Question

Your company has just purchased a new production machine for $100,000. They plan to use this machine for the next 5 years. The machine is expected to provide your company with $35,000 in savings during the first year. Then, annual savings are expected to decrease by 3% each subsequent year (year over year) due to increased maintenance. Assuming that you operate the machine for an average of 3,000 hours per year and that the salvage value of the machine is negligible (i.e. $0) at the end of the 5 year period, then the annual savings per operating hour would

Answer 1

Missing information :

interest rate = 14%

Answer:

annual savings rate per operating hour $0.94

Step-by-step explanation:

initial investment $100,000

total operating hours = 3,000 x 5 = 15,000 hours

savings first year $35,000

then decrease by 3% per year

annual savings:

year 1 $35,000

year 2 $33,950

year 3 $32,931.50

year 4 $31,943.56

year 5 $30,985.25

we need to determine the PV of the savings per year:

PV = $35,000/1.14 + $33,950/1.14² + $32,931.50/1.14³ + $31,943.56/1.14⁴ + $30,985.25/1.14⁵ = $30,701.75 + $26,123.42 + $22,227.82 + $18,913.15 + $16,092.77 = $114,058.91

NPV of investment = $114,058.91 - $100,000 = $14,058.91

annual savings per operating hour = $14,058.91 / 15,000 = $0.94