Capital Budgeting: NPV, WACC, and Project Selection
This paper presents a capital budgeting analysis of four mutually exclusive investment projects (A, B, C, and D) evaluated at three leverage levels: 0%, 20%, and 50% debt. Using the Hamada equation to adjust beta for financial risk and the Capital Asset Pricing Model (CAPM) to estimate the cost of equity, the analysis calculates the Weighted Average Cost of Capital (WACC) and key decision metrics—NPV, IRR, and MIRR—for each scenario. The paper concludes that Project B at 20% leverage offers the highest risk-adjusted NPV and recommends it as the optimal choice, while Project D at 50% leverage is identified as the only unacceptable option due to its negative NPV.
- Introduction and Beta Calculations: Beta values for all projects at each leverage level
- Cost of Equity and CAPM Validity: CAPM and Hamada equation applied to cost of equity
- WACC Across Projects and Leverage Levels: WACC calculated for all twelve project-leverage combinations
- Capital Budgeting Measures: NPV, IRR, and MIRR: Full decision metrics table and unacceptable project identified
- Project Selection and Optimal Capital Structure: NPV-based selection of Project B at 20% leverage
- Cash Flow Analysis and Recommendation: After-tax income calculation and analysis limitations noted
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What makes this paper effective
- Systematically applies multiple quantitative decision metrics (NPV, IRR, MIRR, WACC) to compare projects across three leverage scenarios, demonstrating methodological rigor.
- Clearly justifies why NPV is used as the primary selection criterion over IRR, explaining the economic logic of uninvested capital and firm value maximization.
- Acknowledges limitations in the analysis — specifically the assumption that uninvested capital from Projects C and D generates no return — and recommends corrective investigation.
Key academic technique demonstrated
The paper demonstrates the integration of the Hamada equation with CAPM to derive leverage-adjusted discount rates, then feeds those rates into WACC calculations and full capital budgeting metrics. This chain of quantitative reasoning — from unlevered beta to final project recommendation — is a core technique in corporate finance coursework and shows how financial risk and business risk are separated and re-combined in investment appraisal.
Structure breakdown
The paper opens with beta and cost-of-equity tables at each leverage point, then validates the CAPM methodology, presents WACC results, computes NPV/IRR/MIRR for all twelve scenarios, eliminates unacceptable projects, selects the optimal project and capital structure, calculates after-tax net income for the recommended option, and closes with a critical self-assessment of the analysis's limitations regarding uninvested capital.
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
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.
Cost of Equity and CAPM Validity
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 (Rf) and the market return (Rm) 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%
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 Rf and Rm 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.
WACC Across Projects and Leverage Levels
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%
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.
Capital Budgeting Measures: NPV, IRR, and MIRR
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%
Project B:
0% leverage: NPV $5.573M, IRR 14.16%, MIRR 11.10%
20% leverage: NPV $5.366M, IRR 13.67%, MIRR 11.14%
50% leverage: NPV $3.237M, IRR 8.50%, MIRR 11.65%
Project C:
0% leverage: NPV $4.970M, IRR 14.50%, MIRR 12.44%
20% leverage: NPV $4.819M, IRR 14.11%, MIRR 12.40%
50% leverage: NPV $2.978M, IRR 9.10%, MIRR 12.02%
Project D:
0% leverage: NPV $1.788M, IRR 4.37%, MIRR 7.24%
20% leverage: NPV $1.653M, IRR 4.05%, MIRR 7.22%
50% leverage: NPV −$0.173M, IRR −0.44%, MIRR 7.05%
The only unacceptable scenario is Project D at the 50% leverage level, which yields a negative NPV of −$0.173 million and a negative IRR. All other project-leverage combinations produce positive net present values and are therefore financially acceptable on that basis alone.
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