18.3 Capital Budgeting & Investment Decisions

Capital Budgeting & Investment Decisions

Capital budgeting is the systematic process of planning, analyzing, and selecting long-term capital investments that commit significant financial resources for multi-year horizons. In the Philippine CPA Licensure Examination (CPALE), candidates must be proficient in isolating relevant incremental after-tax cash flows, applying corporate income tax rates (including the $25\%$ regular rate under the CREATE Law), calculating depreciation tax shields, and resolving ranking conflicts between Net Present Value ($NPV$) and Internal Rate of Return ($IRR$).

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1. Nature and Process of Capital Budgeting

Core Characteristics of Capital Projects

1. Long-Term Horizon: Extends across multiple accounting periods, exposing the entity to inflation, market shifts, and technological obsolescence.
2. Substantial Capital Commitment: Demands substantial initial resource allocation, rendering poor decisions costly to reverse.
3. Irreversibility: Disposing of specialized plant or machinery on short notice typically incurs substantial capital losses.

The Capital Budgeting Cycle

                              The Capital Budgeting Stages

   ┌───────────────┐     ┌───────────────┐     ┌───────────────┐     ┌───────────────┐
   │ Identification│ ──► │  Cash Flow    │ ──► │  DCF Project  │ ──► │ Implementation│
   │  & Screening  │     │  Forecasting  │     │  Evaluation   │     │  & Post-Audit │
   └───────────────┘     └───────────────┘     └───────────────┘     └───────────────┘

Cash Flows vs Accounting Net Income

Accrual accounting under PFRS matches revenues and expenses through non-cash accruals, deferrals, and allocations. In contrast, capital budgeting relies strictly on cash inflows and cash outflows:

• Non-cash expenses (such as depreciation and amortization) are excluded from operating disbursements.
• Depreciation is relevant solely because it serves as a deductible expense on the corporate income tax return, generating a cash-saving tax shield.
• Sunk costs (prior expenditures like past engineering feasibility studies) are strictly irrelevant.
• Opportunity costs (revenues foregone by utilizing existing corporate assets for the project) must be recognized as cash outflows.

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2. Determining Relevant Project Cash Flows

A capital investment's cash flow stream is categorized into three sequential phases:

1. Net Initial Investment Outlay ($CF_0$)

$\text{Net Initial Investment} = \text{Acquisition Cost} + \text{Freight \& Installation} + \Delta NWC - \text{Net Disposal Proceeds of Old Asset}$

Where:

• Acquisition Cost: Invoiced purchase price of the new machinery or facility.
• Freight, Shipping, Site Preparation, and Installation: Capitalized asset setup expenditures.
• Additional Net Working Capital ($\Delta NWC$): Incremental cash tied up in receivables and safety inventory required to support expanded operations.
• Net Proceeds from Old Asset Sale: $\text{Net Proceeds} = \text{Market Selling Price} - \text{Tax on Gain (or } + \text{Tax Benefit on Loss)}$ $\text{Gain/Loss on Sale} = \text{Disposal Price} - \text{Tax Book Value of Old Asset}$ If Gain: $\text{Tax Expense} = \text{Gain} \times T$ (deducted from gross sales proceeds). If Loss: $\text{Tax Savings} = \text{Loss} \times T$ (added to gross sales proceeds).

2. Operating Cash Flows After Taxes ($CFAT$)

Operating cash flows represent the recurring net cash inflows generated across each year of asset operation.

Direct Method (Receipts less Payments)

$CFAT = (\text{Incremental Cash Revenues} - \text{Incremental Cash Expenses}) \times (1 - T) + (\text{Depreciation} \times T)$

Indirect Method (Net Income Adjustment)

$CFAT = \text{Incremental Accounting Net Income After Tax} + \text{Depreciation}$

The Depreciation Tax Shield Formulation

$\text{Operating Cash Flow} = (S - C)(1 - T) + (D \times T)$

Where:

• $S$: Incremental cash revenues.
• $C$: Incremental cash operating expenses.
• $D$: Tax-allowable depreciation charge.
• $T$: Statutory corporate income tax rate ($25\%$ under CREATE Act for large domestic corporations; $20\%$ for qualifying MSMEs).
• $D \times T$: The Depreciation Tax Shield, reflecting cash taxes saved by deducting depreciation from taxable operating revenues.

3. Terminal Year Cash Flows ($CF_n$)

Occurs in the project's final operational year ($n$):

1. Final year recurring operating cash flow ($CFAT_n$).
2. Net after-tax salvage value of the project asset at decommissioning: $\text{Terminal Salvage Net Proceeds} = \text{Salvage Value} - [(\text{Salvage Value} - \text{Book Value}_n) \times T]$
3. Complete recovery of initial net working capital ($\Delta NWC$). Working capital recovery is $100\%$ non-taxable because it represents the collection of receivables and drawdown of inventory without generating taxable gain.

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3. Non-Discounted Evaluation Techniques

Non-discounted techniques provide rapid operational screening without accounting for the time value of money.

The Payback Period

Measures the time required for cumulative after-tax cash inflows to recover the net initial investment outlay.

• Uniform (Even) Annual Cash Flows: $\text{Payback Period} = \frac{\text{Net Initial Investment Outlay}}{CFAT}$
• Uneven Annual Cash Flows: Accumulate annual $CFAT$ year-by-year until the cumulative figure equals the initial outlay: $\text{Payback} = \text{Years before full recovery} + \frac{\text{Unrecovered Cost at Start of Year}}{\text{Total Cash Inflow during the Year}}$
• Bailout Payback Period: Computes the payback period assuming the project could be abandoned at any point, incorporating the asset's declining salvage value at the end of each year alongside cumulative operating cash flows.
• Evaluation:
  • Strengths: Simple to compute; serves as an indicator of liquidity risk and corporate exposure in volatile environments.
  • Limitations: Ignores the time value of money; entirely disregards cash flows received after the payback cutoff date; fails to assess overall project profitability.

The Accounting Rate of Return ($ARR$)

Measures project profitability using accrual accounting net income rather than cash flow.

$\text{ARR}_{\text{Initial}} = \frac{\text{Average Annual Net Income After Tax}}{\text{Net Initial Investment}}$

$\text{ARR}_{\text{Average}} = \frac{\text{Average Annual Net Income After Tax}}{\text{Average Investment}} = \frac{\text{Average Net Income}}{\frac{\text{Initial Outlay} + \text{Terminal Salvage Value}}{2}}$

• Evaluation:
  • Strengths: Aligns directly with published financial statement reporting metrics ($ROA$, $ROE$).
  • Limitations: Uses accrual accounting income rather than cash flows; ignores the time value of money.

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4. Discounted Cash Flow (DCF) Techniques

DCF methods incorporate the time value of money by discounting future cash flows at the firm's required hurdle rate (Weighted Average Cost of Capital, $WACC$).

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5. NPV vs IRR: Analysis of Ranking Conflicts

When evaluating independent projects with conventional cash flow patterns (an initial outflow followed by a series of net inflows), NPV and IRR yield identical accept or reject decisions.

However, when projects are mutually exclusive (accepting one precludes accepting the other), ranking conflicts frequently emerge.

                                    The Fisher Crossover Rate

     Net Present Value
          ▲
          │  Project A NPV Profile (Steeper: Larger Scale / Long Life)
          │  Project B NPV Profile (Flatter: Accelerated Near-Term Cash)
   NPV_A  ┼───●
          │    \ 
   NPV_B  ┼─────●───\ 
          │      \   \ 
          │       \   \ 
          │        \   \ 
          │         \   \ 
          │          ▼   ▼
          ├───────────●──────────────────────────  Fisher Crossover Rate (NPV_A = NPV_B)
          │            \ \ 
          │             \ \ 
        0 ┼──────────────●─●─────────────────────► Discount Rate (%)
          │               \ \                      IRR_B > IRR_A
          ▼                ▼ ▼

Root Causes of Conflict Between NPV and IRR

1. Scale Differences (Project Size): A large-scale project may generate a massive positive $NPV$ (e.g., $\text{PHP }10{,}000{,}000$) despite a modest $IRR$ of $16\%$, while a small project may yield an impressive $IRR$ of $40\%$ but an $NPV$ of only $\text{PHP }500{,}000$. Management cannot spend percentages; total peso wealth addition ($NPV$) takes precedence.
2. Cash Flow Timing (Pattern) Differences: Project A may concentrate cash inflows in its initial years, while Project B yields large cash inflows in later years. The steepness of their NPV profile curves differs relative to changes in the discount rate.
3. Unequal Project Lives: Projects with different useful lives require annualized comparisons (e.g., Equivalent Annual Annuity) or replacement chain models.

The Reinvestment Rate Assumption

The fundamental theoretical flaw in the IRR method lies in its implicit reinvestment rate assumption:

• IRR Assumption: Future cash inflows are assumed to be reinvested at the project's own $IRR$ over the remainder of the project life. When a project boasts an $IRR$ of $35\%$, it assumes the firm can reliably find other investments earning $35\%$.
• NPV Assumption: Future cash inflows are assumed to be reinvested at the firm's Cost of Capital ($WACC$). This is a realistic assumption because the firm can always use cash to retire debt or repurchase equity yielding the cost of capital.
• Theoretical Superiority of NPV: Because its reinvestment assumption is economically valid, $NPV$ is theoretically superior to $IRR$ for shareholder wealth maximization.

Multiple IRRs and Unconventional Cash Flows

When a project's cash flow stream exhibits unconventional patterns (cash flows switch signs more than once, such as $-, +, +, -, +$, common in mining extraction with environmental restoration outlays at project completion), Descartes' Rule of Signs dictates that there can be multiple internal rates of return, rendering standard IRR unreliable. Under such conditions, NPV or the Modified Internal Rate of Return ($MIRR$) must be utilized.

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6. Payback Reciprocal, Capital Rationing, Unequal Lives, and Sensitivity Analysis

Payback reciprocal. 1 / Payback period is a rough estimate of a project's IRR when cash inflows are even and the project life is at least about twice the payback period. A project with a 4-year payback and a long life has an approximate IRR of 1 / 4 = 25%, which overstates the true IRR when the life is short.

Capital rationing. When the capital budget is limited, choose the combination of projects with the highest total NPV that fits the budget. The profitability index is a useful ranking tool, but it can fail when projects are indivisible.

Ranking by PI selects B and C (cost PHP 900,000, total NPV PHP 260,000) and leaves PHP 100,000 idle. The combination A and B uses the full PHP 1,000,000 and produces a total NPV of PHP 270,000, so A and B is the better choice.

Unequal lives: equivalent annual annuity (EAA). For mutually exclusive, repeatable projects with different lives, convert each NPV into an annual amount: EAA = NPV / PVIFA(k, n). At 10%, Project X (NPV PHP 100,000 over 3 years) has EAA = 100,000 / 2.4869 = PHP 40,211, while Project Y (NPV PHP 150,000 over 6 years) has EAA = 150,000 / 4.3553 = PHP 34,441. Project X is preferred even though its single-cycle NPV is lower. The replacement chain method (repeating X twice over 6 years) gives the same ranking.

Sensitivity analysis. Change one input at a time (annual cash inflow, project life, discount rate, tax rate, salvage value) and observe the effect on NPV. A common board question asks for the minimum annual cash inflow that makes NPV zero: required annual inflow = Net investment / PVIFA(k, n). For a PHP 1,000,000 investment over 5 years at 12% (PVIFA 3.6048), the break-even annual cash inflow is about PHP 277,410. Scenario analysis changes several inputs together (best, base, and worst case), and simulation assigns probability distributions to many inputs at once.

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7. Comprehensive Worked Computational Example

Scenario: Davao Agro-Industrial Corp. is evaluating two mutually exclusive equipment investments. The company's required rate of return ($WACC$) is $10\%$, and it is subject to a $25\%$ corporate income tax rate under the CREATE Law.

Investment Specifications:

• Machine Alpha:
  • Initial acquisition invoice: $\text{PHP }4{,}000{,}000$
  • Shipping and installation: $\text{PHP }200{,}000$
  • Additional working capital required: $\text{PHP }300{,}000$
  • Old machine trade-in: Book value of old asset is $\text{PHP }400{,}000$; sold immediately for $\text{PHP }200{,}000$
  • Economic life: 5 years, zero tax salvage value
  • Annual pre-tax cash operating savings: $\text{PHP }1{,}800{,}000$
  • Annual straight-line depreciation for tax purposes: $\text{PHP }840{,}000$ ($(\text{PHP }4{,}000{,}000 + \text{PHP }200{,}000) / 5$)
  • Terminal salvage value at end of Year 5: $\text{PHP }0$
  • Working capital recovery at end of Year 5: $\text{PHP }300{,}000$

Relevant Present Value Factors at $10\%$:

• $PVIF_{10\%, 1} = 0.9091$
• $PVIF_{10\%, 2} = 0.8264$
• $PVIF_{10\%, 3} = 0.7513$
• $PVIF_{10\%, 4} = 0.6830$
• $PVIF_{10\%, 5} = 0.6209$
• Cumulative Annuity Factor ($PVIFA_{10\%, 5}$) $= 3.7908$

Step-by-Step Capital Budgeting Analysis

1. Net Initial Investment ($CF_0$)

• Cost of new machine: $\text{PHP }4{,}000{,}000$
• Capitalized installation: $\text{PHP }200{,}000$
• Working capital requirement: $\text{PHP }300{,}000$
• Subtotal gross cash outflow: $\text{PHP }4{,}500{,}000$
• Deduct: Net disposal proceeds from old asset:
  • Gross selling price: $\text{PHP }200{,}000$
  • Tax loss on sale: $\text{Book Value } (\text{PHP }400{,}000) - \text{Sales Price } (\text{PHP }200{,}000) = \text{PHP }200{,}000\text{ Loss}$
  • Tax savings on loss: $\text{PHP }200{,}000 \times 25\% = \text{PHP }50{,}000$
  • Total net cash proceeds from old asset: $\text{PHP }200{,}000 + \text{PHP }50{,}000 = \text{PHP }250{,}000$
• Net Initial Investment Outlay ($CF_0$): $CF_0 = \text{PHP }4{,}500{,}000 - \text{PHP }250{,}000 = \text{PHP }4{,}250{,}000$

2. Annual Operating Cash Flow After Taxes ($CFAT$ for Years 1 through 5)

Using the tax shield formula: $CFAT = \text{Pre-Tax Savings} \times (1 - T) + (\text{Depreciation} \times T)$ $CFAT = (\text{PHP }1{,}800{,}000 \times [1 - 0.25]) + (\text{PHP }840{,}000 \times 0.25)$ $CFAT = (\text{PHP }1{,}800{,}000 \times 0.75) + \text{PHP }210{,}000 = \text{PHP }1{,}350{,}000 + \text{PHP }210{,}000 = \text{PHP }1{,}560{,}000$

3. Terminal Year Non-Operating Cash Flow (End of Year 5)

• Recovery of initial working capital: $\text{PHP }300{,}000$ (non-taxable)
• Total cash flow in Year 5: $\text{PHP }1{,}560{,}000\text{ (Operating)} + \text{PHP }300{,}000\text{ (Recovery)} = \text{PHP }1{,}860{,}000$

4. Net Present Value ($NPV$)

• Present Value of Operating Cash Flows (Years 1 to 5): $\text{PV of CFAT} = \text{PHP }1{,}560{,}000 \times PVIFA_{10\%, 5} = \text{PHP }1{,}560{,}000 \times 3.7908 = \text{PHP }5{,}913{,}648$
• Present Value of Working Capital Recovery (Year 5): $\text{PV of Recovery} = \text{PHP }300{,}000 \times PVIF_{10\%, 5} = \text{PHP }300{,}000 \times 0.6209 = \text{PHP }186{,}270$
• Total Present Value of Inflows: $\text{PHP }5{,}913{,}648 + \text{PHP }186{,}270 = \text{PHP }6{,}099{,}918$
• Deduct Initial Investment Outlay ($CF_0$): $-\text{PHP }4{,}250{,}000$
• Net Present Value ($NPV$): $NPV = \text{PHP }6{,}099{,}918 - \text{PHP }4{,}250{,}000 = \text{PHP }1{,}849{,}918$

5. Profitability Index ($PI$)

$PI = \frac{\text{PV of Cash Inflows}}{CF_0} = \frac{\text{PHP }6{,}099{,}918}{\text{PHP }4{,}250{,}000} = 1.435$

6. Undiscounted Payback Period

$\text{Payback} = \frac{\text{PHP }4{,}250{,}000}{\text{PHP }1{,}560{,}000} = 2.72\text{ years}$ (Recovered comfortably prior to project termination).