FINC 3310

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FINC 3310

• Chapter Eleven
• Project Analysis and Evaluation

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Project Analysis and Evaluation

• We have spent a lot of time developing our
  capital budgeting analytical skills, from the
  identification of the relevant cash flows to the
  economically appropriate methods of evaluating
  them. Now, comes the question, How good are our
  analyses? Or, how dependent is the result on
  the forecasts we have made?
• In this lecture, we want to address the "what
  ifs" possible in our analysis.
  
• What if sales forecasts are off?
• What if cost savings are off?
• What if, what if, what if???

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Project Analysis and Evaluation

• What we have done are base case NPVs. Now we
  want to examine the effects on NPV of errors or
  changes or realizations other than forecasted.
  That is, think of our calculated NPVs as
  expected values, with distributions. What we are
  going to look at now are ways to assess the
  dispersion of the distribution, i.e. how far away
  from the expected could the real outcome be?

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Looking at the What ifs

• Scenario Analysis Change assumptions about the
  model, like the sales forecast, economic
  environment, and change all values accordingly,
  often with a best case and worst case. What
  happens to NPV?
• Sensitivity Analysis a "specialized" scenario
  analysis where only one variable is changed at a
  time. Is there one (or more) that really affects
  the NPV outcome?

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Forecasting Risk

• Forecasting risk is the possibility that we may
  make a bad decision due to errors in our
  projected cash flows.
  
• If slight changes in a variable strongly affect
  NPV, then the forecasting risk associated with
  that variable is high!

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Operating Leverage and Project Risk

• A key point we often find a key variable (in
  terms of forecasting risk) to be sales volume.
  Why? Because of the presence of operating
  leverage.

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Operating Leverage and Project Risk

• Define costs for analysis as fixed or variable.
• variable we will assume a constant dollar
  amount, v, per unit of output, Q
  
• fixed a constant amount independent of output
• So TC FC D VC
• FC D Qv
• It is the presence of fixed costs in a projects
  operating structure that generates operating
  leverage. Lets explore this a little more
  (ignoring taxes).

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Operating Leverage and Project Risk

• Find Accounting Breakeven where project NI
  0
  
• Price 10 unit
• v 6 per unit
• FC D 120 80 200
• Q

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Operating Leverage and Project Risk

• Why is this helpful?
• Recall, often sensitivity analysis reveals sales
  volume as a "key" variable. Using Q we can see
  the volume we need to generate to break even, and
  we can evaluate how likely that is to occur.
  That is, we can look at the risk involved.
• What happens to Q as FC rise or fall and
  everything else remains the same? This is the
  impact of operating leverage and its relationship
  to project risk.
• NOTE if a project just breaks even in accounting
  sense, it is losing money on a financial or
  opportunity cost sense. We could have made more
  elsewhere.

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Operating Leverage and Cash Flow

• Recall that OCF is given by (ignoring taxes)
• OCF (S-VC-FC-D) D
• At Q, OCF D Why?
• By definition, Q is that quantity of sales
  where
  
• S - VC - FC - D 0
• so,
• OCF D
• What is the economic implication of this?

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Operating Leverage and Cash Flow

• What happens at other places (sales levels) than
  Q?
  
• OCF S-VC-FC (P-V)Q-FC (why?)
• Rearranging the equation above yields, for any
  level of OCF
  
• And, we can see this
• relationship in the
• figure

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Operating Leverage and Cash Flow

• Lets consider a crucial idea for an investment
  project - its Financial Breakeven - where NPV0
  
• Step One Determine the level of OCF that results
  in NPV0
  
• Suppose the project we have been looking at
  requires an investment of 480 and will have a
  six year life (thus the D80). Also suppose the
  required rate of return is 14.
• NPV0OCF(PVIFA14,6) - 480
• OCF 480/3.8887 123

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Operating Leverage and Cash Flow

• Step Two Use the OCF equation to solve for Q at
  that level of OCF.
  
• WHY? How far away from the forecasted sales
  level the financial breakeven occurs is an
  indication of forecasting risk in the NPV
  analysis.

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Operating Leverage and Cash Flow

• Summarizing our work so far A general result is
  that the higher the degree of operating leverage,
  the greater the sensitivity to forecasting risk.
  That is, more fixed costs increase leverage, and
  increase the dependency of project success on
  high sales levels to break even. Thus, your
  NPV analysis becomes more sensitive to the sales
  forecasts accuracy.

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Degree of Operating Leverage (DOL)

• One way to measure the sensitivity to operating
  leverage is to calculate the degree of operating
  leverage, or DOL, defined as
  
• or,
• Note that DOL is different at every level of OCF!
  (higher OCF is less leveraged, while lower OCF
  is more leveraged, for a given level of FC)

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Putting It All Together

• Consider the following example of two similar
  investment proposals, but with quite different
  fixed cost structures and thus different degrees
  of operating leverage and risk.
• Sue's Pizza Sam's Pizza
• P12 P12
• V7 V4
• FC100,000 FC250,000
• invest750,000 invest1,250,000
• 5 years SL D 5 years SL D
• 150,000/year 250,000/year

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Putting It All Together Breakeven Points

• What is Accounting Breakeven?
• Sues Sams
• Q (100150)/(12-7) Q (250250)/(12-4)
• 50,000 pizzas 62,500 pizzas
• What is Cash Breakeven?
• Q 100,000/5 Q 250,000/8
• 20,000 pizzas 31,250 pizzas

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Putting It All Together Breakeven Points

• What is Financial Breakeven? (assume r 10
  for both)
  
• Sues Sams
• 750,000 OCF(PVIFA5yrs,10) 1,250,000
  OCF(PVIFA5,10)
  
• 750,000/3.7908 OCF 1,250,000/3.7908 OCF
• OCF 197,847 OCF 329,746
• So, the appropriate quantities are
• QFBE (100,000 197,847)/5 QFBE (250,000
  329,746)/8
  
• 59,569 pizzas 72,468 pizzas
• What is the DOL at QFBE?
• DOL 1 (100,000/197,847) DOL 1
  (250,000/329,746)
  
• 1.5054 1.7582
• Now you can assess risk in the Sue or Sam project.

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Putting It All Together

• What if "reliable" forecast is 65,000 pizzas?
• What if realistic figure is 100,000 pizzas? Why
  is Sam's preferred at that level?
  
• Note how much higher QFBE is above cash breakeven!