Which of the following machines has the lowest user cost? Machine A costs $15,000 and depreciates at a 25% rate,machine B costs $10,000 and depreciates at a rate of 20%,machine C costs $20,000 and depreciates at a rate of 10%,and machine D costs $17,000 and depreciates at a rate of 11%.The expected real interest rate is 5%.
A)Machine A
B)Machine B
C)Machine C
D)Machine D

Question

Quizplus · Accepted Answer

To find the user cost, we need to calculate the total cost of owning and operating the machine over its lifetime. This includes depreciation, interest, and any other expenses.

Using the formula for user cost:

User Cost = (P - S) + (i + d)P/2

where P is the initial purchase price, S is the salvage value (0 in this case), i is the interest rate, and d is the depreciation rate.

For machine A: User Cost = (15000 - 0) + (0.05 + 0.25)*15000/2 = $6,562.50
For machine B: User Cost = (10000 - 0) + (0.05 + 0.20)*10000/2 = $4,000
For machine C: User Cost = (20000 - 0) + (0.05 + 0.10)*20000/2 = $8,500
For machine D: User Cost = (17000 - 0) + (0.05 + 0.11)*17000/2 = $8,295

Therefore, machine B has the lowest user cost of $4,000.

Which of the Following Machines Has the Lowest User Cost