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Made a mistake on this one and need help with an explanation why my method doesn’t work.

360,000/4 years = 90,000 after tax; calculate for before tax = 90,000/(1-40%tax) = 150,000

depreciation = 360,000/6 years = 60,000 X 40% tax = 36,000

$150,000-$36,000= $114,000

Typing this out I just realized that the before tax amount should be a function; that’s why the y=a + bx should be used. Not quite a solid gasp, can someone shed a brighter light on an explanation please?

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Whatney Co. is considering the acquisition of a new, more efficient press. The cost of the press is $360,000, and the press has an estimated six-year life with zero salvage value. Whatney uses straight-line depreciation for both financial reporting and income tax reporting purposes and has a 40 percent corporate income tax rate. In evaluating equipment acquisitions of this type, Whatney uses a goal of a four-year payback period. To meet Whatney’s desired payback period, the press must produce a minimum annual before-tax, operating cash savings of:

a.

$150,000

b.

$110,000

c.

$114,000

d.

$90,000

Explanation

Choice “b” is correct. $110,000 minimum annual before-tax operating cash savings.

Step 1: Determine the after-tax annual cash savings. The question provides the cash outflow and the desired payback period (which is calculated using after-tax cash flows). The $90,000 annual after-tax cash flows is calculated as follows:

Cost of equipment

Expected payback period

=

$360,000

4 years

=

$90,000 annual after-tax cash savings

Step 2: Determine the amount of the annual depreciation expense. Because the question asks for annual before-tax cash savings, we will need to convert the $90,000 after-tax cash savings we calculated in Step 1,above, to a before-tax amount. The depreciation tax shield plays a role in the after-tax cash flows, so the annual depreciation of $60,000 must be calculated, as follows:

Cost of equipment

Estimated useful life

=

$360,000

6 years

=

$60,000 annual depreciation expense

Step 3: Use algebra to determine the before-tax cash savings. Before-tax cash savings is equal to the after-tax cash savings plus the taxes paid. So:

Let B = annual before-tax operating cash savings

$90,000 after tax cash savings + [(B − $60,000 depreciation expense) (.40 tax rate)] = B

$90,000 + [(B − $60,000) (.40)] = B

$90,000 + [.40B − $24,000] = B

$90,000 − $24,000 = .60B

$66,000 = .60B

$110,000 = B = annual before-tax operating cash savings

Proof:

Annual before-tax cash savings $ 110,000

Less: Depreciation expense (60,000)

Taxable income 50,000

Times: Tax rate × .40

Taxes paid $ 20,000

Therefore:

Annual before tax cash saving $ 110,000

Less: Taxes paid (20,000)

Annual after-tax cash saving

BEC 74

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