Question

Timco is considering two mutually exclusive projects. Project X costs 105 and provides after-tax inflows of 90 per year for 2 years. project I costs 109 and provides after tax inflows of 70 per year for three years. the cost of funds is 8%. Which project should Timco choose? Show numbers to prove your point.

Answer 1

both projects have unequal lives. so, we can't compare both project's NPV directly to find out which project Timco should choose.

First we need to calculate NPV of both projects and then use Equivalent annual annuity approach to compare both projects.

NPV is the difference between present value of after-tax inflows and cost of project.

Years	Project X	Project I
0	-105	-109
1	90	70
2	90	70
3		70
Cost of funds	8%	8%
NPV	55.49	71.40

Calculation

now we will use Equivalent annual annuity approach.

equivalent annuity cash flow = (discount rate*NPV)/(1-(1+discount rate)^{-no. of years})

equivalent annuity cash flow of Project X = (0.08*55.49)/(1-(1+0.08)^-2) = 4.4392/(1-1.08^-2) = 4.4392/(1-0.85733882030178326474622770919067) = 4.4392/0.14266117969821673525377229080933 = 31.12

equivalent annuity cash flow of Project I = (0.08*71.40)/(1-(1+0.08)^-3) = 5.712/(1-1.08^-3) = 5.712/(1-0.79383224102016968957984047147284) = 5.712/0.20616775897983031042015952852716 = 27.71

equivalent annuity cash flow of Project X is higher than Project I. so,Timco should choose Project X.