You are considering the purchase of two CAD systems. System A costs $4000 plus an additional $1200 per year maintenance and training fee. System B costs $7000, but maintenance and training are only $300 per year. Your company typically upgrades its CAD systems every four years. If the interest rate is 4%, which choice has the lower present equivalent cost and how much lower is it?

You are considering the purchase of two CAD systems. System A costs $4000 plus an additional $1200 per year maintenance and training fee. System B costs $7000, but maintenance and training are only $300 per year. Your company typically upgrades its CAD systems every four years. If the interest rate is 4%, which choice has the lower present equivalent cost and how much lower is it?

 

 

Answer:

Solution: Given cost of system A = 4000

Maintainance cost = 1200 per year.

Let us calculate the NPV of these cash outflow.

NPV(A) = Cost + A[ (1 – {1/(1+r)}^n)/r]

Cost = present cost of the machine which is already valued.This implies that the value of $4000 is $4000 today.But the value of $1200 every year should be calculate by using the annuity formula.So we have used the above formula.Now let us find out the Present value of these costs.

NPV(A) =4000 + 1200[1 -{1/(1+0.04)}^4]/0.04

=4000 + 4355.874

=8355.874

Similarly calculate the NPV for system B.

NPV(B) = 7000 + 300 [ 1-(1/(1+r)^n]/r

=7000 + 300 [1 -(1/1.04)^4]/0.04

=7000+1088.968

=8088.968.

Since the NPV of the System B is lower than the NPV of system A we will always choose System B.The Present equivalent cost of System B is lower than system A by 266.9 approx.

Asked on February 15, 2018 in economics.
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