Capital Budgeting and Net Present Value (NPV)

Fundamentals of Capital Budgeting

• Definition: Capital budgeting is the formal decision-making process used to determine which long-term investment projects an organization should undertake.
• Scope of Projects: Typical examples include:
  • Launching new product lines.
  • Purchasing or upgrading machinery.
  • Implementing new Information Technology (IT) systems.

Case Study: Airbus 380 (2000)

• In 2000, Airbus faced a massive strategic decision regarding the development and production of the Airbus 380.
• Economic Scale:
  • Estimated Investment: $12 billion.
  • Contextual Magnitude: This investment represented approximately $70\%$ of Airbus's total revenues for that year and $26\%$ of the total revenue for the entire industry.
• The Central Question: How does an organization decide to commit such sizable capital? The answer lies in the application of the Net Present Value (NPV) framework.

The Net Present Value (NPV) Decision Rule

• Core Concept: NPV measures the total added value of a project to the organization by comparing the present value of inflows to the initial outlay.
• The Procedure:
  1. Project Future Cash Flows: Estimate the expected values of all future Free Cash Flows (FCF).
  2. Discount Cash Flows: Apply the opportunity cost of capital to these expected values to adjust for risk and the time value of money.
  3. Subtract Initial Investment: Deduct the up-front cost from the sum of the discounted future cash flows.
• Mathematical Representation:   $NPV = \text{Present Value of all future cash flows} - \text{Initial Investment}$
• The Decision Criteria:
  • If $NPV > 0$: The project should be accepted as it adds value to the organization.
  • If $NPV < 0$: The project should be rejected as it destroys value.

Illustrative Simple NPV Calculation

• Scenario Parameters:
  • Initial Investment ($C_0$): $1,000,000.
  • Future Free Cash Flows ($C_1, C_2, C_3$): $350,000 per year for 3 years.
  • Opportunity Cost of Capital ($r$): $5\%$.
• Calculation:   $NPV = -1,000 + \frac{350}{(1.05)} + \frac{350}{(1.05)^2} + \frac{350}{(1.05)^3}$$NPV = -46.86$
• Conclusion: Because the NPV is negative ($-46.86$), the project should be rejected.

Comprehensive NPV Framework and Formulas

• General Principle: An organization should choose projects that maximize total value, which occurs when NPV is positive.
• NPV Formula over Time:   $0 = -C_0 + \frac{C_1}{(1+r)} + \frac{C_2}{(1+r)^2} + \frac{C_3}{(1+r)^3} + \dots$
  • Where $C_t$ is the expected free cash flow at the end of period $t$.
  • Where $r$ is the opportunity cost of capital.
• Opportunity Cost of Capital defined: It is the expected rate of return that can be earned on alternative investments with identical characteristics in terms of risk and maturity (effectively, what can be earned in securities markets vs. the project).

Determining the Discount Rate: WACC

• Usage: The Weighted Average Cost of Capital (WACC) is used when the project's risk corresponds to the firm's average risk.
• Variables:
  • $r_D$: Cost of debt.
  • $r_E$: Cost of equity.
  • $E$: Market value of equity.
  • $D$: Market value of debt.
  • $\tau_c$: Corporate tax rate (used to account for the interest tax shield).
• WACC Formula:   $r_{wacc} = \frac{E}{E+D} \times r_E + \frac{D}{E+D} \times r_D \times (1 - \tau_c)$

Calculation of Free Cash Flows (FCF)

• Definition: FCF represents the total cash available for financiers, including both debt and equity holders.
• From Incremental Earnings to FCF:
  1. Forecast the net incremental unlevered earnings.
  2. Add back non-cash items (e.g., Depreciation and Provisions).
  3. Subtract investments in Net Working Capital ($\Delta NWC$).
  4. Subtract investments in fixed assets (Capital Expenditures or CapEx).
• The FCF Formula:   $FCF = EBIT \times (1 - \tau_c) + \text{Depreciation} - CapEx - \Delta NWC$

Case Study: Linksys HomeNet Project

Project Assumptions

• Feasibility Study: Linksys spent $300,000 on a study (Note: this is a sunk cost and generally excluded from incremental analysis, though listed in project parameters).
• Project Life: 4 years.
• Sales Volume: 100,000 units per year.
• Unit Price: $260.
• Unit Cost: $110.
• R&D Expenses: $15,000,000 (Up-front in Year 0).
• Equipment Cost: $7,500,000 (Up-front in Year 0).
• Equipment Life: 5 years (for depreciation purposes).
• Annual Overhead: $2,800,000.
• Tax Rate: $40\%$.

Incremental Earnings Forecast ($000s)

Note on Year 5 Depreciation: While the project's sales life is 4 years, the 5-year equipment life necessitates a depreciation expense and tax shield in year 5.

Net Working Capital (NWC) Forecast ($000s)

• Receivables: Calculated as $15\%$ of Sales.
• Payables: Calculated as $15\%$ of Cost of Goods Sold (COGS).

Consolidated Free Cash Flows ($000s)

Final HomeNet NPV Calculation

• Discount Rate: Assuming an opportunity cost of capital of $12\%$.
• Formula Extension:   $NPV = -16,500 + \frac{5,670}{1.12} + \frac{7,920}{1.12^2} + \frac{7,920}{1.12^3} + \frac{7,920}{1.12^4} + \frac{2,850}{1.12^5}$
• Result:   $NPV = 7,164.04$
• Decision: Since $7,164.04 > 0$, the project is value-additive and should be accepted.