Question

Exercise 4: Projects with Different Time Length

There are two projects under consideration:

•Project A has an NPV of $20m and will last three years.

•Project B has an NPV of $60m and will last nine years.

It is anticipated that if either project is chosen it will be possible to repeat it for the foreseeable future.  The interest rate is 1% per year.  Which project will have a higher EANB and why?

Answer 1

EANB ( equivalent annual net benefits) helps us compare two different scenarios having different time periods efficiently

This is because the shorter time scenario is automatically reinvested and thus gives a more accurate comparison

The higher EANB is better

Project A

r = 1%

NPV = 20

n = 3 years

EANB = 1% x 20 / [ 1 - (1.01)^-3 ]

EANB = 0.2/[ 1 - 0.9705]

EANB = 0.2/0.029

EANB = $ 6.8 million

Project B

r = 1%

NPV = 60

n = 9 years

EANB = 1% x 60 / [ 1 - (1.01)^-9 ]

EANB = 0.6/[ 1 - 0.914]

EANB = 0.6/0.085

EANB = $ 7.004 million

The project B has a higher EANB

This is because although project A will end early , the reinvested profits will not yield a return high ( only yielding 1%) enough inorder to catch up with project B