Importance of Equivalent Annual Annuity
What equivalent annual annuity means ? The method of assessing projects with a diverse duration of life is known as Equivalent Annual Annuity or EAA. The overall viability of financial projects can also be determined by specific traditional metrics to assess the profitability of the projects like IRR, Payback period or NPV etc. but to find out financial efficiency of projects equivalent annual annuity is the right metric.
How to calculate equivalent annual annuity?
To explain the present net value of a sequence of investments for a certain period for the equal flow of cash formula is used in capital budgeting to calculate EAA. The formula is
C = (r x NPV) / (1 – (1 + r)^-n )
R is the discount rate of the project
NPV is the Net present value of the cash flows of the project
n is the life of the project in years
The current worth of an investment with irregular flows of cash is used as NPV in the formula. The period of the investment or n’ is not considered while using NPV to compare two investments in different projects. The NPV of the financing for 15 years will be higher than the investment for a period of 4 years. The formula of an equivalent annual annuity can help in factoring the period of the investment by showing its NPV as a sequence of flow of cash.
How to calculate equivalent annual annuity in Excel?
Usefulness of the formula of EAA
What does the equivalent annual annuity tell us ?
The formula of the EAA can be useful to compare two projects with the same NPV, but with different life, term say 15 years and 4 years. The project with 4 years life term will show a higher flow of cash in the formula of EAA as the return will be received sooner by it than the project with 15 years life term. This formula should be applied while distinguishing two investments in real life, as it may not be possible otherwise.
The formula of EAA can also be useful while reinvesting in a project. While using this formula to evaluate the possibilities of reinvestment in a project with a short life term, the income on the investment will not be considered. The reinvestment with similar earnings will not be regarded as the present investment while using this formula for comparing the EAA of two projects based on their life term.
Derivation of the formula of the Equivalent Annual Annuity
The formula of the EAA has been derived from the equation of the annuity payment for a given value. The relevance of using the method of EAA is based on the replacement of present value with NPV or net present worth.
Example for using the formula of Equivalent Annual Annuity
Suppose there are two machines – machine A, a machine to mix dough and machine B, an icing machine. Let the life span of machine A is 6 years and that of machine B is 4 years. Now the owner of a doughnut shop wants to buy one of these machines. So he will compare their equivalent annual annuity by using NPV and life span of each machine. Suppose the NPV of machine A is $4 million and Machine B is $3 million and the cost of capital of doughnut shop is 10% the EAA of each device will be calculated as under
On the basis of the EAA of both the machines it is advisable for the doughnut shop to invest in machine B due to its higher EAA.