Capital Budgeting: NPV, WACC, and Project Selection

Introduction and Beta Calculations

This analysis evaluates four mutually exclusive capital investment projects — A, B, C, and D — at three levels of financial leverage: 0%, 20%, and 50% debt. The Hamada equation is used to adjust each project's beta for the effects of leverage, separating business risk from financial risk. The resulting levered betas form the foundation for estimating the cost of equity and, ultimately, the Weighted Average Cost of Capital (WACC) for each scenario.

The beta values for each project at the different leverage levels are presented below:

Project A: 0% leverage — 0.90 | 20% leverage — 1.0575 | 50% leverage — 1.53
Project B: 0% leverage — 0.80 | 20% leverage — 0.94 | 50% leverage — 1.36
Project C: 0% leverage — 1.00 | 20% leverage — 1.175 | 50% leverage — 1.70
Project D: 0% leverage — 1.10 | 20% leverage — 1.2925 | 50% leverage — 1.87

Cost of Equity and CAPM Validity

As expected, beta rises with leverage for every project, reflecting the increased financial risk borne by equity holders as the proportion of debt financing grows.

The cost of equity for each project at the different leverage levels is derived using the Capital Asset Pricing Model (CAPM). The levered betas calculated via the Hamada equation are applied within the CAPM framework, while the risk-free rate (R_f) and the market return (R_m) remain constant across all scenarios.

Project A: 0% leverage — 9.30% | 20% leverage — 10.40% | 50% leverage — 13.71%
Project B: 0% leverage — 8.60% | 20% leverage — 9.58% | 50% leverage — 12.52%
Project C: 0% leverage — 10.00% | 20% leverage — 11.225% | 50% leverage — 14.90%
Project D: 0% leverage — 10.70% | 20% leverage — 12.05% | 50% leverage — 16.09%

WACC Across Projects and Leverage Levels

CAPM is a valid method for measuring the cost of equity for these projects. The Hamada equation adjusts the risk level for the degree of financial leverage, while R_f and R_m remain constant. Together, they allow CAPM to provide a reliable benchmark for both the business risk inherent to each project and the total risk associated with a given financing structure.

The Weighted Average Cost of Capital (WACC) for each project and leverage combination is calculated using the levered cost of equity and the after-tax cost of debt, weighted by their respective proportions in the capital structure. The full results are presented below:

Project A: 0% leverage — Beta 0.90, Cost of Equity 9.30%, WACC 9.30% | 20% leverage — Beta 1.0575, Cost of Equity 10.40%, WACC 9.72% | 50% leverage — Beta 1.53, Cost of Equity 13.71%, WACC 14.86%

Project B: 0% leverage — Beta 0.80, Cost of Equity 8.60%, WACC 8.60% | 20% leverage — Beta 0.94, Cost of Equity 9.58%, WACC 9.06% | 50% leverage — Beta 1.36, Cost of Equity 12.52%, WACC 14.26%

Capital Budgeting Measures: NPV, IRR, and MIRR

Project C: 0% leverage — Beta 1.00, Cost of Equity 10.00%, WACC 10.00% | 20% leverage — Beta 1.175, Cost of Equity 11.225%, WACC 10.38% | 50% leverage — Beta 1.70, Cost of Equity 14.90%, WACC 15.45%

Project D: 0% leverage — Beta 1.10, Cost of Equity 10.70%, WACC 10.70% | 20% leverage — Beta 1.2925, Cost of Equity 12.05%, WACC 11.04% | 50% leverage — Beta 1.87, Cost of Equity 16.09%, WACC 16.05%

A consistent pattern emerges: WACC rises sharply at the 50% leverage level for every project, driven primarily by the much higher cost of equity at that level of financial risk.

The relevant capital budgeting metrics — Net Present Value (NPV), Internal Rate of Return (IRR), and Modified Internal Rate of Return (MIRR) — are calculated for each project at each leverage level. The complete results are as follows:

Project A:
0% leverage: NPV $5.047M, IRR 10.35%, MIRR 9.88%
20% leverage: NPV $4.822M, IRR 9.92%, MIRR 9.83%
50% leverage: NPV $2.332M, IRR 5.01%, MIRR 9.39%