Xonics Graphics, Inc., is evaluating a new technology for its reproduction equipment. The technology will have a three-year life, will cost $1,000, and will have an impact on cash flows that is subject to risk. Management estimates that there is a fifty-fifty chance that the technology will either save the company $1,000 in the first year or save it nothing at all. If nothing at all, savings in the last two years would be zero as well. Even here there is some possibility that in the second year an additional outlay of $300 would be required to convert back to the original process, for the new technology may decrease efficiency. Management attaches a 40 percent probability to this occurrence if the new technology "bombs out" in the first year. If the technology proves itself in the first year, it is felt that second-year cash flows will be $1,800, $1,400, and $1,000, with probabilities of 0.20, 0.60, and 0.20, respectively. In the third year, cash flows are expected to be either $200 greater or $200 less than the cash flow in period 2, with an equal chance of occurrence. (Again, these cash flows depend on the cash flow in period 1 being $1,000.)
a. Set up a tabular version of a probability tree to depict the cash-flow possibilities, and the initial, conditional, and joint probabilities.
b. Calculate a net present value for each of the three-year possibilities (that is, for each of the eight complete branches in the probability tree) using a risk-free rate of 5 percent.
c. Calculate the expected value of net present value for the project represented in the probability tree.
d. What is the risk of the project?