Question

Your company is considering purchasing a new bottling machine for the line that manufactures juice products. This Swill Fill 2000 is forecast to last for five years and will cost $42,000 to purchase. The new machine will offer labor savings of $4,500 annually through faster changeovers and will save you $5,000 per year in maintenance costs vs. your existing machine. The existing machine does not exhibit unusual wear-and-tear and should be able to go for another five years as well.

Your internal hurdle rate is 12%. Should you go forward with the purchase?

If we assume that the machine can outlive its useful life as stated in the problem above, what is our simple payback period? What is our discounted payback period? Please build a table to demonstrate the payback period over time at least through the point in time where the discounted payback period turns positive.

Answer 1

Savings each year for 5 years = $4500+ $5000 =$9500

NPV of the machine (ignoring salvage value of existing machine and New machine)

= -42000+ 9500/0.12*(1-1/1.12^5)

= - $7754.63

As the NPV is negative, the new machine should not be purchased

If the machine is expected to live beyond 5 years and produce annual savings of $9500, the Calculation of Simple and Discounted payback period is shown below

Year Cashflow Cumulative Cashflows Discounted Cashflows Cumulative Discounted Cashflows
0 -42000 -42000 -42000.00 -42000.00
1 9500 -32500 8482.14 -33517.86
2 9500 -23000 7573.34 -25944.52
3 9500 -13500 6761.91 -19182.60
4 9500 -4000 6037.42 -13145.18
5 9500 5500 5390.56 -7754.63
6 9500 15000 4813.00 -2941.63
7 9500 24500 4297.32 1355.69
8 9500 34000 3836.89 5192.58
As the Cumulative Cashflows turn positive in Year 5

Simple payback period (assuming evenly distributed cashflows)

= 4+ absolute value of Year 4 Cumulative Cashflows/Year 5 cashflows

=4+4000/9500

=4.4211 years

As the Cumulative Discounted Cashflows turn positive in Year 7

Discounted payback period (assuming evenly distributed cashflows)

= 6+ absolute value of Year 6 Cumulative Discounted Cashflows/Year 7 discounted cashflow

=6+2941.63/4297.32

=6.6845 years