-An industrial firm uses an economic analysis to determine which of two machines
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Question
-An industrial firm uses an economic analysis to determine which of two machines to purchase. Each machine is capable of performing the same task in a given amount of time. Assume the MARR is 8%. Which machine should you select?
Machine X (explain why this is a correct answer)
Machine Y
-Determine the amount of money required to generate an infinite number of annual payments of $5000 each if the interest rate is 10% APR, compounded semi-annually?
$50,000
$48,780 (explain why this is the correct answer)
$55,000
$97,561
-I purchase an Audi for $65,000. If I receive a trade in allowance of $5,000 for my old car. What will be my monthly payments if the loan interest rate is 6% APR, compounded quarterly and the loan is for 6 years?
$833
$1,134
$994 (explain why this is the correct answer)
$1,076
Machine X Machine Y Initial Cost $6,000 $12,000 Project Life 7 years 13 years Salvage Value $0 $4,000 Annual Receipts $150 $175Explanation / Answer
1)
PMT = PV*r / (1 - (1+r)-n)
PMT = FV*r / ((1+r)n - 1)
Annual cost = - Annual investment + annual receipts + Annual salvage
Annual Costs of X = (-6000*8% / (1-(1+8%)-7))+ 150 = -1002.43
Annual Costs of Y = (-12000*8% / (1-(1+8%)-13))+ 175 + (4000*8% / ((1+8%)13 -1))= -1157.17
X has the lower annual cost,hence prefer X
2)
Semi annual 10%
EAR = (1+10%/2)2 - 1 = 10.25%
Amount = 5000/10.25% = 48780.49
3)
Loan amount = 65000 - 5000 = 60000
n = 6*12 = 72 (months)
r = 6%/12 = 0.5% (monthly rate)
PMT = PV*r / (1 - (1+r)-n)
= 60000*0.5% / (1 - (1+0.5%)-72)
= 994.37
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