Answer (D) is correct . Given a periodic constant cash flow, the payback period is calculated by dividing cost by the annual cash inflows, or cash savings. To achieve a payback period of 3?years, the annual increment in net cash inflow generated by the investment must be $150,000 ($450,000 ÷ 3-year targeted payback period). This amount equals the total reduction in cash operating costs minus related taxes. Depreciation is $90,000 ($450,000 ÷ 5 years). Because depreciation is a noncash deductible expense, it shields $90,000 of the cash savings from taxation. Accordingly, $60,000 ($150,000 – $90,000) of the additional net cash inflow must come from after-tax net income. At a 40% tax rate, $60,000 of after-tax income equals $100,000 ($60,000 ÷ 60%) of pre-tax income from cost savings, and the outflow for taxes is $40,000. Thus, the annual reduction in cash operating costs required is $190,000 ($150,000 additional net cash inflow required + $40,000 tax outflow).
Answer (A) is incorrect because The amount of $60,000 is after-tax net income from the cost savings.
Answer (B) is incorrect because The amount of $100,000 is the pre-tax income from the cost savings.
Answer (C) is incorrect because The amount of $150,000 ignores the impact of depreciation and income taxes.
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