Chapter 10: Project Analysis and Evaluation

Learning Objectives

• Perform and interpret sensitivity analysis for a proposed investment.
• Perform and interpret scenario analysis for a proposed investment.
• Determine and interpret cash, accounting, and financial break-even points.
• Explain how the degree of operating leverage can affect the cash flows of a project.
• Discuss how capital rationing affects the ability of a company to accept projects.

Chapter Outline

• Evaluating NPV Estimates.
• Scenario and Other What-If Analyses.
• Break-Even Analysis.
• Operating Cash Flow, Sales Volume, and Break-Even.
• Operating Leverage.
• Capital Rationing.

Evaluating NPV Estimates

• A positive NPV indicates that a closer look is needed:
  • Projected cash flows may not align with actual cash flows.
  • Example: A cash flow projection of $700 in Year 4 means the average of possible cash flows is $700.
• Forecasting Risk: The risk of errors in projected cash flows leading to incorrect decisions.
• Source of Value: This addresses what factors contribute to a positive NPV; essential elements are the market competition level.

Scenario and Other What-if Analyses 1

• Initial NPV estimation based on projected cash flows is called the base case. After this:
  • Investigate different future assumptions.
  • Establish upper and lower bounds on project components.
• Example with project cost of $200,000:
  • Life: 5 years, no salvage value.
  • Required return: 12%, Tax rate: 21%.
  • Variable information includes unit sales (6,000), price per unit ($80), and variable costs ($60).

Scenario and Other What-if Analyses 2

• Calculate base-case NPV by determining net income:
  • Calculations:
  • Sales: $480,000
  • Variable costs: $360,000
  • Fixed costs: $50,000
  • Depreciation: $40,000
  • EBIT = Sales - Variable Costs - Fixed Costs - Depreciation = $30,000
  • Taxes (21%) = $6,300
  • Net Income = $23,700
• Operating Cash Flow: $30,000 + $40,000 - $6,300 = $63,700 per year.
• Base-case NPV: NPV = -200,000 + 63,700 imes 3.6048 = 29,624.

Scenario Analysis

• Scenario Analysis examines the effect of various scenarios on NPV estimates (such as best and worst case scenarios).
• Scenarios:
  • Worst Case: Unit sales = 5,500, Price per unit = $75, Variable cost = $62.
  • Best Case: Unit sales = 6,500, Price per unit = $85, Variable cost = $58.
• Net Income and Cash Flow Calculations for different scenarios show varying NPVs and IRRs:
  • Base case: NPV = $29,624
  • Worst case: NPV = −122,732
  • Best case: NPV = 201,915

Sensitivity Analysis

• Investigates NPV changes by altering one variable at a time.
• Example Under Base Case Conditions:
  • Varying unit sales impacts cash flow and NPV calculations:
  • Worst Case (5,500 units): NPV = 1,147
  • Best Case (6,500 units): NPV = 58,102
• Graphically, the steeper the line from NPV to unit sales, the more sensitive the estimates are to changes.

Simulation Analysis

• Combines aspects of scenario and sensitivity analyses by allowing all items to vary simultaneously.
• Involves random selections of variable values, calculating NPV repeatedly to derive an average and spread of estimates.

Break-even Analysis

Fixed and Variable Costs

• A tool to analyze sales volume vs. profitability.
• Variable costs are zero when output is zero:
  VC = Q imes v
  (Where $VC$ = total variable cost, $v$ is cost per unit, $Q$ is output quantity).
• Example:
  • VC = $2 per unit hence for 1,000 units, VC = 1,000 imes 2 = 2,000.

Relationship between Total Costs

• Total costs (TC) = Variable Costs (VC) + Fixed Costs (FC).
  • Example with v = 3 and FC = 8,000 gives:
  • TC = 3 imes Q + 8,000.
• Total costs for production at certain volumes can be tabulated and graphed.

Average Cost Versus Marginal Cost

• Blume Corporation Example: Given variable costs and fixed costs, calculation of total production costs helps determine average costs per unit.
• The sales decision for additional units should consider the marginal cost vs. potential revenue.

Accounting Break-even

• The level of sales where net income equals zero:
  Q_{BE} = rac{(FC + D)}{(P - v)}
• Real world application using variable prices and fixed costs is illustrated using a computer disk sales example.

Break-even Measures Summary

1. General Break-Even Expression: Operating cash flow (OCF) relates to production quantity (Q).
2. Accounting Break-even: Occurs when net income is zero.
3. Cash Break-even Point: Operating cash flow equals zero.
4. Financial Break-even Point: The sales level that gives a zero NPV.

Operating Leverage

• Definition: Degree to which fixed costs are used in producing goods. High operating leverage poses higher risks, amplifying potential changes in revenue's impact on cash flow.
• Measurement of Operating Leverage (DOL):
  DOL = rac{ ext{Percentage change in OCF}}{ ext{Percentage change in Q}}

Capital Rationing

• Occurs when a firm has positive NPV projects but cannot secure necessary financing. It involves soft rationing and hard rationing scenarios, influencing project selection.

Selected Concept Questions

• What is forecasting risk?
• Why is it a concern for financial managers?
• What problems does capital rationing create for discounted cash flow analysis?