you $80M or $40M, with equal probability. The machine stops working at t=1, regardless of the quality. You observe the output of the machine and thus you will know the quality of the machine at t=1. Similar projects of similar risk have a required rate of return of 10 percent.
a) What is the expected NPV from this project?
Suppose you also get a maintenance warranty with your purchase. At t=1, you can pay another $50M to keep the machine going for another period. At t=2, the machine will yield you $90M with 60 percent probability, and $70M with 40 percent probability if the machine is high quality. The machine will yield you $40M or $20M with equal probability if the machine is low quality.
b) At t=1, would you want to pay to keep the machine going for another period if the machine was high quality? What about if the machine was low quality?
c) What is the NPV of your investment project given your choices in part (b)?
d) Suppose you had to pay for the maintenance warranty at time t=0. What is the maximum you would be willing to pay for it?