Capital Budgeting

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.

$Project Relationships and Portfolio Feasibility$

Relationship	Feasibility condition	Economic modeling consequence
Independent	One can be accepted without requiring another decision	NPVs add when portfolio cash flows sum without project interaction; risk dependence still matters for portfolio risk
Mutually exclusive	Alternatives satisfy the same need; choose at most one	Compare on a common service basis and select by value, not stand-alone percentage rank
Contingent	One project requires another project or condition	Encode the dependency in the feasible portfolio
Interacting	One project's acceptance changes another's cash flows, resources, or risk	Model joint effects; simple NPV additivity may fail

$Net Present Value (NPV)$

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.

$Unconstrained Capital-Budgeting Rule$

For independent projects, accept every feasible project with positive NPV when no binding capital or strategic constraint prevents doing so.
For mutually exclusive alternatives, select the feasible alternative with the largest NPV on the common study basis.

$Profitability Index (PI)$

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

Variables

Symbol	Description	Unit
$PI$	Profitability index under the stated convention	-
$I_0$	Initial 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.

$Selection Metric Under the Constraint$

Measure or constraint	What it contributes	Limitation to check
NPV at MARR	Total modeled value on a common basis	Forecast, rate, risk, and service assumptions govern the result
Profitability index	Value relative to an investment magnitude under a stated definition	A ratio ranking can miss the best indivisible-project combination
IRR	Percentage return for a cash-flow stream	Stand-alone percentages do not maximize portfolio value or resolve mutual exclusivity
Payback	Capital recovery timing	Omits some value and is not a complete NPV rule
Capital budget	Maximum funding available	Requires selection of a feasible combination, including dependencies and interactions

Small-Portfolio Capital-Rationing Model

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

\max\sum_{j=1}^{m}NPV_jx_j

\text{subject to }\sum_{j=1}^{m}C_jx_j\le B,\quad x_j\in\{0,1\}

Variables

Symbol	Description	Unit
$NPV_j$	Net present value of project j	-
$C_j$	Capital required by project j	-
$B$	Available capital budget	-
$x_j$	Binary decision: 1 if selected, 0 otherwise	-
$m$	Number 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.

Available capital budgetPHP

Drainage A