Principles of Managerial Finance

CHAPTER 10 Risk and Refinements in Capital Budgeting 443

Ignoring the differences in project lives, we can see that both projects are

acceptable (both NPVs are greater than zero) and that project Y is preferred

over project X. If the projects were independent and only one could be accepted,

project Y—with the larger NPV—would be preferred. On the other hand, if the

projects were mutually exclusive, their differing lives would have to be consid-

ered. Project Y provides 3 more years of service than project X.

The analysis in the above example is incomplete if the projects are mutually

exclusive (which will be our assumption throughout the remaining discussions).

To compare these unequal-lived, mutually exclusive projects correctly, we must

consider the differing lives in the analysis; an incorrect decision could result from

simply using NPV to select the better project. Although a number of approaches

are available for dealing with unequal lives, here we present the most efficient

technique—the annualized net present value (ANPV) approach.

Annualized Net Present Value (ANPV) Approach

The annualized net present value (ANPV) approach converts the net present

value of unequal-lived projects into an equivalent annual amount (in NPV terms)

that can be used to select the best project.^7 This net present value based approach

can be applied to unequal-lived, mutually exclusive projects by using the follow-

ing steps:

Step 1 Calculate the net present value of each project j, NPVj, over its life, nj,

using the appropriate cost of capital, k.

7. The theory underlying this as well as other approaches for comparing projects with unequal lives assumes that
   each project can be replaced in the future for the same initial investment and that each will provide the same
   expected future cash inflows. Although changing technology and inflation will affect the initial investment and
   expected cash inflows, the lack of specific attention to them does not detract from the usefulness of this technique.

annualized net present value
(ANPV) approach
An approach to evaluating
unequal-lived projects that
converts the net present value of
unequal-lived, mutually
exclusive projects into an
equivalent annual amount (in
NPV terms).