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This answer results from using the pre-tax decrease in net income ($200,000) to calculate the present value of outsourcing the finishing work. When net income increases, income taxes also increase. It works the other way when net income decreases. When net income decreases, income taxes also decrease. Therefore, the $200,000 decrease in pre-tax net income will cause a decrease in taxable income and a decrease in income tax due. As a result, the net amount of annual decrease in cash flow will be less than $200,000.
If expenses increase each year by $200,000, net income before tax will decrease by $200,000 per year. That will cause income taxes to decrease by 40% of that amount, so income taxes will decrease by $200,000 × 40%, or $80,000. The effect on annual net cash flow will be a $200,000 decrease in net income caused by the increase in expenses and an $80,000 increase in net income caused by the decrease in income taxes that results from the $200,000 decrease in taxable income. The net effect is ($200,000) + $80,000, or decreased cash flow of $120,000 per year. (The same result could be calculated by multiplying $200,000 by 1 ? the tax rate.) Multiplying $(120,000) by the PV factor for an annuity for 5 years at 10%, 3.791, we get a present value of outsourcing the finishing work of ($454,920), a net cash outflow.
This is the annual before-tax cash outflow of $200,000 multiplied by 40% and then discounted using the present value of an annuity factor for 10% for 5 years. The after-tax effect of the increased cash outflow of $200,000 should be multiplied by 1 ? the tax rate, not by the tax rate, to find the after-tax effect of the increased cash outflow.