Capital Budgeting Decision Models

Overview of Decision Models

Capital budgeting involves evaluating investment projects using various decision models. These models help determine which projects a firm should undertake to maximize shareholder value.

• Payback Period: Measures the time required to recover the initial investment from project cash flows. Simple and fast, but ignores cash flows after the cutoff date and the time value of money.

• Net Present Value (NPV): Calculates the present value of all cash inflows and outflows using a discount rate (usually WACC). NPV is the best decision model as it properly ranks projects across sizes, time horizons, and risk levels.

• Internal Rate of Return (IRR): The discount rate that makes the NPV of a project zero. Provides a single measure of return but can be misleading with multiple IRRs or mutually exclusive projects.

• Profitability Index (PI): Ratio of the present value of inflows to the present value of outflows. Useful for ranking projects when capital is constrained.

Cash Flow Analysis

Importance of Cash Flow

Cash flow represents the actual inflow and outflow of cash, which is more relevant for decision-making than accounting profits. Firms can spend operating cash flow but not net income, and cash flow is broader than net income.

• Operating Cash Flow (OCF): Measures cash generated from operations.

• Incremental Cash Flow: The increase in cash flow from undertaking a specific project, considering only relevant changes.

Estimating Cash Flow for Projects

When analyzing projects, only incremental cash flows should be considered. Seven key issues to track:

• Sunk costs (not relevant)

• Opportunity costs

• Erosion

• Synergy gains

• Working capital

• Capital expenditures

• Depreciation or cost recovery of assets

Sunk Costs

Sunk costs are expenses already incurred and should not be included in project evaluation. For example, prior marketing research costs are sunk and irrelevant to future decisions.

Erosion Costs

Erosion costs arise when a new product reduces the revenue of existing products. These must be included in incremental cash flow calculations.

• Example: If launching a new dessert reduces sales of an existing product, the lost contribution margin is an erosion cost.

• Formula: Erosion cost = (Unit sales before launch - Unit sales after launch) × (Selling price - Unit cost)

• Calculation: (100,000 - 85,000) × ($3.50 - $1.75) = $26,250

Pro Forma Financial Statements and Cash Flow

Pro Forma Statements

Pro forma financial statements forecast future operations and are used to estimate project cash flows.

• Operating Cash Flow (OCF):

• If no interest expense:

• Cash Flow From Assets (CFFA):

Depreciation and After-Tax Salvage Value

Computing Depreciation

• Straight-Line Depreciation: Spreads the cost evenly over the asset's useful life.

• MACRS: Accelerated method for U.S. tax purposes, allowing higher deductions in early years.

After-Tax Salvage Value (ATSV)

When an asset is sold, calculate the net cash flow after taxes:

• Step 1: Find taxable gain or loss:

• Step 2: Calculate tax impact (using marginal tax rate ): If gain: If loss:

• Step 3: Find total ATSV: If gain: If loss: General formula:

Weighted Average Cost of Capital (WACC)

Definition and Formula

WACC is the minimum acceptable rate of return a firm should earn on its investments, reflecting the average risk. It is used as the discount rate for NPV calculations.

• Formula: Where: = capital structure weights = cost of each component = marginal corporate tax rate

• Expanded:

Risk-Adjusted WACC

Different projects may have different risks. Adjust the WACC to reflect the appropriate risk and capital structure for each division or project.

Cost of Capital Components

Cost of Equity ()

The return required by equity investors, given the risk of the firm's cash flows. Two main methods:

• Dividend Growth Model: Rearranged:

• Security Market Line (SML) / CAPM:

Cost of Debt ()

The required return on a company's debt, typically estimated using yield to maturity (YTM) or current market rates. The cost of debt is not the coupon rate.

• Example: For a semi-annual bond:

Cost of Preferred Stock ()

Preferred stock pays a constant dividend and is valued as a perpetuity.

• Formula:

• Example: or 4.84%

Determining Weights for WACC

Weights are the percentages of the firm financed by each component. Use target weights if possible; otherwise, use market values.

• Book Value < Market Value < Target (Good < Better < Best)

Risk and Return

Risk-Return Trade-off

There is a reward for bearing risk, and the greater the potential reward, the greater the risk.

Percent Return

• Dividend Yield:

• Capital Gains Yield:

• Total Percent Return:

Example: Calculating Total Dollar and Percent Returns

Risk Premiums

• Risk-free rate: Return on a riskless investment (e.g., Treasury Bills).

• Risk premium: Excess return on a risky asset over the risk-free rate; reward for bearing risk.

Arithmetic vs. Geometric Mean

• Arithmetic Mean (AM): Simple average:

• Geometric Mean (GM): Compound average:

Example: Calculating Geometric Average Return

Geometric Average Return: 8.26%

Market Efficiency

Operational Efficiency

Refers to the speed and accuracy with which trades are processed. U.S. markets are highly operationally efficient, matching buyers and sellers at the best available prices.

Informational Efficiency

Describes how quickly and accurately information is reflected in asset prices. Three forms:

• Weak-form: Prices reflect all past market data; technical analysis is not useful.

• Semi-strong form: Prices reflect all publicly available information; fundamental analysis is not useful.

• Strong-form: Prices reflect all information, public and private; no investor can consistently achieve excess returns.

Tables

Sample Cash Flow Table: Projects L and S

Example: Depreciation and After-Tax Salvage Value Table

Example: Calculating Total Dollar and Percent Returns

Key Formulas

• NPV:

• IRR:

• Profitability Index:

• WACC:

• Dividend Growth Model:

• CAPM:

• Percent Return:

• Geometric Mean:

Additional info: These notes expand on the original slides and handwritten content, providing full definitions, formulas, and examples for key financial accounting and capital budgeting concepts relevant to college-level study.