This Example

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 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%) = -$1,100,000 + ($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. Let x be the percent change in X 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] (PIA, 10%, 5) -2.0% = demonstrated the calculation of sensitivity to decision reversal. Explain why this calculation is essentially a breakeven problem. 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 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%) = -$1,100,000 + ($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. Let x be the percent change in X 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] (PIA, 10%, 5) -2.0% = demonstrated the calculation of sensitivity to decision reversal. Explain why this calculation is essentially a breakeven