Question

You are trying to choose between purchasing one of two machines for a factory. Machine A costs $17,299.00 to purchase and has a 3.00 year life. Machine B costs $18,503.00 to purchase but has a 4.00 year life. Regardless of which machine you purchase, it will have to be replaced at the end of its operating life.

Which machine should you choose and what is the cost TODAY of running the machine for the next 27.00 years? Assume a discount rate of 15.00 percent.

Answer 1

cost of machine A, C1 = 17299

Equivalent Annual cost for machine A = C1/PVIFA

discount rate, r = 15% = 0.15

PVIFA( 15% , 3 years) = present value interest rate factor of annuity

= [((1+r)ⁿ - 1)/((1+r)ⁿ*r)] = [((1.15)³ - 1)/((1.15)³*0.015)] = 2.2832251

Equivalent Annual cost for machine A , E1= C1/PVIFA = 17299/2.2832251 = 7576.563463

cost of machine B, C2 = 18,503

Equivalent Annual cost for machine B = C2/PVIFA

discount rate, r = 15% = 0.15

PVIFA( 15% , 4 years) = present value interest rate factor of annuity

= [((1+r)ⁿ - 1)/((1+r)ⁿ*r)] = [((1.15)⁴ - 1)/((1.15)⁴*0.015)] = 2.8549784

Equivalent Annual cost for machine B , E2= C2/PVIFA = 18503/2.8549784 = 6480.9598

you should choose machine B since it has the lowest Equivalent Annual cost

Cost today of running machine A for 27 years = E1*PVIFA

PVIFA( 15% , 27 years) = present value interest rate factor of annuity

= [((1+r)ⁿ - 1)/((1+r)ⁿ*r)] = [((1.15)²⁷ - 1)/((1.15)²⁷*0.015)] = 6.5135343

Cost today of running machine A for 27 years = E1*PVIFA = 7576.563463*6.5135343 = $49350.21

Cost today of running machine B for 27 years = E2*PVIFA = 6480.9598*6.5135343 = $42213.95