Capital Budgeting and Cash Flow Analysis: Exam 3 Review Study Notes

Capital Budgeting Decision Models

Payback Period

The payback period is the time required for the cumulative cash inflows from a project to equal the initial investment. It is a simple method used to assess the risk and liquidity of a project, but it does not consider the time value of money or cash flows beyond the payback point.

• Calculation: Add up the cash inflows until the initial investment is recovered.

• Formula: $\text{Payback Period} = \text{Years before full recovery} + \frac{\text{Unrecovered amount at start of year}}{\text{Cash flow during year}}$

• Example: For Project L, with cash flows of -100, 10, 60, 80, the payback period is $2 + \frac{30}{80} = 2.375$ years.

• Limitations: Ignores time value of money and cash flows after the payback period.

Net Present Value (NPV)

Net Present Value (NPV) is the sum of the present values of all cash inflows and outflows associated with a project, discounted at the project's cost of capital. NPV is the most economically sound method for evaluating investment projects.

• Formula: $\text{NPV} = \sum_{t=0}^{N} \frac{CF_t}{(1 + r)^t}$, where $CF_t$ is the cash flow at time $t$, and $r$ is the discount rate.

• Decision Rule:

  • For independent projects: Accept if NPV > 0.

  • For mutually exclusive projects: Accept the project with the highest positive NPV.

• Example:

  Year	CFL	PV of CFL (10%)
  0	-100	-100.00
  1	10	9.09
  2	60	49.59
  3	80	60.11

  NPVL = $18.78$

Internal Rate of Return (IRR)

The Internal Rate of Return (IRR) is the discount rate that makes the NPV of all cash flows from a project equal to zero. It represents the project's expected rate of return.

• Formula: $0 = \sum_{t=0}^{N} \frac{CF_t}{(1 + IRR)^t}$

• Calculation: Use financial calculators or spreadsheet functions (e.g., =IRR() in Excel).

• Decision Rule: Accept the project if IRR > required rate of return (hurdle rate).

• Limitations: Multiple IRRs can occur with non-conventional cash flows; assumes reinvestment at IRR, which may not be realistic.

Profitability Index (PI)

The Profitability Index (PI) is the ratio of the present value of future cash inflows to the initial investment. It is useful for ranking projects when capital is limited.

• Formula: $\text{PI} = \frac{\text{PV of future cash inflows}}{\text{Initial investment}}$

• Decision Rule: Accept if PI > 1.

• Interpretation: Indicates the value created per dollar invested.

Cash Flow Analysis for Projects

Incremental Cash Flows

When evaluating projects, only incremental cash flows—the additional cash flows generated by the project—should be considered. These include changes in revenues, expenses, and working capital directly attributable to the project.

• Relevant Cash Flows: Opportunity costs, erosion (cannibalization) costs, changes in working capital, capital expenditures, and depreciation.

• Non-relevant Cash Flows: Sunk costs and financing costs.

• Example: If a new product reduces sales of an existing product, the lost margin is an erosion cost and must be included in the analysis.

Sunk Costs

Sunk costs are costs that have already been incurred and cannot be recovered. They should not be included in the project's cash flow analysis.

• Example: Money spent on market research before deciding on a project is a sunk cost.

Opportunity Costs

Opportunity costs represent the value of the next best alternative foregone as a result of choosing a particular project.

• Example: Using an idle asset for a project means losing the potential sale value of that asset.

Erosion (Cannibalization) Costs

Erosion costs occur when a new project reduces the cash flows of existing products or services.

• Calculation: Lost margin = (Selling price – unit cost) × (Units lost)

• Example: If sales of an existing product drop from 100,000 to 85,000 units after a new product launch, and the margin per unit is $1.75, the erosion cost is$(100,000 - 85,000) \times 1.75 = $26,250$.

Working Capital Changes

Projects often require changes in net working capital (NWC), such as increased inventory or receivables. These are cash outflows at the start and inflows when liquidated at the end of the project.

• Formula: $\text{Change in NWC} = \text{Increase in current assets} - \text{Increase in current liabilities}$

Depreciation and After-Tax Salvage Value

Straight-Line Depreciation

Straight-line depreciation spreads the cost of an asset evenly over its useful life.

• Formula: $\text{Depreciation} = \frac{\text{Initial cost} - \text{Salvage value}}{\text{Useful life (years)}}$

• Features: Same amount each year; easy to calculate.

After-Tax Salvage Value (ATSV)

When an asset is sold, the after-tax salvage value accounts for taxes paid on gains or tax shields from losses.

• Formula: $\text{ATSV} = \text{Salvage Value} - T \times (\text{Salvage Value} - \text{Book Value})$

• Where: T = marginal tax rate

• Book Value: $\text{Book Value} = \text{Initial Cost} - \text{Accumulated Depreciation}$

Cost of Capital and Weighted Average Cost of Capital (WACC)

Weighted Average Cost of Capital (WACC)

WACC is the average rate a company is expected to pay to finance its assets, weighted by the proportion of each source of capital (debt, equity, preferred stock).

• Formula: $\text{WACC} = \frac{E}{V}R_e + \frac{P}{V}R_p + \frac{D}{V}R_d(1-T)$

• Where:

  • E = market value of equity

  • P = market value of preferred stock

  • D = market value of debt

  • V = E + P + D (total market value of the firm)

  • $R_e$ = cost of equity

  • $R_p$ = cost of preferred stock

  • $R_d$ = cost of debt

  • T = corporate tax rate

• Application: Used as the discount rate for NPV calculations.

Cost of Equity

The cost of equity is the return required by equity investors, estimated using models such as the Dividend Growth Model or the Capital Asset Pricing Model (CAPM).

• Dividend Growth Model: $R_e = \frac{D_1}{P_0} + g$

• CAPM: $R_e = R_f + \beta (E(R_m) - R_f)$

• Where:

  • $D_1$ = expected dividend next year

  • $P_0$ = current stock price

  • $g$ = growth rate

  • $R_f$ = risk-free rate

  • $\beta$ = systematic risk of asset

  • $E(R_m)$ = expected market return

Cost of Debt

The cost of debt is the yield to maturity (YTM) on existing debt, adjusted for tax deductibility.

• Formula: $R_d(1-T)$

• Example: If YTM is 7.37% and tax rate is 21%, after-tax cost of debt is $7.37\% \times (1 - 0.21) = 5.82\%$

Cost of Preferred Stock

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

• Formula: $R_p = \frac{D}{P}$

• Example: If annual dividend is $1.25 and price is $25.85,$R_p = \frac{1.25}{25.85} = 4.84\%$

Capital Market Returns and Efficiency

Arithmetic vs. Geometric Average Returns

Arithmetic average return is the simple average of returns over multiple periods, while geometric average return is the average compound return per period.

• Arithmetic Average: $\text{Arithmetic Average} = \frac{\sum_{i=1}^{n} R_i}{n}$

• Geometric Average: $\text{Geometric Average} = \left(\prod_{i=1}^{n} (1 + R_i)\right)^{1/n} - 1$

• Geometric average is always less than or equal to arithmetic average unless all returns are equal.

Forms of Market Efficiency

The Efficient Market Hypothesis (EMH) states that security prices reflect all available information. There are three forms:

• Weak Form: Prices reflect all past trading information; 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; even insider information cannot provide an advantage.

Form	Information Reflected
Weak	Past prices and volume
Semi-Strong	All public information
Strong	All public and private information

Summary Table: Project Cash Flows Example

Year	Project L	Project S	ΔCF
0	-100	-100	0
1	10	70	-60
2	60	50	10
3	80	20	60

Additional info: These notes expand on the original slides and review content, providing definitions, formulas, and examples for key capital budgeting and financial analysis concepts relevant to Financial Accounting and Finance students.