Question

The business where you work had a sales pitch from a company automating some document handling processes at a cost of R500 000 per year for the next 5 years. It is estimated that doing so will save the company R2 000 000 in today’s terms. Assume a discount rate of 5% is applicable. Would it be worthwhile for the company to go for the automation process or retain its current practice?

Answer 1

Let’s compute present value of annual cost using formula for PV of annuity.

PV = P x [1-(1+r) -n]/r

PV = Present value of deposits

P = Periodic cash flow = $ 500,000

r = Rate of return = 0.05

n = Number of periods = 5

PV = $ 500,000 x [1- (1+0.05) -5]/0.05

     = $ 500,000 x [1- (1.05) -5]/0.05

     = $ 500,000 x [(1- 0.783526166468459)/0.05]

     = $ 500,000 x (0.216473833531541/0.05)

     = $ 500,000 x 4.32947667063082

     = $ 2,164,738.33531541 or $ 2,164,738.34

It will be worthwhile for the company to retain its current practice, as the present value of expenses for automation is more than present value of savings.