1. Precision Tool is analyzing two machines to determine which one it should purchase. The company requires a 15 percent rate of return and uses straight-line depreciation to a zero book value over the life of its equipment. Machine A has an initial cost of $892,000, annual maintenance cost of $28,200, and a 4-year life with a market salvage value of $50,000. Machine B costs $1,118,000 initially, has annual maintenance costs of $19,500, and a 5-year life with a market salvage value of $65,000. Both machines will be depreciated straight-line to zero. Whichever machine is purchased will be replaced at the end of its useful life. Assuming a 35% tax rate, Precision Tool should purchase Machine _____ because it lowers the firm's annual cost by approximately _______ as compared to the other machine. Please explain and show your work
Please Not in excel work.
We have following information -
Required rate of rate of return = 0.15
Tax rate = 0.35
Both machine A & B fully depreciated in their useful life
Machine -A | Machine-B | |
Useful life | 4 years | 5 years |
Initial Cost | $892,000 | $1,118,000 |
Annual Depreciation (Initial cost/Useful life) | $223,000 | $223,600 |
Depreciation Tax shield (Depreciation*Tax rate) | $78,050 | $78,260 |
Annual Maintenance cost | $28,200 | $19,500 |
Salvage Value | $50,000 | $65,000 |
We can calculate Equivalent Annual Cost of Machine in following manner.
Where,
r = required rate of return
n= useful life
PVIAF = Present value interest annuity factor (cumulative)
Lets calculate Net Present value (NPV) of Machine -A
PVIAF(0.15,4) = 2.8550
PVIF (0.15,4) = 0.57175
Thus,
NPV of A = 892,000 + 28,200*2.8550 - 78,050*2.8550 - 50,000*0.57175
= 892,000+80,511-222,832.75-28,587.5
= $ 721,090.75
Equivalent Annual cost of A = $ 721,090.75/2.8550
= 252,571.19
PVIAF(0.15,5) = 3.3522
PVIF (0.15,5) = 0.49718
Thus,
NPV of B = 1,118,000 + 19,500*3.3522 - 78,260*3.3522 - 65,000*0.49718
= 1,118,000 + 65,367.9 - 262,343.17 - 32,316.7
= $ 888,708.03
Equivalent Annual Cost of Machine -B = $ 888,708.03/3.3522
= $ 265,111.88
As the Equivalent Annual cost of Machine-B is higher than Machine -A by $ 12,540.69 thus Machine-A is preferable.
Precision Tools should purchase Machine A because it lower's firm's annual cost by approximately $ 12,504.69 as compared to other machine.
NPVofmachine Equivalent Annual Cost(EAC) PVIAF(r, n)
NPVofAInitialCost Annual Maintenance PVIAF(0.15, 4) DepreciationTarshield PVIAF (0.15,4)- Salvaqevalue PVIF (0.15,4)
NPV of B Initial Cost Annual Maintenance * PVI AF(0.15.5)- DepreciationTarshield * PVIAF (0.15, 5) - Salvagevalue* PVIF(0.15, 5)
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