Capital Allocation Calculator - Optimal Portfolio Selection

Defining project costs and cash inflows (NPV)

To begin modeling your capital budget, you must first define the candidate projects. In the left panel, add rows for each project under consideration. For each project, input a unique project name (or identifier) along with two critical financial metrics:

- Outlay Cost: The initial capital expenditure (CAPEX) required to launch and execute the project. This cost is treated as a hard subtraction from the overall budget pool.
- Project NPV: The estimated Net Present Value that the project is expected to generate. This value represents the present value of future cash inflows discounted at your hurdle rate, minus the outlay.

Ensure all values are stated in consistent currency units to maintain structural calculation integrity.

Setting your portfolio budget constraints

Once you have populated your candidate list, set the Capital Budget Cap. This represents the total amount of investment funding available for allocation during the budget period.

After defining the budget limit and the projects, click the "Solve Portfolio" button. The results panel will automatically refresh to display the optimal subset of selected projects, the maximum cumulative NPV created, the total cost outlay, and the remaining unallocated cash. You can toggle tabs on the results card to inspect the sensitivity grid and compare the results to greedy PI heuristics.

Why simple PI ranking leads to sub-optimal subsets

A common approach to capital allocation is the "Greedy" method, where projects are ranked in descending order of their Profitability Index (PI = NPV / Cost). Analysts fund the highest-ranked projects one by one until the budget runs out. While intuitive, this approach often yields sub-optimal results in the presence of indivisible projects and tight budgets.

For example, if the budget is $100,000, and we have Project X (Cost $60,000, NPV $45,000, PI 0.75), Project Y (Cost $50,000, NPV $35,000, PI 0.70), and Project Z (Cost $50,000, NPV $35,000, PI 0.70). The greedy method selects Project X first because of its higher PI. However, this leaves only $40,000 in the budget, which is not enough to fund either Project Y or Z. The total NPV created is $45,000, with $40,000 left uninvested.

The economic value of mathematical optimization (knapsack solver)

A mathematical solver looks at the entire combination of projects to find the optimal solution. In the example above, a binary knapsack solver recognizes that by bypassing Project X, it can select *both* Project Y and Project Z.

This combination costs exactly $100,000 (utilizing the budget fully) and generates a total NPV of $70,000 ($35,000 + $35,000). By employing the optimal model instead of the greedy ranking, the firm generates an extra $25,000 of wealth from the same $100,000 budget cap.

This is the essence of capital optimization: maximizing the yield of capital resources by analyzing the full combinatorics of candidates.

Measuring total NPV yield and allocated budget ratios

To evaluate the efficiency of your capital program, the calculator computes the Allocation Efficiency Ratio:

Allocation Efficiency = ( Total Cost of Selected Projects / Total Budget Cap ) * 100

This ratio measures how much of the available funding is actively deployed. A higher ratio indicates that the solver successfully identified a combination of projects that utilizes the available capital, minimizing uninvested cash reserves that drag down overall returns.

Understanding the profitability index threshold limit

The Profitability Index (PI) serves as the primary efficiency metric for individual projects. It measures the value generated per dollar of capital outlay:

Profitability Index (PI) = Net Present Value (NPV) / Initial Cost

A project is value-creative only if its PI is greater than 0. Projects with a negative NPV (PI < 0) should be excluded from candidate lists entirely. While the solver does not rely on simple PI rankings to select projects, it uses PI values to verify that every funded candidate generates returns exceeding its initial cost.

Sample projects and budget constraint inputs

Let's walk through an illustrative allocation scenario for a business with a capital budget cap of $300,000. The company has four investment candidates:

• Project A: Cost = $100,000, NPV = $20,000 (PI = 0.20)
• Project B: Cost = $150,000, NPV = $35,000 (PI = 0.23)
• Project C: Cost = $200,000, NPV = $45,000 (PI = 0.225)
• Project D: Cost = $80,000, NPV = $15,000 (PI = 0.187)

Comparing optimal solver vs greedy PI ranking step-by-step

Let's analyze how both methods allocate the $300,000 budget:

1. Greedy PI Ranking Method:
- Sort by PI: Project B (0.233) → Project C (0.225) → Project A (0.20) → Project D (0.187).
- Select B (Cost $150k, NPV $35k). Remaining Budget = $150k.
- Try to select C (Cost $200k) → Exceeds budget. Skip.
- Select A (Cost $100k, NPV $20k). Remaining Budget = $50k.
- Try to select D (Cost $80k) → Exceeds budget. Skip.
- Greedy Outcome: Select A & B. Total Cost = $250,000. Total NPV = $55,000. Leftover Cash = $50,000.

2. Optimal Binary Knapsack Solver:
- Evaluates all combinations. Identifies that selecting Project B and Project C costs exactly $350,000 (exceeds budget), but selecting Project A and Project C costs exactly $300,000.
- Optimal Outcome: Select A & C. Total Cost = $300,000. Total NPV = $65,000 ($20k + $45k). Leftover Cash = $0.

The optimal solver generates an extra $10,000 in NPV wealth (an 18.18% return increase) by utilizing the budget fully, illustrating the advantage of mathematical portfolio modeling over simple heuristics.