Question

When comparing two investments with the different lives, why the investors need to compare the equivalent annual annuity rather than the net present value, explain in details and give examples

Answer 1

Equivalent Annual Annuity is a method of evaluating projects with different life durations.

Traditionally project profitability metrices such as NPV, IRR or payback period provide a very valuable perspective on how financially viable projects are overall.

EAA is a metric used to determine financially efficient projects are.

Let us understand clearly with the following example-:

EAA essentially smoothes out all cash flows and generates a single average cash flow for all periods that( when discounted) equal the project's NPV. EAA formula is

Where

r= project discount rate( WACC)

NPV=Net present value of project cash flows

n=project life ( in years)

Suppose Daniel has a Doughnut shop and he is considering to purchase one of two machines.

Machine A is a dough mixing machine and it's it's working life is 6 years. During this time, the Machine will enable Daniel to rwlize significant cash savings and represent an NPV of $4 mn.

Whereas Machine B is an icing machine that has a working life of 4 years. During this time the Machine will allow Daniel to reduce icing waste and represent an NPV of $ 3 mn

Daniel' s Doughnuts has a cost of capital of 10% which machine should Daniel invest in?

So

This EAA number tells us what the average cash flow bfrom each machine will be, given their NAVs and useful lives. Using EAA method, Machine B is more efficient Daniel would convinced for buying it. EAA method told the financial efficiency of each project.

If we observe the NPV approach we can see machine A has higher NPV than machine B.

But which machine Daniel decides to invest in depends on the business situation and goals.

So, investors look in business prospects and it's financial efficiency in projects therefore they opt EAA rather than NPV method.