A firm is evaluating two machines. The first costs $250,000 and will require annual maintenance of $30,000 per year for 10 years. At the end of 10 years, the salvage value will be $75,000.
The second machine costs $400,000 and will require $225,000 at the end of the fifth year. The salvage value after 10 years will be $175,000. Which machine should the firm select if interest in 8.5% compounded annually?
To determine which machine the firm should select, we need to compare the present value (PV) of cash flows for both machines. The machine with the lower PV of cash flows would be the better choice.
Let's start with the first machine:
Cost of machine: $250,000
Annual maintenance cost: $30,000
Salvage value after 10 years: $75,000
To calculate the present value of cash flows for the first machine, we need to discount each cash flow back to its present value using the interest rate of 8.5% compounded annually.
The formula to calculate the present value of a cash flow is:
PV = CF / (1 + r)^n
Where PV is the present value, CF is the cash flow, r is the interest rate, and n is the number of years.
For the first machine:
Year 0: Initial cost of machine (-$250,000)
Years 1-10: Annual maintenance costs (-$30,000)
Year 10: Salvage value (+$75,000)
Using the formula, we can calculate the present value for each cash flow:
PV of initial cost = -$250,000 / (1 + 0.085)^0 = -$250,000
PV of annual maintenance costs = -$30,000 / (1 + 0.085)^1 + -$30,000 / (1 + 0.085)^2 + ... + -$30,000 / (1 + 0.085)^10
PV of salvage value = $75,000 / (1 + 0.085)^10
Now let's move on to the second machine:
Cost of machine: $400,000
Payment at the end of the fifth year: $225,000
Salvage value after 10 years: $175,000
Using the same formula, we can calculate the present value for each cash flow:
PV of initial cost = -$400,000 / (1 + 0.085)^0 = -$400,000
PV of payment at the end of the fifth year = -$225,000 / (1 + 0.085)^5
PV of salvage value = $175,000 / (1 + 0.085)^10
Now, sum up the present values of all the cash flows for each machine:
PV of cash flows for the first machine = PV of initial cost + PV of annual maintenance costs + PV of salvage value
PV of cash flows for the second machine = PV of initial cost + PV of payment at the end of the fifth year + PV of salvage value
Compare the two PVs calculated. The machine with the lower PV is the better choice.
If the PV of cash flows for the first machine is lower, the firm should select the first machine. If the PV of cash flows for the second machine is lower, the firm should select the second machine.