Ch. 11: Project Analysis and Evaluation

Just because we have a positive NPV project, should we invest?

• Our NPV estimate is only as good as our assumptions, namely projected cash flows
• Garbage in, garbage out
• Evaluating NPV estimates
  • Forcasting (estimation) risk
    • Scenario analysis
    • Sensitivity analysis
    • Simulation analysis
  • Identify sources of value
    • Economies of scale
    • Product differentiation
    • Cost advantages
    • Access to distribution channels
    • Favorable government policy

Evaluating NPV Estimates

• Example
  • Project costs $200,000, has a five-year life, and has no salvage value. Depreciation is straight-line to zero. Required return is 12 percent. Tax rate is 34 percent.
  • Projections: Unit Sales = 6,000 (±500); Price per unit = $80 (±5); VC per unit = $60 (±2); FC per year = $50,000 (±5,000)
  • Base-case NPV = $15,567
• Scenario Analysis
  • Determine the NPV under what-if scenarios
  • Commonly used scenarios
    • Worst Case (minimum NPV)
      • Low Sales, High Costs
      • Worst-case NPV = $–111,719
    • Best Case (maximum NPV)
      • High Sales, Low Costs
      • Best-case NPV = $159,504
• Sensitivity Analysis
  • Form of scenario analysis where only one variable at a time is changed
  • Examples
    • Varying sales: Best-case NPV = $39,357; Worst-case NPV = $–8,226
    • Varying FC: Best-case NPV = $27,461; Worst-case NPV = $3,670
  • Can identify where forecasting errors will do the most damage
• Simulation Analysis
  • Make assumptions on the distribution of input variables
  • Draw a random set of input variables
  • Map out the surface of possible NPVs
• At the end of the day, we still have to make a decision

Break-Even Analysis

• Unit sales is usually the lynchpin for whether a project will be successful or not
• What level of sales do we need not to lose money?
• Costs
  • VCs - costs that change when the quantity of output changes
  • FCs - costs that do not vary with quantity of output
  • Total, Average, and Marginal Costs
• Accounting Break-Even
  • How many units must we sell to have zero NI?
  • NI = (Sales - VCs - FCs - Depreciation) * (1-T)
  • Q = (FC + D)/(P-v)
  • Advantages
    • Easy
    • Earnings matter to managers
    • Focus on opportunity losses vs. out-of-pocket losses
  • Cash-flow at Accounting Break-Even
    • OCF = $1,000,000
    • Exactly equals depreciation
      • We get back our initial investment
      • Zero return
      • Negative NPV
• Cash Break-Even
  • How many units must we sell to have zero OCF?
  • OCF = [(P-v)Q - FC - D] + D = (P-v)Q - FC (ignoring taxes)
  • Q = (FC + OCF)/(P-v) or FC/(P-v) when OCF = 0
  • Original investment is a complete loss
• Financial Break-even
  • How many units must we sell to have zero NPV?
  • Q = (FC + OCF*)/(P-v)
  • Similar to finding the bid price
• Example
  • A new product requires an initial investment of $5 million and will be depreciated to an expected salvage of zero over 5 years.
  • The price of the new product is expected to be $25,000, and the variable cost per unit is $15,000.
  • The fixed cost is $1 million.
  • Accounting Break-Even: Q = 200 units
  • Cash Break-Even: Q = 100 units
  • Financial Break-Even
    • Assume a required return of 18%
    • Q = 260 units

Operating Leverage

• Relationship between Sales and OCF
• Related to the amount of fixed costs we have to overcome (capital intensiveness)
• Serves to magnify changes in sales into changes in OCF
• Degree of Operating Leverage = 1 + FC/OCF
  • % change in OCF = DOL * % change in Q
  • higher the FCs, higher the DOL, more variable OCFs
• Example
  • Suppose sales are 300 units in our previous example
  • DOL = 1.5
  • What if sales increase by 20%?
  • 30% change in OCF, OCF increases to $2.6M
• Changing DOL can impact the forecasting risk associated with sales

Capital Rationing

• Case when a firm cannot finance a positive NPV project
• Soft rationing: temporary constraint, often self-imposed
• Hard rationing: permanent constraint