# Equivalent Annuity Cash Flow 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.

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 annuity is generally used to compare two different projects to determine which will be more attractive to pursue.

## Sample Equivalent 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.