Chapter 13: Cost of Capital and Project-Based WACC

The Weighted Average Cost of Capital (WACC) serves as the overall rate of return a firm must earn on its existing assets to maintain the value of its stock.
The WACC Equation: $R_{wacc} = [w_d \times R_d(1-T_c)] + (w_{ps} \times R_{ps}) + (w_E \times R_E)$
- $w_d$ (or $D\%$ ): The weight of debt (bond) in the capital structure.
- $R_d$ : The before-tax cost of debt.
- $1-T_c$ : The after-tax adjustment, where $T_c$ is the corporate tax rate.
- $w_{ps}$ (or $P\%$ ): The weight of preferred stock.
- $R_{ps}$ : The cost of preferred stock.
- $w_E$ (or $E\%$ ): The weight of common equity.
- $R_E$ : The cost of common equity.
Calculation Constraints:
- The sum of all weights must equal one: $w_d + w_{ps} + w_E = 1$ .
- Market Value Emphasis: It is critical to note that these weights are computed using market values, not book values.

Key Steps in the WACC Method:
1. Incremental Free Cash Flow: Determine the incremental free cash flow of the proposed investment.
2. Weighted Average Cost of Capital: Compute the firm's WACC.
3. Valuation: Compute the value of the investment by discounting the incremental free cash flow using the WACC calculated in step 2.
WACC as a Benchmark:
- WACC can be utilized as a companywide benchmark discount rate for projects that possess a comparable risk to the rest of the existing firm.
- It is appropriate only if the project will not alter the firm’s target debt-equity ratio.
Acceptance Criterion: A project is considered viable only if it generates an expected return that is at least equal to the firm’s WACC ( $Expected\,Return \ge WACC$ ).
Tax Benefit: This specific methodology explicitly incorporates the tax benefit of leverage (the interest tax shield).

The Conglomerate Problem: A conglomerate (e.g., Hutchison Whampoa Limited, which operates in Ports & Related Services, Retailing, Energy, Infrastructure, Telecommunications, and Property & Hotels) should not evaluate all projects based on a single firm-wide WACC.
Project Risk vs. Firm Risk:
- WACC is the required rate of return for a new acquisition or project only when:
  1. The project has the same basic risk as the firm's current operations/assets.
  2. The project is financed in the same manner as the rest of the company.
- If the project risk differs from the overall firm risk, the firm's WACC is an inappropriate discount rate.
Consequences of Incorrect Discount Rate Usage:
- Scenario: A firm's WACC is $12\%$ . It evaluates a new project that is more risky than its average assets.
- Result of using existing WACC: If the firm uses its $12\%$ WACC, it will likely incorrectly accept the project. This occurs because the discount rate is too low for the level of risk, leading to an insufficient return to compensate for that risk.
- Conversely, if a project is significantly safer than the firm average, using the firm's high WACC might result in incorrectly rejecting a project that provides a return higher than required by its specific (lower) risk.

Market Risk Adjustments: To calculate the cost of capital for a project with market risk different from the firm, one should use the WACC of competitors whose businesses are similar to the new project.
Divisional Benchmarking: Firms with multiple divisions with varying risk characteristics should calculate a distinct cost of capital for each division. Divisions can be benchmarked against single-line-of-business companies ("pure plays") that compete specifically in that sector.
Theoretical Basis: Project cost of capital is an opportunity cost concept. It depends on the risk of the use of funds, not the source of those funds.

Problem Context:
- Cisco's WACC: $13.3\%$
- Risk-free rate ( $R_f$ ): $4.5\%$
- Market risk premium ( $MRP$ ): $5\%$
- New Project: Selling DVRs (a new line of business with different systematic risk).
Analysis (The "Pure Play" Approach):
- To estimate the cost of capital for the DVR investment, identify a specialist company like TiVo, Inc.
- TiVo's Beta ( $\beta$ ): $2.9$
- TiVo has zero debt, meaning its cost of equity ( $R_E$ ) equals its cost of capital for its assets.
Calculation using CAPM:
- $Cost\,of\,Equity = R_f + \beta(MRP)$
- $Cost\,of\,Equity = 4.5\% + 2.9(5\%) = 19\%$
Evaluation:
- The correct rate for the project is $19\%$ .
- Cisco’s WACC ( $13.3\%$ ) is only appropriate for its existing business. Using it for the DVR project would be too low and could lead to the mistaken acceptance of a negative NPV (Net Present Value) project.

Scenario: Cola Inc. (soft drink leader) adds a sports drink division.
Capital Structure Data:
- New Division Financing: $30\%$ debt, $70\%$ equity.
- Cost of debt ( $R_d$ ): $8\%$
- Risk-free rate ( $R_f$ ): $3\%$
- Market risk premium: $12\%$
- Tax rate ( $T_c$ ): $35\%$
Beta Selection:
- Cola Inc. Beta: $0.8$
- Supersports Inc. Beta: $0.3$
- Decision: Use the Beta of Supersports Inc. ( $0.3$ ) because the sports drink project risk aligns with the competitor, not the parent company.
Calculation:
- $Cost\,of\,Equity = 3\% + 0.3(12\%) = 6.6\%$
- $WACC = [0.3 \times 8\%(1-0.35)] + [0.7 \times 6.6\%]$
- $WACC = 1.56\% + 4.62\% = 6.18\%$
Evaluation:
- Cola Inc.’s existing WACC would have been too high for this project. Using the existing WACC would have resulted in incorrectly rejecting a positive NPV project.

Hypothetical Scenario: Pepsi is considering an aerospace project. It is assumed Pepsi and Boeing (an aerospace peer) have the same target capital structure.
Data Points:
- Pepsi WACC: $8\%$
- Boeing WACC: $10\%$
Net Present Value (NPV) Outcomes:
- At $8\%$ discount rate: $NPV = \$500,000$
- At $10\%$ discount rate: $NPV = -\$1,000,000$
Investment Decision:
- Should Pepsi invest? No.
- The project risk is that of the aerospace industry, not the soft drink industry. Therefore, the Boeing WACC of $10\%$ is the appropriate discount rate. At that rate, the project has a negative NPV and should be rejected.

Question: The WACC of your firm is 12%. It is evaluating a new project which is more risky than its average assets. What is likely to happen if the WACC is used as the discount rate for this project?
- Response: Option 2: Incorrectly accept the project which provides insufficient return to compensate for its risk.
Question: Which beta should Cola Inc. use for the sports drink division?
- Response: Option 2: 0.3 (the beta of the comparable firm in the specific industry).
Question: Should Pepsi invest in the aerospace project (referencing the $500k vs -$1M NPV scenario)?
- Response: Option 2: No.

Homework: HW 11 is due on May 12 (Tuesday).
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