Step 1 :Define the cost of Machine A as \(\text{cost}_A = 80000\) cedis.
Step 2 :Define the cash flows of Machine A for each year as \(\text{cash_flows}_A = [25000, 45000, 40000, 20000, 19000]\).
Step 3 :The payback period is the time it takes for an investment to generate an amount of income or cash equal to the cost of the investment.
Step 4 :We can find the payback period by adding the cash flows for each year until the total is equal to or greater than the cost of the machine.
Step 5 :By adding the cash flows for the first three years, we get a total cash flow of \(\text{total_cash_flow} = 110000\) cedis, which is greater than the cost of Machine A.
Step 6 :Therefore, the payback period for Machine A is \(\text{payback_period}_A = 3\) years.
Step 7 :Final Answer: The payback period for machine A is \(\boxed{3}\) years.