Question

ZZY Inc. is considering replacing a machine. These are the data for both the used and new machine. Used machine: the machine was purchased for $15323 two years ago, the current salvage value is $11758 and is expected to have a scrap value of $6110 whenever it is retired. This used machine still has 5 years left of service. From now on, the operating and Maintenance costs are $2469 for the first year and expected to increase by $1044 thereafter. New Machine: machine costs $13823 and is expected to have a scrap value of $8546 whenever it is retired. Operating and Maintenance costs are $1777 for the first year and expected to increase by $1122 thereafter. The service life of this machine is 4 years. If the MARR is 9%, determine the minimum equivalent uniform annual cost associated with the optimal economic life of the machine that offers the lowest EUAC.

Answer 1

Here we have 2 alternatives- either to continue with the existing machine or to replace it with different new machine. The machine which results in lowest annualized cost shall be the best alternative to go for. (Since the life of used machine is 5 years and life of new machine is 4 years, we cannot directly compared their outflows, we need to find annualized outflow)

Let us first evaluate the Used Machine -

Present value of outflow on operating and maintenance cost = (2469/1.09^1)+(3513/1.09^2)+(4557/1.09^3)+(5601/1.09^4)+(6645/1.09^5) = $ 17027.48

Present value of inflow (salvage) at the end of Yr 5 = 6110/1.09^5 = $ 3971.08

Net P.V. of outflow = 17027.48 - 3971.08 = $ 13056.40

Annualized Cost (EUAC) = 13056.40/(1/1.09^1)+(1/1.09^2)+(1/1.09^3)+(1/1.09^4)+(1/1.09^5) = 13056.40/3.889651 = $ 3356.70

Now let us evaluate New Machine-

Firstly if we go for new machine, we will get the salvage value as on today of the old machine = $ 11758 (inflow)

Outflow as on today to buy the new machine = $ 13823

Scrap value received at the end of Yr 4 = 8546/1.09^4 = $ 6054.20 (inflow)

Present value of outflow on operating and maintenance cost = (1777/1.09^1)+(2899/1.09^2)+(4021/1.09^3)+(5143/1.09^4) = $ 10818.69

Net P.V. of outflow = 10818.69+13823-6054.20-11758 = $ 6829.484

Annualized outflow (EUAC) = 6829.484/(1/1.09^1)+(1/1.09^2)+(1/1.09^3)+(1/1.09^4) = $ 2108.048

We see that the equivalent uniform annualized cost of new machine is the lowest and therefore new machine should be purchased.