Capital Budgeting

Learning Objectives

  • Distinguish independent, mutually exclusive, contingent, and capital-constrained project decisions.
  • Use NPV at the MARR as a value-based project-screening and selection measure.
  • Explain the roles and limitations of IRR, profitability index, payback, and other secondary metrics.
  • Select a value-maximizing portfolio under a finite capital budget for a small set of independent projects.
  • Recognize interactions, indivisibility, timing, risk, and strategic constraints that make simple ranking insufficient.

Capital Budgeting

Capital budgeting is the process of evaluating, selecting, and allocating limited capital among long-lived projects or assets while considering their future economic consequences and organizational constraints.

Independent Projects

Independent projects can be accepted together if each is feasible and sufficient capital and other resources are available.

Mutually Exclusive Projects

Mutually exclusive projects are alternative ways of satisfying the same need such that selecting one prevents selection of the others for that decision.

Contingent Projects

A contingent project can be undertaken only if another project or condition is also accepted, such as a production expansion that requires a supporting utility upgrade.

Net Present Value (NPV)

NPV is the present worth of all signed project cash flows at the organization's stated decision rate. For independent unconstrained projects, positive NPV indicates economic value above the MARR under the model.

Unconstrained Capital-Budgeting Rule

Profitability Index (PI)

A profitability index is a ratio measure of discounted benefits or net future inflows relative to the required initial investment, under a clearly stated convention. It can help describe value per unit of constrained capital but does not always produce the globally optimal indivisible-project portfolio.

One Common Profitability-Index Form

Present value of future positive net inflows divided by initial investment magnitude for a conventional project.

PI=PV(future net inflows)I0PI=\frac{PV(\text{future net inflows})}{I_0}

Variables

SymbolDescriptionUnit
PIPIProfitability index under the stated convention-
I0I_0Initial investment magnitude-

Capital Rationing

Capital rationing occurs when the set of economically attractive projects requires more capital than the available budget, so a subset must be selected.

Small-Portfolio Capital-Rationing Model

Select binary project decisions to maximize total NPV subject to the capital budget.

max⁡∑j=1mNPVjxj\max\sum_{j=1}^{m}NPV_jx_jsubject to ∑j=1mCjxj≤B,xj∈{0,1}\text{subject to }\sum_{j=1}^{m}C_jx_j\le B,\quad x_j\in\{0,1\}

Variables

SymbolDescriptionUnit
NPVjNPV_jNet present value of project j-
CjC_jCapital required by project j-
BBAvailable capital budget-
xjx_jBinary decision: 1 if selected, 0 otherwise-
mmNumber of candidate projects-

Interactive Capital-Rationing Laboratory

Change the budget, project first costs, and NPVs to see which combination maximizes portfolio NPV for a small set of indivisible projects.

Capital-Rationing Portfolio Laboratory

Concept and model scope

Choose the combination of independent, indivisible projects that maximizes total NPV without exceeding a limited capital budget. Ranking individual IRRs or profitability indices alone can miss the best portfolio.

Drainage A
Pump B
Plant C
Fleet D
Retrofit E
Selected portfolio
Plant C + Retrofit E
An exact branch-and-bound subset search is used for this small teaching portfolio; dominated branches are pruned without changing the optimum.
Capital used
₱6,900,000
₱100,000 remains unallocated.
Portfolio NPV
₱1,730,000
Objective: maximize total modeled NPV subject to the capital budget.
ProjectCostNPVPortfolio
Drainage A₱2,400,000₱580,000Not selected
Pump B₱3,200,000₱920,000Not selected
Plant C₱4,100,000₱1,040,000Selected
Fleet D₱1,700,000₱310,000Not selected
Retrofit E₱2,800,000₱690,000Selected

This model assumes project NPVs are additive and projects are independent except for the budget. Real portfolios with mutual exclusivity, prerequisites, resource coupling, schedule interactions, or risk limits require those constraints to be modeled explicitly.

Present-Worth Alternative Comparator

Concept and model scope

Discount every cash flow to time zero using one MARR and compare alternatives on the same study basis.

MARR10.00%
Common study life8 years
Alternative A
Alternative B
PW — Alternative A
₱1,741,625
Meets the MARR screen.
PW — Alternative B
₱1,968,658
Meets the MARR screen.
Preferred on this common basis
Alternative B
PW(B) − PW(A) = ₱227,033.

For unequal lives, do not force a common-life comparison without stating the repeatability assumption. Annual worth or a fixed study period is often clearer.

Why Highest IRR Is Not the Portfolio Objective

IRR is a percentage measure. Under a value-maximization objective, a smaller project with a very high IRR can create less total economic value than a larger positive-NPV project. For mutually exclusive alternatives, use incremental analysis or compare NPV directly at the MARR.

Why PI Ranking Can Fail for Indivisible Projects

Sorting projects by PI resembles a fractional-knapsack heuristic. Real capital projects are often indivisible, and a combination of lower-ranked projects can use the budget more efficiently and create more total NPV. Evaluate feasible combinations or use an optimization model when the constraint matters.

Portfolio Interaction

Portfolio interaction exists when accepting one project changes another project's cash flows, resource requirements, feasibility, or risk. In that case, project NPVs are not simply additive independent numbers.

Economic Metrics Do Not Replace Governance

Safety, code compliance, environmental obligations, liquidity, debt covenants, strategic fit, staffing, risk concentration, and sequencing may constrain the feasible portfolio. Capital budgeting should document these constraints rather than conceal them inside an arbitrary hurdle rate.

Do Not Double Count Financing

If project cash flows are evaluated using a MARR that already reflects the financing/opportunity-cost framework, inserting loan principal and interest into the project operating cash flows can double count financing effects unless the analysis is explicitly from an equity-financing viewpoint.

Capital-Budgeting Workflow

  1. Define strategic and technical feasibility before economic ranking.
  2. Build project cash flows on a common price, tax, and rate basis.
  3. Compute NPV and any required secondary metrics.
  4. Separate independent, mutually exclusive, and contingent relationships.
  5. If capital is unconstrained, apply the appropriate independent or mutually exclusive rule.
  6. If capital is constrained, optimize the feasible project portfolio rather than relying only on individual rankings.
  7. Test sensitivity to budget, MARR, cost overruns, schedule changes, and benefits.
  8. Document non-economic constraints and portfolio interactions.
Key Takeaways
  • Capital budgeting allocates scarce capital among long-lived engineering projects.
  • Positive NPV is the primary value-based screen for independent projects under the modeled MARR.
  • Mutually exclusive alternatives are not selected by highest stand-alone IRR.
  • Capital rationing turns project selection into a portfolio optimization problem.
  • PI can be informative but may fail to identify the best indivisible-project combination.
  • Project interactions and non-economic constraints can invalidate simple additivity.
  • A transparent capital-budgeting recommendation states its economic, technical, risk, and governance assumptions.