Machines A, B, C, and D are mutually exclusive are expected to produce real cash

Question

Machines A, B, C, and D are mutually exclusive are expected to produce real cash flows with the real opportunity cost of capital is 12%.

Machine A

Year 0 = -$1,000

Year 1 = $1,100

Year 2 = $1,210

Machine B

Year 0 = -$1,200

Year 1 = $1,100

Year 2 = $1,210

Year 3 = $1,330

Machine 4

Year 0 = -$5000

Year 1 = $0

Year 2 = $500

Year 3 = $1,000

Year 4 = $2,000

Year 5 = $3,000

Machine D

Year 0 = -$6,000

Year 1 = $500

Year 2 = $1,000

Year 3 = $2,000

Year 4 = $3,000

Year 5 = $4,000

a. Calculate the NPV of each machine

b. Calculate the equivalent annual cash flows for each machine

c. As the machines are mutually exclusive, which machine should you buy?

d. If the machines are independent, which machine(s) should you buy?

Explanation / Answer

a&b. Details Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Machine A        (1,000.00)        1,100.00         1,210.00 Discount Factor @12%                   1.00            0.8929             0.7972 PV of Cash flows        (1,000.00)            982.14             964.60 NPV =              946.75 EAC= r*NPV/[1-(1+r)^-n where r = rate of return n= periods EAC considering NPV = EAC = 0.12*946.75/[1-1.12^-2]              560.19 EAC considering NPV = $          560.19 EAC considering cash flow= $      1,366.82 Details Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Machine B        (1,200.00)        1,100.00         1,210.00     1,330.00 Discount Factor @12%                   1.00            0.8929             0.7972         0.7118 PV of Cash flows        (1,200.00)            982.14             964.60         946.67 NPV =           1,693.42 EAC= r*NPV/[1-(1+r)^-n where r = rate of return n= periods EAC considering NPV = EAC = 0.12*1693.42/[1-1.12^-2]              705.05 EAC considering NPV = $          705.05 EAC considering cash flow= $      1,515.51 Details Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Machine C        (5,000.00)                     -                     500           1,000             2,000           3,000 Discount Factor @12%                   1.00            0.8929             0.7972         0.7118           0.6355        0.5674 PV of Cash flows        (5,000.00)                     -               398.60         711.78       1,271.04     1,702.28 NPV =            (916.31) EAC= r*NPV/[1-(1+r)^-n where r = rate of return n= periods EAC considering NPV = EAC = 0.12*-916.31/[1-1.12^-5]            (254.19) EAC considering NPV = $        (254.19) EAC considering cash flow= $      1,803.16 Details Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Machine D        (6,000.00)                  500               1,000           2,000             3,000           4,000 Discount Factor @12%                   1.00            0.8929             0.7972         0.7118           0.6355        0.5674 PV of Cash flows        (6,000.00)            446.43             797.19     1,423.56       1,906.55     2,269.71 NPV =              843.44 EAC= r*NPV/[1-(1+r)^-n where r = rate of return n= periods EAC considering NPV = EAC = 0.12*843.44/[1-1.12^-5]              233.98 EAC considering NPV = $          233.98 EAC considering cash flow= $      2,912.80 c If the machines are mutually exclusive , Machine B should be purchased for higher NPV & EAC d If the machines are independent , the Machine B,A,D are preferable to purchase in that order.

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