Red Sox Corporation wants to purchase a new machine for $350,000. Management predicts that the machine can produce sales of $205,000 each year for the next 5 years. Expenses are expected to include direct materials, direct labor, and factory overhead (excluding depreciation) totaling $85,000 per year. The firm uses straight-line depreciation with no residual value for all depreciable assets. Pique's combined income tax rate is 35%. Management requires a minimum after-tax rate of return of 10% on all investments. What is the payback period for the new machine (rounded to nearest one-tenth of a year) ? (Assume that the cash inflows occur evenly throughout the year.)

The payback period for the new machine is 3.5 years.

Explanation:

Pay Back Period: The pay back period shows that period in which the borrower has to repay the borrowed amount taken by the financial institution.

In Mathematically,

Payback Period = Initial Investment : Annual cash inflows

where initials investment is $350,000 given

And, the annual cash flows is to computed which is shown below:

= Sales - all expenses - Depreciation - tax rate + depreciation

where,

Sales - all expenses - Depreciation = Net income before tax

Net income before tax - tax rate = Net income after tax

Net income after tax + depreciation = Annual cash inflows

And Depreciation = (Purchase cost - Residual value) : Useful life

So,

Depreciation = $350,000 : 5 = $ 70,000

$205,000 - $85,000 - $70,000 = Net income before tax = $50,000

$40,000 - 35% = Net income after tax = $32,500

$32500 + $ 70,000 = Annual cash inflows = $102,500

Since the depreciation is non cash expense, so it is added back.

Now Payback period = Initial Investment : Annual cash inflows

= $350,000 : $102,500

= 3.5 years.

Thus, the payback period for the new machine is 3.5 years.