Two different methods are being considered for elevating rock into a crusher. It
ID: 1124314 • Letter: T
Question
Two different methods are being considered for elevating rock into a crusher. It is expected that the rock crusher will be in service for 6 years. Estimated disbursements for the two methods are shown. Compare the equivalent uniform annual costs of the two methods using a before income tax i* of 25%.
Method A Method B
First Cost $8,400 $5,600
Salvage value after 6 years $1,200 $2,000
Annual fuel cost $400 $900
Annual maintenance cost $260 $600
Extra annual income tax $96
Please also explain how to calculate the NPV for each year.
Explanation / Answer
(1) EUAC
Annual total cost = Fuel + Maintenance + Income tax
Method A: $(400 + 260 + 96) = $756
Method B: $(900 + 600 + 0) = $1,500
EUAC, Method A ($) = 8,400 x A/P(25%, 6) + 756 - 1,200 x P/F(25%, 6) x A/P(25%, 6)**
= 8,400 x 0.3388 + 756 - 1,200 x 0.2621 x 0.3388 = 2,845.92 + 756 - 106.56
= 3,496.36
EUAC, Method B ($) = 5,600 x A/P(25%, 6) + 1,500 - 2,000 x P/F(25%, 6) x A/P(25%, 6)**
= 5,600 x 0.3388 + 1,500 - 2,000 x 0.2621 x 0.3388 = 1,897.28 + 1,500 - 177.60
= 3,219.68
Method B has a lower EUAC and is preferred.
**We are computing EUA of costs, so capitalized present worth of salvage value is deducted since this is a benefit.
(2) NPV of costs
NPV, Method A ($) = 8,400 + 756 x P/A(25%, 6) - 1,200 x P/F(25%, 6)**
= 8,400 + 756 x 2.9514 - 1,200 x 0.2621 = 8,400 + 2,231.26 - 314.52
= 10,316.74
NPV, Method B ($) = 5,600 + 1,500 x P/A(25%, 6) - 2,000 x P/F(25%, 6)**
= 5,600 + 1,500 x 2.9514 - 2,000 x 0.2621 = 5,600 + 4,427.10 - 524.2
= 9,502.90
Since Method B has lower NPV of costs, this is preferred.
**We are computing NPV of costs, so present worth of salvage value is deducted since this is a benefit.
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