A municipality is considering the purchase of two large lawn mowers which will be used to maintain baseball diamonds, soccer fields, parks and road boulevards. Increased fuel efficiency and improved speed, reducing employee hours, contribute to savings. Both machines have a useful life of six years. Machine A, costing $5,000, offers savings of $1000 a year and disposal value of $500. The Machine B costs $7,000, offers saving of $1,300 a year and a disposal value of $1,500. The municipality uses a 7% discount factor to assess its capital purchases.

Question

Quizplus · Accepted Answer

To determine the best choice, we need to calculate the net present value (NPV) for each machine using the given discount rate of 7%.

For Machine A:
Initial investment: $5,000
Savings per year: $1,000
Disposal value: $500
Useful life: 6 years

Calculating the present value of savings:

PV = $1,000 x ((1-1/(1+0.07)^6)/0.07) = $4,089.60

Calculating the present value of disposal value:

PV = $500/(1+0.07)^6 = $356.44

Calculating the NPV:

NPV = Present value of savings + Present value of disposal value - Initial investment
NPV = $4,089.60 + $356.44 - $5,000 = -$553.96

For Machine B:
Initial investment: $7,000
Savings per year: $1,300
Disposal value: $1,500
Useful life: 6 years

Calculating the present value of savings:

PV = $1,300 x ((1-1/(1+0.07)^6)/0.07) = $5,045.65

Calculating the present value of disposal value:

PV = $1,500/(1+0.07)^6 = $1,069.14

Calculating the NPV:

NPV = Present value of savings + Present value of disposal value - Initial investment
NPV = $5,045.65 + $1,069.14 - $7,000 = -$885.21

Therefore, Machine A has a lower NPV of -$553.96 while Machine B has a lower NPV of -$885.21. However, Machine B has a higher NPV compared to Machine A. Therefore, the best choice is to purchase Machine B because it offers a higher net present value over the entire six-year useful life.

A Municipality Is Considering the Purchase of Two Large Lawn