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\"Il Verizon 10:57 AM @ 93% Expert Q&A; Done 3.The analysis period is infinite a

ID: 2782437 • Letter: #

Question

"Il Verizon 10:57 AM @ 93% Expert Q&A; Done 3.The analysis period is infinite at the annual interest rate of 5% Initial machine cost Anmual maintenance costs Annual benefitsLife SIM 50,000 150,000 10 years It is assumod to replace the machine every 10 years at $1 M for an infinite period The annual maintenance costs and benefits will be changed as follows . Annual maintenance costs increase $10,000 every year for the useful life periosd Annual benefits decrease $15,000 every year for the useful life period Calculate the equivalent uniform annual benefit (EUAB) and oquivalent uniform annual cost (EUAC). (15 points) Please show all work and do not use excel. Please use cash flow diagram and interest factors.I appreciate it!

Explanation / Answer

Annual benefits form a decreasing annuity over the machine life i.e. the cash flows are:

150,000 135,000 120,000 105,000 90,000   75,000 60,000 45,000 30,000 15,000

PV of this annuity @5% = 150,000/1.051 + 135,000/1.052 + 120,000/1.053 + 105,000/1.054 + 90,000/1.055 + 75,000/1.056 + 60,000/1.057 + 45,000/1.058 + 30,000/1.059 + 15,000/1.0510

PV of Benefits = 683,480

EUAB =683,480 / {(1-(1.05)-10)/0.05} = 683,480/7.7217 =$88,513.72

Annual maintenance costs form a growing annuity over the machine life i.e. the cash flows are:

50,000 60,000 70,000 80,000 90,000   100,000 110,000 120,000 130,000 140,000

PV of this annuity @5% = 50,000/1.051 + 60,000/1.052 + 70,000/1.053 + 80,000/1.054 + 90,000/1.055 + 100,000/1.056 + 110,000/1.057 + 120,000/1.058 + 130,000/1.059 + 140,000/1.0510

PV of Maintenance Costs =$702,607

EUAC of Maintenance costs =$702,607 / {(1-(1.05)-10)/0.05} = 702,607 / 7.7217 =$90,990.85

EUAC =$90,990.85 + 1,000,000/{(1-(1.05)-10)/0.05}

           =$90,990.85 + 1,000,000/7.7217

           =$90,990.85 + 129,504.58

           = $220,495.43