Chapter 10: Project Analysis and Evaluation

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?