Final answer:
The simple rate of return on the machine is closest to 4.2%. This is calculated by finding the difference between the annual cash inflow and annual depreciation and then dividing by the initial investment.
Step-by-step explanation:
To calculate the simple rate of return for Zenith Operations' investment in a machine with a cost of $75,000, a useful life of eight years, and no salvage value, we will use the straight-line depreciation method. As per this method, the annual depreciation expense will be the cost of the machine divided by its useful life. With no mention of additional revenues or savings generated by the machine, this annual depreciation can be assumed as the annual cost.
The machine has a payback period of six years, meaning that the machine is expected to generate enough savings or revenue to cover its initial cost in six years. Since there is no salvage value, the entire cost is divided over its useful life.
Annual Depreciation = Cost of Machine / Useful Life = $75,000 / 8 = $9,375 per year.
Assuming that the annual cash inflows to achieve the payback period are uniform, this implies that the machine generates annual cash inflows equal to the initial investment divided by the payback period.
Annual Cash Inflow = Cost of Machine / Payback Period = $75,000 / 6 = $12,500 per year.
To find the simple rate of return, we compare the annual incremental revenue (or savings) to the initial investment. Since we have not been given specific revenue details, we approximate using the payback calculation:
Simple Rate of Return = (Annual Cash Inflow - Annual Depreciation) / Initial Investment = ($12,500 - $9,375) / $75,000 = $3,125 / $75,000 = 0.04167, or 4.2% when rounded to one decimal place.
Therefore, the closest simple rate of return on the machine is 4.2%, which matches option (b).