please refer to example 11-4 (second picture) to answer this question

9. Consider a proposal to enhance the vision system used by a postal service to sort mail. The new system is estimated to cost $1.2 million and will incur an additional $250,000 per year in maintenance costs. The system will produce annual savings of $600,000 each year (primarily by decreasing the percentage of misdirected mail and reducing the amount of mail that must be sorted manually). The MARR is 15% per year, and the study period is five years at which time the system will be technologically obsolete (worthless). 9-1. (1 point) What is the PW of this proposal? 9-2. (2 points) Determine how sensitive the decision to invest in the system is to the estimates of investment cost. EXAMPLE 11-4 Decision Reversal Consider a proposal to enhance the vision system used by a postal service to sort mail. The new system is estimated to cost $1.1 million and will incur an additional $200,000 per year in maintenance costs. The system will produce annual savings of $500.000 each year (primarily by decreasing the percentage of misdirected mail and reducing the amount of mail that must be sorted manually). The MARR is 34 CHAPTER 11 / BELAKEVEN AND SENSITIVITY ANALYSIS 10% per year, and the study period is five years at which time the system will be technologically obsolete (worthless). The PW of this proposal is PW(10%) = -S1.100,000 + ($500,000 - $200,000)(P/A, 10%, 5) = $37.236. Determine how sensitive the decision to invest in the system is to the estimates of investment cost and annual savings. Solution Our initial appraisal of the project shows it to be a profitable venture. Now let's look at what happens if we are wrong in our estimates. Essentially, we need to find the breakeven investment cost and the breakeven annual savings Letx be the percent change in investment cost that would cause us to reverse our decision. Then PW(10%) = 0 = -$1,100,000(1 + x) + ($500,000 - $200,000) (P/A, 10%.5) *=+3.4% Similarly, let y be the percent change in annual savings PW(10%) = 0 = $1,100,000 + ($500,000(1 + y) $200,000](P/A, 10%, 5) y = -20% If the investment cost increases by more than 3.4%, the new vision system would no longer be acceptable. Likewise, if the estimate of annual savings is lower by more than 2% of its most likely value, the project would be a no-go. The responsible engineer now needs to take a hard look at how the original estimates were made and decide whether or not more detailed estimates are required