The Best Company is reviewing two options for replacing a piece of machinery. The first machine costs $86,500 and has a four-year life. The second machine costs $123,000 and has a six-year life. Neither machine will have a salvage value. The machines will be replaced at the end of their life. Determine which machine to purchase? The discount rate is 20%. Can i do it using PVIFA Formula by substituting 'x' to the cash flows?

For Machine A :

C0 = $86,500

Since, we have cash flows only in the beginning, PV at 20% = $86,500

Time period = 4 years

Rate of interest = 20% = 0.20

Let x be the cash flow for each year in the EAC formula:

PVIFA (NPV) = CF x [1/r 1/r(1+r)^t]

86,500 = x [1/0.20 1/0.20(1+0.20)⁴]

86,500 = 2.58(x)

86,500/2.58 = x

EAC-> $33,527.13 = x

For Machine B :

C0 = $123,000

Since, we have cash flows only in the beginning, PV at 20% = $123,000

Time period = 6 years

Rate of interest = 20% = 0.20

Let y be the cash flow for each year in the EAC formula:

PVIFA (NPV) = CF x [1/r 1/r(1+r)^t]

123,000 = y [1/0.20 1/0.20(1+0.20)⁶]

123,000 = y(3.325)

123,000/3.325 = y

EAC-> $36,992.48 = y

Since, Machine A as lower EAC, we purchase machine A as it would maximize profits.