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.