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−DTI=R-E-D

Variables

SymbolDescriptionUnit
TITIModeled taxable income-
RRTaxable revenue-
EEDeductible cash operating expenses-
DDAllowable 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)T=t(TI)

Variables

SymbolDescriptionUnit
TTModeled income-tax cash flow-
ttAssumed effective tax rate-
TITIModeled 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.

After-Tax Operating Cash Flow

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

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

Variables

SymbolDescriptionUnit
ATCFATCFAfter-tax operating cash flow-
RRRevenue-
EECash operating expenses-
TTModeled tax-
ttAssumed effective tax rate-
DDModeled depreciation deduction-

Depreciation Tax Shield

Under a simplified model in which the deduction is fully usable, the depreciation tax shield is the tax reduction tDtD 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.

Generic After-Tax Sale Proceeds

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

SAT=S−t(S−BV)S_{\text{AT}}=S-t(S-BV)

Variables

SymbolDescriptionUnit
SATS_{\text{AT}}After-tax sale proceeds-
SSSale price-
BVBVBook value at the sale date-
ttAssumed 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.

NPVAT=−I0+∑t=1nATCFt(1+iAT)t+SAT(1+iAT)nNPV_{\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

SymbolDescriptionUnit
NPVATNPV_{\text{AT}}After-tax net present value-
I0I_0Time-zero project investment-
ATCFtATCF_tAfter-tax operating cash flow in period t, excluding terminal disposal proceeds-
SATS_{\text{AT}}After-tax terminal sale or salvage proceeds-
iATi_{\text{AT}}After-tax MARR per period-
nnStudy 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.

Full-Life After-Tax Cash-Flow Laboratory

Concept and model scope

Build a complete after-tax project cash-flow stream: depreciation by year, modeled taxable income, tax, operating cash flow, terminal disposal, and after-tax NPV. Tax policy remains an explicit modeling assumption rather than a universal rule.

Useful life8 years
Assumed effective income-tax rate25.00%
After-tax MARR10.00%
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.
YearDepreciationEnding BVTaxable incomeTaxOperating ATCFTerminal saleTotal 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.

Depreciation Schedule Laboratory

Concept and model scope

Compare accounting allocation patterns while keeping basis, book value, market value, salvage, and actual cash flow conceptually separate.

Useful life8 years
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.
YearBeginning BVDepreciationEnding 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)T=t(TI) can produce a negative tax when TI<0TI<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

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