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After-Tax Economic Analysis

Gross Income (GI) – total income realized from all revenue-producing sources, including items such as the sales of assets, royalties, license fees, etc…

Income Tax – amount of taxes based on gross income. Corporate taxes are typically paid quarterly, and are actual cash flows.

Operating Expenses (E) – all corporate costs incurred in the transaction of business.

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After-Tax Economic Analysis

Taxable Income (TI) – the amount upon which taxes are based.

TI = ______________

Where D is depreciation defined in previous lecture.

Tax Rate (T) – percentage of TI owed in taxes. This rate is graduated, based on TI. (See table 17-1)

Net Profit after taxes (NPAT) – amount remaining each year when income taxes are subtracted from taxable income.

NPAT = _____________

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After-Tax Economic Analysis

Corporate Federal Income Tax Rate Schedule (2003)

TI Limits TI Range Tax Rate TMaximum Tax

for TI RangeMaximum Tax

Incurred

$1-$50,000 $50,000 0.15 $7,500 $7,500

$50,001-$75,000 25,000 0.25 6,250 13,750

$75,001-$100,000 25,000 0.34 8,500 22,250

$100,001-$335,000 235,000 0.39 91,650 113,900

$335,001-$10 mil 9.665 mil 0.34 3.2861 mil 3.4 mil

over $10 - $15 mil 5 mil 0.35 1.75 mil 5.15 mil

over $15 - $18.33 mil 3.33 mil 0.38 1.267 mil 6.417 mil

over $18.33 mil unlimited 0.35 unlimited unlimited

Graduated tax rate schedule (table 17-1, pg. 571)

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After-Tax Economic Analysis

Average Tax Rate – because the marginal tax rate varies as TI varies, the average tax rate is calculate as:

Ave tax rate = total taxes / TI

Effective Tax Rate (Te) – the total rate paid by corporations, including federal, state and local taxes. Note state taxes can be deducted from federal taxes. So:

Te = state rate + (1-state rate)( federal rate)

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Example: Problem 17.5

a) Average Tax Rate

Taxes on $300,000 = ____________________

Ave tax rate = _______________________

Effective Tax Rate (assume state tax = 7%

Te = ______________________________

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CFBT – vs – CFAT

• Cash flow before tax (CFBT) – all cash flows throughout the year without considering taxes. Note, all our PW, FW, AW analysis to this point have been CBFT cash flows.

CFBT = GI – E – P + S

where P is initial investments and S is salvage.

• Cash flow after tax (CFAT) – includes the cash flow impact of taxes.

CFAT = CFBT - taxes

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CFBT – vs – CFAT• Knowing CFAT = CFBT – taxes …

• Taxes are calculated taking depreciation (D) into account, however depreciation is not a cash flow, but taxes are.

Taxes = TI(Te)

TI = GI – E – D

CFAT = GI – E – P + S – (GI – E – D)(Te)

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After-Tax Economic AnalysisExample 17.3 from Book

Cash Flow Before Taxes

Year GI E P and S CFBT

0 ($550,000) ($550,000)

1 $200,000 ($90,000) $110,000

2 $200,000 ($90,000) $110,000

3 $200,000 ($90,000) $110,000

4 $200,000 ($90,000) $110,000

5 $200,000 ($90,000) $110,000

6 $200,000 ($90,000) $150,000 $260,000

Total $260,000

Cash Flow After Taxes

Year GI E P and S D TI Taxes CFAT

0 ($550,000) ($550,000)

1 $200,000 ($90,000) $110,000 $0 $0 $110,000

2 $200,000 ($90,000) $176,000 ($66,000) ($23,100) $133,100

3 $200,000 ($90,000) $105,600 $4,400 $1,540 $108,460

4 $200,000 ($90,000) $63,360 $46,640 $16,324 $93,676

5 $200,000 ($90,000) $63,360 $46,640 $16,324 $93,676

6 $200,000 ($90,000) $150,000 $31,680 $78,320 $27,412 $232,588

Total $550,000 $221,500

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Definitions

Capital Gains (CG): Occurs when selling price is greater than first cost.

Capital gain = selling price – first cost

CG = SP – P

Depreciation Recovery (DR): Occurs when a depreciable asset is sold for more than the current book value.

Depreciation recapture = selling price – book value

DR = SP – BVt

Capital Loss (CL): Occurs when a depreciable asset is disposed of for less than its current book value.

CL = BVt - SP

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After-Tax Economic Analysis

$0 BV P SP

DR CG

When selling price exceeds first cost then both a capital

gain and a depreciation recovery occur.

$0 BV SP P

DR

When selling price exceeds book value but is less than

he first cost then a depreciation recovery occurs.

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After-Tax Economic Analysis

$0 SP BV P

CL

When selling price is below book value a capital

loss occurs.

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After-Tax Economic Analysis

Considering capital gains, depreciation recovery and

capital losses,

TI = gross income – expenses – depreciation + depreciation recapture + capital gains – capital loss

TI = GI – E – D + DR + CG - CL

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• Relationship between before-tax MARR and after-tax MARR:

Before-tax MARR =

Te for corporations is often between 30 and 50%.

After-Tax PW and AW Analysis

After-tax MARR 1 - Te

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After-Tax PW and AW Analysis

• Approach 1: Find the PW or AW of an alternative using the CFAT and the After-tax MARR. That alternative with the largest PW (AW) is chosen.

Note, PW must use LCM (least common multiple of years.)

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After-Tax Economic Analysis

Using cash flows from Example 17.3, and an after-tax MARR of 7%, the PW of this alternative is:

PW = - $550,000

+ $110,000(P/F, 7%, 1)

+ $133,100(P/F, 7%, 2)

+ $108,460(P/F, 7%, 3)

+ $ 93,676(P/F, 7%, 4)

+ $ 93,676(P/F, 7%, 5)

+ $232,588(P/F, 7%, 6)

= ______________

Year CFAT

0 ($550,000)

1 $110,000

2 $133,100

3 $108,460

4 $93,676

5 $93,676

6 $232,588

Total $221,500