## Example Unit Profit per Machine Hour

Tiger Machine Tool Company is considering the proposed acquisition of a new metal-cutting machine. The required initial investment of \$75,000 and the projected cash benefits and annual operating hours over the 3-year project life are as follows.

End of Year Net Cash Flow Operating Hours

1 24,400 2,000

2 27,340 2,000

3 55,760 2,000

Compute the equivalent savings per machine hour at i = 15%. Solution. Bringing each flow to its equivalent at time zero, we find

PW(15%) = -\$75,000 + \$24,400(P/F,15%,1) + \$27,340((F,15%,2) + \$55,760(P/F, 1 5% ,3) = \$3553

Since the project results in a surplus of \$3553, the project would be acceptable. We first compute the annual equivalent savings from the use of the machine. Since we already know the NPW of the project, we obtain the AE by

With an annual usage of 2000 hr, the equivalent savings per machine hour would be

Savings per machine hour = \$1556/\$2000 hr = \$0.78/hr

Comments. Note that we cannot simply divide the NPW amount (\$3553) by the total number of machine hours over the 3-year period (6000 hr), or \$0.59/hr. This \$0.59 figure represents the instant savings in present worth for each hourly use of the equipment, but does not consider the time over which the savings occur. Once we have the annual equivalent worth, we can divide by the desired time unit if the compounding period is 1 year. If the compounding period is shorter, then the equivalent worth should be calculated for the compounding period.