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Finance · level 2

Equivalent annual annuity

Two assets with different lives cannot be compared on NPV. Convert each NPV into the level annual payment it is worth and compare those.

Theory: Corporate Finance 

Worked example: Machine A has NPV $700K over a 10-year life at 12%. What is its equivalent annual annuity?

NPV$700K
life10 yrs
annuity factor5.65
EAA$123.89K

Step by step

  1. 1

    Annuity factor

    (1 − 1.12^−10) / 0.12 = 5.65

  2. 2

    EAA = NPV ÷ factor

    $700K / 5.65 = $123.89K a year

  3. 3

    Use

    Compare machines with different lives on EAA, not NPV — the one you can repeat is worth its annual value forever.

Machine A has NPV $700K over a 10-year life at 12%. What is its equivalent annual annuity? = 123,889

The theory behind it

Intuition

Finance is time and risk applied to cash: move every cash flow to the same date at a rate that reflects its risk, then compare.

Common pitfalls

  • ×Discounting a nominal flow at a real rate (or vice versa).
  • ×Mixing enterprise-value and equity-value numbers in the same ratio.

In the interview

Valuation, WACC, LBO and accretion rounds — where a wrong bridge is a wrong answer.