Equivalent Annual Annuity Calculator
** Note: This calculator does the math for the percentage in variable r, so there is no need to put it in decimal form (i.e. if it is 8%, enter an 8. Additionally, the calculator converts variable n to negative, so enter it as a positive value.
Equivalent Annuity Cash Flow Formula
C = r(NPV) ÷ 1 - (1 + r)-n
C = Equivalent Annuity Cash Flow
r = Rate per period
NPV = Net Present Value
n = Number of periods
This formula is used in capital budgeting; the net present value of an investment is shown as a series of equal cash flows for the length of the investment. Additionally, it should be noted that equivalent annual annuity is generally used to compare two different projects to determine which will be more attractive to pursue.
For example, assume Shoeburger Corp has the option to pursue two different projects; where project One has a 7 year term and project Two has a 16 year term. If we make the assumption that both projects have the same Net Present Value (NPV), the 7 year project will have a faster return because it is shorter, so it will reflect higher cash flow when evaluating the equivalent annual annuity. However, this is a really simple example to illustrate the problem the formula seeks to solve. Equivalent Annual Annuity takes reinvestment into consideration whereas NPV does not.
Sample Equivalent Annual Annuity Problem
Widget Co. has 2 potential projects they are considering. Project A will have a 5 year term and project B will last for 14 years. The results of their perspective NPV assumptions yield an NPV of $80,000 for project A and $130,000 for project B. The assumed rate for both of the projects is 7%.
Project A
C = .07(80,000) ÷ 1 - (1 + .07)-5
Project A Equivalent Annual Annuity (C) = $19,511
Project B
C = .07(130,000) ÷ 1 - (1 + .07)-14
Project A Equivalent Annual Annuity (C) = $14,864
In looking at both of these potential investments, project A yields a higher return. Despite project B having a better NPV, project A will allow the firm to reinvest additional earnings when compared to the period of time project B would require.