RatedrillEquivalent annual cost
A time value of money problem from Ratedrill. Solve it with one answer box, with fresh numbers on every attempt and the formula, calculator keystrokes and Excel version in the worked answer, and it is checked the moment you submit.
The task
A machine costs $20,000 today and $2,000 a year to run, paid at the end of each year, for 12 years, with no salvage value. At 10% per year, what is its equivalent annual cost: the level end-of-year amount over 12 years with the same present value as all of its costs?
What this problem teaches
The formula: EAC = PV of all costs × r / (1 - (1 + r)^-n). Equivalent annual cost lets you compare machines with different lives: the one with the lower EAC is cheaper per year of service.
A hint if you get stuck
Spread the purchase price into a level annuity over the life (PMT from PV = cost), then add the running cost, which is already a level annual amount.
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