After-Tax Economic Analysis

After-Tax Economic Analysis

$Learning Objectives$

Distinguish accounting taxable income from project cash flow.
Compute a simplified after-tax operating cash flow from revenue, cash expenses, depreciation, and a stated tax rate.
Explain the depreciation tax shield without treating depreciation as a cash expense.
Compute a generic after-tax terminal sale amount from sale price and book value under explicit gain/loss assumptions.
Build a full-life after-tax cash-flow stream and evaluate it at a stated after-tax MARR.
Keep tax rates, depreciation methods, loss treatment, and jurisdiction-specific rules as stated inputs rather than universal constants.

$Taxable Income$

In a simplified project model, taxable income is the amount subject to the stated income-tax assumption after allowable deductions such as cash operating expenses and modeled depreciation are applied.

Simplified Taxable Income

Generic educational form before jurisdiction-specific adjustments.

TI=R-E-D

Variables

Symbol	Description	Unit
$TI$	Modeled taxable income	-
$R$	Taxable revenue	-
$E$	Deductible cash operating expenses	-
$D$	Allowable depreciation deduction under the stated model	-

Simplified Income Tax

Tax computed with an explicitly stated effective tax rate for the educational model.

T=t(TI)

Variables

Symbol	Description	Unit
$T$	Modeled income-tax cash flow	-
$t$	Assumed effective tax rate	-
$TI$	Modeled taxable income	-

$After-Tax Operating Cash Flow$

After-tax operating cash flow is project revenue minus cash operating expenses and tax cash flow. Depreciation is not subtracted a second time because it is not a cash expense.

$Simplified After-Tax Cash-Flow Bridge$

Stage	Generic model	Meaning and assumption
Taxable income	$TI=R-E-D$	Deductible cash expense $E$ and allowable modeled depreciation $D$
Modeled tax	$T=t(TI)$	Uses the stated effective rate and loss-utilization assumption
After-tax operating cash flow	$ATCF=R-E-T$	Subtract cash expenses and tax once; depreciation is noncash
Simplified equivalent form	$ATCF=(R-E)(1-t)+tD$	Valid only when the modeled deduction is fully usable at rate $t$

These equations define an educational model; they do not determine an actual taxpayer's liability.

After-Tax Operating Cash Flow

Equivalent forms for a simple model with fully usable depreciation deductions.

ATCF=R-E-T=(R-E)(1-t)+tD

Variables

Symbol	Description	Unit
$ATCF$	After-tax operating cash flow	-
$R$	Revenue	-
$E$	Cash operating expenses	-
$T$	Modeled tax	-
$t$	Assumed effective tax rate	-
$D$	Modeled depreciation deduction	-

$Depreciation Tax Shield$

Under a simplified model in which the deduction is fully usable, the depreciation tax shield is the tax reduction $tD$ associated with the depreciation deduction.

$Depreciation Method Changes Tax Timing$

Two depreciation methods can allocate similar total basis over an asset life while producing different year-by-year deductions. Earlier allowable deductions generally move tax savings earlier, which can increase present value when the tax savings are actually usable. This is a timing effect; it does not make depreciation itself a cash receipt.

$After-Tax Salvage or Sale Proceeds$

A terminal sale can create a modeled tax on a gain above book value or a tax benefit on an allowable loss below book value. The generic expression depends on the assumed tax treatment.

$Terminal Disposal Model Inputs$

Relationship between sale price $S$ and book value $BV$	Generic model signal	Facts that still require jurisdiction-specific verification
$S>BV$	Modeled gain may create a tax cash outflow	Gain classification, basis adjustments, recapture, rate, and timing
$S=BV$	No modeled gain/loss from the difference alone	Other transaction costs, taxes, or basis rules may still apply
$S<BV$	Modeled loss may create a tax benefit	Deductibility, limitation, carry treatment, and usability

Do not treat the generic $S-t(S-BV)$ expression as a universal tax rule or assume a modeled loss immediately creates a refund.

Generic After-Tax Sale Proceeds

Simplified expression when the sale-price minus book-value difference is taxed or deducted at rate t.

S_{\text{AT}}=S-t(S-BV)

Variables

Symbol	Description	Unit
$S_{\text{AT}}$	After-tax sale proceeds	-
$S$	Sale price	-
$BV$	Book value at the sale date	-
$t$	Assumed effective tax rate on the modeled gain/loss	-

$After-Tax MARR$

The after-tax MARR is the decision rate used to discount after-tax project cash flows. It must be stated on a basis consistent with the modeled cash-flow periods and the decision viewpoint.

Full-Life After-Tax Net Present Value

Discounts annual after-tax operating cash flows and terminal after-tax sale proceeds to time zero.

NPV_{\text{AT}}=-I_0+\sum_{t=1}^{n}\frac{ATCF_t}{(1+i_{\text{AT}})^t}+\frac{S_{\text{AT}}}{(1+i_{\text{AT}})^n}

Variables

Symbol	Description	Unit
$NPV_{\text{AT}}$	After-tax net present value	-
$I_0$	Time-zero project investment	-
$ATCF_t$	After-tax operating cash flow in period t, excluding terminal disposal proceeds	-
$S_{\text{AT}}$	After-tax terminal sale or salvage proceeds	-
$i_{\text{AT}}$	After-tax MARR per period	-
$n$	Study life	-

$Interactive Full-Life After-Tax Laboratory$

Choose a generic depreciation method, tax rate, loss-utilization assumption, after-tax MARR, and terminal sale price. The simulator builds the year-by-year depreciation, taxable income, tax, operating ATCF, disposal proceeds, and complete after-tax NPV.

Asset basis / time-zero investmentPHPDepreciation salvage floorPHP

Useful life8 years

Modeled depreciation methodAnnual taxable revenuePHP/yearAnnual deductible cash expensesPHP/year

Assumed effective income-tax rate25.00%

After-tax MARR10.00%

Modeled loss treatmentSale price at end of year 8PHP

After-tax project NPV

₱670,378

Nonnegative at the 10.00% after-tax MARR.

Year 1 depreciation

₱437,500

Accounting deduction; not a cash payment.

Year 1 after-tax operating cash flow

₱821,875

Modeled taxable income = ₱512,500; tax = ₱128,125.

After-tax terminal sale proceeds

₱612,500

Book value at disposal = ₱500,000; sale minus book = ₱150,000; modeled disposal tax effect = ₱37,500.

Year	Depreciation	Ending BV	Taxable income	Tax	Operating ATCF	Terminal sale	Total CF
1	₱437,500	₱3,562,500	₱512,500	₱128,125	₱821,875	₱0	₱821,875
2	₱437,500	₱3,125,000	₱512,500	₱128,125	₱821,875	₱0	₱821,875
3	₱437,500	₱2,687,500	₱512,500	₱128,125	₱821,875	₱0	₱821,875
4	₱437,500	₱2,250,000	₱512,500	₱128,125	₱821,875	₱0	₱821,875
5	₱437,500	₱1,812,500	₱512,500	₱128,125	₱821,875	₱0	₱821,875
6	₱437,500	₱1,375,000	₱512,500	₱128,125	₱821,875	₱0	₱821,875
7	₱437,500	₱937,500	₱512,500	₱128,125	₱821,875	₱0	₱821,875
8	₱437,500	₱500,000	₱512,500	₱128,125	₱821,875	₱612,500	₱1,434,375

This is a generic educational model, not a jurisdiction-specific tax calculator. Actual basis rules, allowable depreciation, tax rates, loss utilization, recapture, gain classification, incentives, and disposal treatment must be verified from current authoritative rules for the applicable jurisdiction, entity, and analysis date.

Asset basis / first costPHPEstimated salvage floorPHP

Useful life8 years

Depreciation method

Depreciable amount

₱2,200,000

Basis minus the modeled salvage floor.

Year 1 depreciation

₱275,000

Accumulated depreciation

₱2,200,000

Ending book value = ₱300,000.

Year	Beginning BV	Depreciation	Ending BV
1	₱2,500,000	₱275,000	₱2,225,000
2	₱2,225,000	₱275,000	₱1,950,000
3	₱1,950,000	₱275,000	₱1,675,000
4	₱1,675,000	₱275,000	₱1,400,000
5	₱1,400,000	₱275,000	₱1,125,000
6	₱1,125,000	₱275,000	₱850,000
7	₱850,000	₱275,000	₱575,000
8	₱575,000	₱275,000	₱300,000

Straight-line and SYD allocate the stated depreciable amount across the modeled life. Pure declining-balance methods can finish above a salvage floor unless a switch or final adjustment is separately specified. Depreciation is accounting allocation; it is not itself an annual cash payment.

$Book Value Matters to Tax Modeling, Not Directly to Market Price$

Book value can affect the modeled taxable gain or loss on disposal. It still does not determine the market sale price. Estimate sale price and book value separately.

$Tax Loss Benefits Are Not Automatically Usable$

The simple expression $T=t(TI)$ can produce a negative tax when $TI<0$ . Actual ability to use a tax loss may depend on other taxable income, carryforward/carryback rules, entity status, and law. State the assumption explicitly rather than automatically treating every accounting loss as an immediate cash refund.

$Do Not Mix Before-Tax and After-Tax Bases$

Once project cash flows have been converted to an after-tax basis, evaluate them using the stated after-tax decision rate for that analysis. Mixing a before-tax cash-flow stream with an after-tax rate, or vice versa, generally produces an inconsistent comparison.

$Jurisdiction and Date Matter$

Corporate tax rates, VAT or sales taxes, depreciation classes, recapture, capital-gain rules, incentives, withholding, and loss rules vary by jurisdiction and can change over time. Do not present one tax rate or depreciation convention as universally valid.

$After-Tax Project Workflow$

STEP-BY-STEP

Define the tax viewpoint, jurisdictional assumptions, and analysis date.
Build before-tax revenues and cash expenses by period.
Establish the depreciation basis, method, and book-value schedule under the stated assumption.
Compute modeled taxable income and tax cash flow for each period.
Convert to after-tax operating cash flow without subtracting depreciation as cash.
Model disposal proceeds and any stated gain/loss tax effect at the sale date.
Assemble the complete after-tax cash-flow timeline, including the time-zero investment.
Discount the resulting stream at the stated after-tax decision rate.
Test tax-rate, depreciation timing, salvage, loss-utilization, and MARR assumptions for sensitivity.

After-Tax Project Cash-Flow Workflow

Build a transparent, jurisdiction-scoped tax model, distinguish taxable income from cash flow, and evaluate the full after-tax timeline.

The formulas in this lesson are generic educational models. Actual deductions, tax rates, loss utilization, sale treatment, and depreciation rules depend on jurisdiction, entity, date, and facts. Do not use an assumed tax shield unless the deduction can be used under the modeled assumptions.

Start → State jurisdiction, date, viewpoint, and assumptions; State jurisdiction, date, viewpoint, and assumptions → Actual tax decision or illustration?; Actual tax decision or illustration? — Actual decision → Verify current rules with authoritative source; Actual tax decision or illustration? — Illustration → Label generic rate and deduction assumptions; Verify current rules with authoritative source → Applicable treatment verified for these facts?; Applicable treatment verified for these facts? — Yes → Build revenue, cash expenses, and depreciation basis; Applicable treatment verified for these facts? — No or uncertain → Hold actual tax result pending verification; Label generic rate and deduction assumptions → Build revenue, cash expenses, and depreciation basis; Build revenue, cash expenses, and depreciation basis → Deduction usable?; Deduction usable? — Yes → Apply supported deduction in modeled period; Deduction usable? — No or uncertain → Model timing or carry treatment explicitly; Apply supported deduction in modeled period → Compute modeled taxable income and tax; Model timing or carry treatment explicitly → Compute modeled taxable income and tax; Compute modeled taxable income and tax → Model sale proceeds and stated tax effect; Model sale proceeds and stated tax effect → Assemble full ATCF and discount at after-tax MARR; Assemble full ATCF and discount at after-tax MARR → Cash-flow, tax, and rate bases consistent?; Cash-flow, tax, and rate bases consistent? — Yes → Report after-tax result and scope; Cash-flow, tax, and rate bases consistent? — No → Reconcile assumptions before reporting result

Start: terminator
State jurisdiction, date, viewpoint, and assumptions: process
Actual tax decision or illustration?: decision
Verify current rules with authoritative source: process
Applicable treatment verified for these facts?: decision
Hold actual tax result pending verification: terminator
Label generic rate and deduction assumptions: process
Build revenue, cash expenses, and depreciation basis: process
Deduction usable?: decision
Apply supported deduction in modeled period: process
Model timing or carry treatment explicitly: process
Compute modeled taxable income and tax: process
Model sale proceeds and stated tax effect: process
Assemble full ATCF and discount at after-tax MARR: process
Cash-flow, tax, and rate bases consistent?: decision
Reconcile assumptions before reporting result: terminator
Report after-tax result and scope: terminator

Key Takeaways

Taxable income and cash flow are different quantities.
Depreciation is noncash but can affect tax cash flow through taxable income.
A simple after-tax operating formula is $(R-E)(1-t)+tD$ when the modeled deduction is fully usable.
Depreciation methods can change the timing and present value of usable tax effects.
Terminal sale tax effects depend on sale price relative to book value and the stated tax treatment.
Full-life after-tax evaluation requires the time-zero investment, yearly ATCFs, terminal after-tax proceeds, and a consistent after-tax MARR.
Book value does not determine market value.
Tax rates and rules are jurisdiction- and date-specific assumptions that must be verified for real applications.

$References$

Engineering Economy, 18th edition — William G. Sullivan, Elin M. Wicks, and Joseph H. Wilck, Pearson, 2024; chapter 7 covers depreciation, income taxes, gain/loss on disposal, and after-tax cash-flow analysis. Its tax examples reflect the text's assumptions and are not Philippine tax rules.