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

- Forcasting (estimation) risk

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

- Worst Case (minimum NPV)

- 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