Question

The Best Company is reviewing two options for replacing a piece of machinery. The first machine costs $8,000 and will have operating costs of $1,000 per year during its 5 -year life. The second machine costs $10,500 and will have $1,100 per year during its 8 -year life. Neither machine will have a salvage value. The machines will be replaced at the end of their life. Determine which machine to purchase? The discount rate is 8%.

Answer 1

To decide which machine to purchase, we need to calculate the total present value of the costs for each machine and choose the one with the lower total cost. This involves accounting for the initial purchase price and the present value of the annual operating costs, considering a discount rate of 8%.

Step-by-step explanation:

To determine which piece of machinery to purchase, we must compare the total costs of owning and operating each machine over their respective lifespans. The comparison should be made using the present value of the costs since the discount rate is given as 8%. This involves calculating the initial purchase cost plus the present value of the operating costs over the life of the machine.

For the first machine, the initial cost is $8,000, and the present value of the operating costs (costs of $1,000 per year) over the 5-year life can be found using the formula for the present value of an annuity: PV = PMT * [(1 - (1 + r)^-n) / r], where PMT is the annual payment ($1,000), r is the discount rate (8% or 0.08), and n is the number of periods (5 years).

For the second machine, the initial cost is $10,500, and the present value of the operating costs ($1,100 per year) over the 8-year life is calculated similarly using the annuity formula.

The machine to purchase is the one with the lower total present value of costs.