The annualized Net Present Value (ANPV) technique is the best method to use when comparing mutually exclusive projects which have unequal duration. ANPV is the most efficient technique to convert Net Present Values (NPVs) of projects with unequal duration into an ANPV for each specific project, which can then be compared.

To find ANPV, the following calculation must be made:

1 – Find NPVs for each project

2 – Divide the NPV of each project by PVIFAr,n (Present Value Interest Factor for Annuity) at the project’s required cost of capital and number of periods. The amount for PVIFAr,n can be found in financial tables.

3 – The project with the higher Annualized Net Present Value (ANPV) is preferred.

Alternatively, ANPV can be found by using a financial calculator, as shown below:

PV = use NPV

N = Number of periods over the duration of the project (e.g. number of years)

I = required cost of capital (e.g. 10%)

Find PMT = this will be the annualized net present value (ANPV)

### Test yourself

ABC Corporation has two mutually exclusive projects A and B that it can invest in. Initial investments investments required for project A and B are $150,000 and $200,000 respectively. The duration of project A is 4 years and of project B is 3 years. Expected annual cash inflows from project A are $40,000 and from project B is $70,000. The terminal cash flows from projects A and B are $21,000 and $34,000 respectively. The cost of capital of ABC Corporation is 9% and both projects have an average risk, which means that alteration for risk adjusted discount rate is not required. The 9% for cost of capital should be used for both projects.

What is the ANPV for projects A and B?

SOLUTION:

By using a financial calculator, we can find the solution to this problem. First we need to establish the net present value (NPVs) for projects A and B.

NET PRESENT VALUE (NPV) FOR PROJECT A:

Clear calculator: second function, “C ALL”

CFo: -150,000

CF1: 40,000

CF2: 40,000

CF3: 40,000

CF4: 61,000 (40,000 + 21,000)

I: 9

Second function, NPV: 5,534.28

NET PRESENT VALUE (NPV) FOR PROJECT B:

Clear calculator: second function, “C ALL”

CFo: -200,000

CF1: 70,000

CF2: 70,000

CF3: 104,000 (70,000 + 34,000)

I: 9

Second function, NPV: 3,444.86

However, because the projects have different duration, we need to convert Net Present Values (NPVs) found above into ANPV for each project.

CONVERTING NPV TO ANPV FOR PROJECT A:

Clear calculator: second function, C ALL

PV: – 5,534.28

N: 4

I: 9

Find PMT: $1,708.26

CONVERTING NPV TO ANPV FOR PROJECT B:

Clear calculator: second function, C ALL

PV: – 3,444.86

N: 3

I: 9

Find PMT: $1,360.91

Since the ANPV of project A ($1,708.26) is higher than that of project B ($1,360.91), project A should be selected.

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