Question

You need a new computer to be able to run your small business on the road. You have identified two alternatives: a $1,000 computer that will last 3 years and a $2,000 computer that will last twice as long as the first one. You estimate that the annual benefits from both computers will be $800. Which of the two computers is a better choice if your opportunity cost of capital is 10 percent? Use both EAA and the replacement chain methods to justify your choice.

Answer 1

Initial Cost of First Computer = 1000
Annual Benefits = 800
NPV of first computer = -1000 + 800*(1-(1+10%)^-3)/10% = 989.48
EAA = NPV/(1-(1+r)^-n)/r = 989.48/(1-(1+10%)^-3)/10% = 397.89

Initial Cost of First Computer = 2000
Annual Benefits = 800
NPV of second computer = -2000 + 800*(1-(1+10%)^-6)/10% = 1484.21
EAA = NPV/(1-(1+r)^-n)/r = 1484.21/(1-(1+10%)^-6)/10% = 340.79

Better option is first computer because EAA is higher

Cash flow for first computer in
Year 0 = -1000, Year 1 =800 , Year 2 =800 , Year 3 =800-1000 = -200 , Year 4 =800, Year 5 = 800, Year 6 = 800

NPV of first computer = -1000 + 800/1.1 + 800/1.1² -200/1.1³ + 800/1.1⁴ + 800/1.1⁵  + 800/1.1⁶​​​​​​​ = 1732.89
NPV of second computer = -2000 + 800*(1-(1+10%)^-6)/10% = 1484.21

NPV of first computer is higher hence better.

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