When two projects are mutually exclusive, the firm may choose one project or the other, but not both. If mutually exclusive projects have different lives, and the projects are expected to be replaced indefinitely as they wear out, an adjustment needs to be made in the decision-making process. There are two procedures to make this adjustment:
Least common multiple of lives approach.
Extend life of shorter period to match the time of longer time period at a multiple of each. This is equivalent to calculating the replacement chain NPV, or calculating the discounted combined NPV of the shorter project.
Equivalent annual annuity (EAA) approach.
Find each project’s NPV.
NPVpress = $3,245
NPVprinter= $2,577
Find an annuity (EAA) with a present value equal to the project’s NPV over its individual life at the WACC.
EAApress: PV = –3,245; FV = 0; N = 6; I = 12; compute PMT = $789
EAAprinter: PV = –2,577; FV = 0; N = 3; I = 12; compute PMT = $1,073
Note the negative sign in front of the PV value. This is for the calculator’s sign convention and not to signify that the NPV is negative.
Select the project with the highest EAA. In this example, the printer should be accepted because: EAAprinter > EAApress