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Chapter 11: Decisions to Select a Project When Lives of Projects are Unequal: Annualized

NPV (ANPV) Criterion

When projects are of unequal lives then a simple NPV comparison may lead to a wrong decision.

In order to have a better decision, we need to estimate annualized NPV (ANPV). Following

example will show you detailed calculation of this method.

There are two projects: project A and project B, but their useful lives are not equal. Project A has

3 years of life whereas useful life of project B is 5 years.

Project

A

Project

B

0 -10,000 -15,000

1 5000 6000

2 8000 7000

3 6000 8000

4 4000

5 2000

Remember I used negative sign for year 0 CF because it is cash outflow, i.e. firm invests money

to purchase the project.

Assume cost of capital (required rate of return) for both projects is 10%.

By using a financial calculator:

NPVA = $5,664.91

NPVB = $6,224.08

Based on simple NPV comparison, your decision should be to invest in project B because

NPVB > NPVA.

Since these two projects are of unequal lives therefore we need to find their annualized NPV.

ANPVA = NPVA / PV Annuity FactorA

ANPVB = NPVB / PV Annuity Factor B

Use following steps to find the PV Annuity Factor for projects A and B:

PV Annuity FactorA PV Annuity Factor B

3 press N 5 press N

10 press I/Y 10 press I/Y

1 press +|- press PMT 1 press +|- press PMT

CPT PV and the answer is 2.4869 CPT PV and the answer is 3.7908

2

ANPVA = NPVA / PV Annuity FactorA = $5,664.91 / 2.4869 = $2,277.90

ANPVB = NPVB / PV Annuity Factor B = $6,224.08 / 3.7908 = $1,641.89

OR Use direct financial calculator functions:

ANPVA: ANPVB:

10 press I/Y 10 press I/Y

3 press N 5 press N

5664.91 press +|- press PV 6224.08 press +|- press PV

CPT PMT and the answer is: CPT PMT and the answer is:

2,277.90 1,641.89

Based on ANPV (which is the right way to decide when projects are of unequal lives), you

should select project A because ANPVA > ANPVB.