Software System Evaluation. A new software system will cost $2 million initially and take around 2 years to install (the actual time to complete installation will be lognormally distributed with a mean of 2 years and a standard deviation of 0.5 years). Development costs each year will be normally distributed with a mean of $1 million and a standard deviation of $0.25 million. (Each year is an independent sample.) The system will cost $5 million per year to operate in the first year.
Thereafter, the growth rate will be normally distributed with a mean of 10 percent and a standard deviation of 3 percent.
The system will generate benefits in the first year given by a normal distribution with a mean of $6 million and a standard deviation of $0.5 million. (Benefits start accruing only after the system is complete.) After the first year, benefits will increase at a rate given by a normal distribution with a mean and standard deviation of 30 percent.
Determine the present value of net benefits for this software over the next five years at a discount rate of 10 percent.
a. What is the expected present value of net benefits over a five-year period?
b. What is the probability that net benefits will be positive?