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ANPV chap 11
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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.
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