Question

One company bought a milling machine for $ 100,000. The company has the intention to use the machine for the next 5 years. The machine is expected to save the company $ 35,000 during the first year of operation. From then on the annual savings are expected decrease 3% every year due to maintenance costs. Assuming an operation of 3,000 hours per year and that the machine will have no residual value ("Salvage Value") at the end of the 5 years, determine the equivalent savings per hour of operation at a compound annual interest of 14%.

Answer 1

Initial Cost = 100,000

Life = 5 years

Savings = 35,000 in 1^st year that decreases by 3% every year

Operation = 3000 hours per year

Annual Interest rate = 14%

Calculate Annual Savings per hour

Step 1

Calculate PW of savings.

This is decreasing geometric gradient cash flow series. Use the following formula and calculate PW.

Present Value = A1 [1 – (1 – g) ^N (1+i) ^–N ÷ i + g]

PV = 35,000 [1 – (1 – 0.03) ⁵ (1+0.14) ^–5 ÷ 0.14 + 0.03]

PV = 114,059

Step 2

Calculate NPW

NPW = -100,000 + 114,059

NPW = 14,059

Step 3

Calculate Annual Equivalent Savings

A = PW (A/P, 14%, 5)

A = 14,059 (0.29128) = 4,095

Step 3

Calculate the equivalent savings per hour

Savings per hour = 4,095/3,000 = 1.365