Question

Machine A was purchased last year for $10,000 and had an estimated market value of $1,100 at the end of its 6-year life. Annual operating costs are $1,050. The machine will perform satisfactorily for the next five years. A salesman for another company is offering Machine B for $51,000 with an market value of $5,100 after 5 years. Annual operating costs will be $650. Machine A could be sold now for $8,000, and MARR is 13% per year. Using the outsider viewpoint, what is the difference in the equivalent uniform annual cost (EUAC) of buying Machine B compared to continuing to use Machine A; i.e., EUAC(Machine B) – EUAC(Machine A)

Answer 1

Machine A

PW of Salvage Value = 1100 / (1+13%)^6 = 1100/1.13^6 = 1100/2.082 = $528.35

Net Initial Cost = -10000+528.35 = -$9471.65

Equivalent annual cost (EAC) of -9471.65 given by PW = P*(1-(1+r)^-n)/r

or, -9471.65 = P*(1-(1+13%)^-6)/13%

or, -9471.65 = P*(1-(1.13)^-6)/0.13

or, -9471.65 = P*(1-0.4803)/0.13

or, -9471.65 = P*(0.5197)/0.13

or, P =  -9471.65 *0.13/ 0.5197

or, P = -$2369.28

Hence Total EAC = -2369.28- 1050 = -3419.28

Machine B

PW of Salvage Value = 5100 / (1+13%)^5 = 5100/1.13^5 = 5100/1.8424 = $2768.08

$8000 will be received from sale of Machine A

Net Initial Cost =-51000+8000+2768.08 = -40231.92

Equivalent annual cost (EAC) of -40231.92 given by PW = P*(1-(1+r)^-n)/r

or, -40231.92 = P*(1-(1+13%)^-5)/13%

or, -40231.92 = P*(1-(1.13)^-5)/0.13

or, -40231.92 = P*(1-0.5428)/0.13

or, -40231.92= P*(0.4572)/0.13

or, P =  -40231.92*0.13/ 0.4572

or, P = -$-11439.52

Hence Total EAC = -11439.52- 650 = -12089.52

EAC Machine B - EAC Machine A = -12089.52 - (-3419.28) = -12089.52 +3419.28=-8670.24

Hence the Answer is -$8670.24. It means that EAC of replacing to machine B is higher by $8670.24