how to calculate the equivalent annual cost
example of the equivalent annual costas stated earlier eac allows managers to compare npvs of different projects over different periods to accurately determine the best option consider two alternative investments in machinery equipment 1 machine a has the following 2 machine b has the following the cost of capital for the company making the decision is 5 next we calculate the eac which is equal to the net present value npv divided by the present value annuity factor or a t r while taking into account the cost of capital or r and the number of years in question or t the annuity factor is calculated as follows annuity factor 1 1 1 r t r where r cost of capital t number of periods begin aligned text annuity factor frac 1 frac 1 1 r t r textbf where r text cost of capital t text number of periods end aligned annuity factor r1 1 r t1 where r cost of capitalt number of periods using the formula above the annuity factor or a t r of each project must be calculated these calculations would be as follows machine a a t r 1 1 1 05 3 05 2 72 begin aligned text machine a a t r frac 1 frac 1 1 05 3 05 2 72 end aligned machine a a t r 051 1 05 31 2 72 machine b a t r 1 1 1 05 5 05 4 33 begin aligned text machine b a t r frac 1 frac 1 1 05 5 05 4 33 end aligned machine b a t r 051 1 05 51 4 33 next the initial costs must be divided by the annuity factor or a t r while adding in the annual maintenance cost the calculation for eac is eac machine a 105 000 2 72 11 000 49 557 begin aligned text eac machine a frac 105 000 2 72 11 000 49 557 end aligned eac machine a 2 72 105 000 11 000 49 557 eac machine b 175 000 4 33 8 500 48 921 begin aligned text eac machine b frac 175 000 4 33 8 500 48 921 end aligned eac machine b 4 33 175 000 8 500 48 921 by standardizing the annual cost a manager in charge of a capital budgeting decision where cost is the only issue would select machine b because it has an eac that is 636 lower than machine a the difference between the equivalent annual cost and the whole life costwhole life cost is the total expense of owning an asset over its entire life from purchase to disposal as determined by financial analysis it is also known as a life cycle cost which includes purchase and installation design and building costs operating costs maintenance associated financing costs depreciation and disposal costs whole life cost also takes into account certain costs that are usually overlooked such as those related to environmental and social impact factors the equivalent annual cost eac is the annual cost of owning operating and maintaining an asset over its entire life while the whole life cost is the total cost of the asset over its entire life limitations of using the equivalent annual costa limitation with eac as with many capital budgeting decisions is that the discount rate or cost of capital must be estimated for each project unfortunately the forecast can turn out to be inaccurate or variables can change over the life of the project or life of the asset that s be considered 