Final answer:
The payback period for the machine is 5 years.
Step-by-step explanation:
The payback period is the time it takes for an investment to recover its initial cost.
To calculate the payback period for the machine in question, divide the cost of the machine ($30,000) by the annual cash operating cost savings ($6,000). The payback period is:
Payback period = Cost of the machine / Annual cash operating cost savings
Payback period = $30,000 / $6,000 = 5 years