Introduction

Taxes change project cash flows— reducing profits on winers and softening losses on losers

• Always evaluate projects on an after-tax basis

• Personal vs corporate tax: individuals rates with credits/deductions; corporations— generally flat rate, tax on profit = revenue - expenses

  $$ \text{Corporate tax rate: }t \in [0,1] $$

• After-tax (AT) MARR: lower rate

  $$ \text{MARR}{AT} \approx \text{MARR}{BT}\,(1 - t) \newline \text{CF}_{AT} = (\text{Revenue} - \text{Cash OpEx})\,(1 - t)

  $$

What Taxes Hit

• First cost (CapEx): tax savings via depreciation/CCA (not immediately expensed unless rules allow

  • Faster depreciation → earlier tax shields → higher PW

    $$ \text{Shield}_k = (\text{Dep}k)\,t \newline \text{First-cost present worth with straight-line depreciation (life = n years):} \newline\text{PW}{\text{first cost}} = -\text{CapEx} \;+\; t\left(\frac{\text{CapEx}}{n}\right)\,(P/A, i, n) $$

• Operating savings/costs: multiply by 1-t

  $$

  $$

• Salvage: taxable if book value is below proceeds, multiply salvage by 1-t

  $$ \text{PW}_{\text{salv}} = \text{Salvage}\,(1 - t)\,(P/F, i, n) $$

Evaluation Metrics

• PW/AW (after tax): convert each component (CapEx tax shields, net savings, salvage to PW or AW and sum)

  $$

  PW_{\text{AT}}= -\text{CapEx} +\underbrace{\left(\frac{\text{CapEx}}{n}\right)t}_{\text{Depreciation shield}}(P/A,i^{*},n)

  • \underbrace{(\text{Net\ savings})(1-t)}_{\text{After-tax ops cash flow}}(P/A,i^{*},n)
  • \underbrace{S(1-t)}_{\text{After-tax salvage}}(P/F,i^{*},n)

  $$

• IRR (after tax): compute IRR on after tax cash flows

  $$ 0 = \sum_{k=0}^{n} \frac{\text{CF}{AT}(k)}{(1 + i^{})^{k}}\quad\Rightarrow\quad i^{} = \text{IRR}{AT} $$

  • Use the approximation only as a first pass; do the exact IRR if it’s close to the after-tax MARR

How to evaluate a project (after-tax):

1. Choose discount rate: use after tax MARR: $\text{MARR} {AT} \approx \text{MARR}{BT}(1-t)$
2. Depreciation/CCA: compute $\text{Dep}_k$ each year per tax rules → tax shield $t \text{Dep}_k$
3. Operating flows: $\text{Net Savings} _k (1-t)$
4. Salvage: if book value = 0, after-tax salvage = $\text{Salvage} (1-t)$
5. PW or AW: discount and sum (or annualize)
   1. Accept if PW ≥ 0 ( or AW≥ 0) at after-tax MARR
6. IRR (optional): compute IRR on after-tax cash flows and compare to after-tax MARR; approximation okay only for screening