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Based on the NPV, project 2 should be chosen.
When the NPV is adjusted for unequal lives using the equivalent annual annuity, the decision does not change.
The net present value of a project is the cost of an asset or project less the sum of the discounted cash flows from the project.
NPV of Project 1
Cost of the project: -2,090,000
Discounted year 1 cash flow: 580,000 / (1.097) = 528,714.68
Discounted year 2 cash flow: 580,000 / (1.097)^2 = 481,964.15
Discounted year 3 cash flow: 580,000 / (1.097)^3 = 439,347.45
Discounted year 4 cash flow: 580,000 / (1.097)^4 = 400,499.04
Discounted year 5 cash flow: 580,000 / (1.097)^5 = 365,085.73
Sum of discounted cash flows = 2,215,611.05
NPV = 2,215,611.05 -2,090,000 = $125,611.05
NPV of Project 2
Cost of the project: -2,090,000
Discounted year 1 cash flow: 500,000 / (1.09) = 458,715.60
Discounted year 2 cash flow: 500,000 / (1.09)^2 = 420,840
Discounted year 3 cash flow: 500,000 / (1.09)^3 = 838,550.06
Discounted year 4 cash flow: 500,000 / (1.09)^4 = 354,212.61
Discounted year 5 cash flow: 500,000 / (1.09)^5 = 324,965.69
Discounted year 6 cash flow: 500,000 / (1.09)^6 = 298,133.66
Sum of discounted cash flows = 2,242,959.30
NPV = 2,242,959.30 - -2,090,000 = $152,959.30
Based on the NPV, project 2 should be chosen because it has a higher NPV.
Equivalent annual annuity = [tex]\frac{r(NPV)}{1 - \frac{1}{(1 + r)^{n} } }[/tex]
- r = discount rate
- n = number of years
Equivalent annual annuity for project 1:
[tex]\frac{0.097 (125,611.05)}{1 - \frac{1}{1.097^{5} } }[/tex] = $32,882.31
Equivalent annual annuity for project 2:
[tex]\frac{0.09 (152,959.30)}{1 - \frac{1}{1.09^{6} } }[/tex] = $34,079.65
Project 2 would be chosen because the equivalent annual annuity is higher.
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