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?
cost of 1st machine
= 250000 + 30000( 1 - 1.085^-10)/.085 - 75000(1.085)^-10
= 413,669.04
cost of 2nd machine
= 400000 + 225000(1.085)^-5 - 175000(1.085)^-10
= 472,235.27
1st is cheaper, I used the present time as my "focal point in time"
check my arithmetic
To determine which machine the firm should select, we need to compare the present value (PV) of costs and salvage values for both machines. The machine with the lower PV will be the more cost-effective option.
For the first machine:
1. To calculate the PV of the initial cost, we use the formula:
PV = Initial cost / (1 + interest rate)^n
where the interest rate is 8.5% and the time period is 0 years.
PV1 = $250,000 / (1 + 0.085)^0 = $250,000
2. To calculate the PV of the annual maintenance costs, we use the formula:
PV = Annual cost / (1 + interest rate)^n
where the interest rate is 8.5% and the time period is 1 - 10 years.
PV2 = ($30,000 / (1 + 0.085)^1) + ($30,000 / (1 + 0.085)^2) + ... + ($30,000 / (1 + 0.085)^10)
= $206,185.70
3. To calculate the PV of the salvage value at the end of 10 years, we use the formula:
PV = Salvage value / (1 + interest rate)^n
where the interest rate is 8.5% and the time period is 10 years.
PV3 = $75,000 / (1 + 0.085)^10 = $40,279.61
4. Calculate the total PV for the first machine:
Total PV1 = PV1 + PV2 - PV3
= $250,000 + $206,185.70 - $40,279.61
= $415,906.09
For the second machine:
1. To calculate the PV of the initial cost, we use the formula:
PV = Initial cost / (1 + interest rate)^n
where the interest rate is 8.5% and the time period is 0 years.
PV1 = $400,000 / (1 + 0.085)^0 = $400,000
2. To calculate the PV of the maintenance costs at the end of the fifth year, we use the formula:
PV = Future cost / (1 + interest rate)^n
where the interest rate is 8.5% and the time period is 5 years.
PV2 = $225,000 / (1 + 0.085)^5 = $162,261.69
3. To calculate the PV of the salvage value at the end of 10 years, we use the formula:
PV = Salvage value / (1 + interest rate)^n
where the interest rate is 8.5% and the time period is 10 years.
PV3 = $175,000 / (1 + 0.085)^10 = $94,049.09
4. Calculate the total PV for the second machine:
Total PV2 = PV1 + PV2 - PV3
= $400,000 + $162,261.69 - $94,049.09
= $468,212.60
Comparing the total PV for both machines, we can see that:
Total PV1 = $415,906.09
Total PV2 = $468,212.60
Therefore, the firm should select the first machine, as it has a lower present value and is the more cost-effective option.