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Practical Problems in Capital Budgeting Lecture 3 Fall 2010

Advanced Corporate Finance FINA 7330

Ronald F. Singer

Topics Covered

• Sensitivity Analysis– Break Even Analysis

• Monte Carlo Simulation• Real Options and Decision Trees

What is Project Analysis

• At any one time the firm has a number of projects that are possible.

• Typically, a number of projects are recommended by division heads

• The problem: Which of the proposed projects should be ultimately taken?

• Critical to this decision is what can go wrong: – i.e. Uncertainty

How To Handle Uncertainty

• Sensitivity Analysis – What happens if certain variables are forecasted incorrectly?

• Scenario Analysis – What happens if a logical set of variables are forecasted incorrectly?

• Simulation Analysis – Alternative results when a large number of different scenarios are proposed.

• Break Even Analysis – What is the minimum level of sales (prices, costs) which still allows the project a non-negative NPV

Steps in Sensitivity Analysis

• Define Costs as a function of output • Define Revenue as a function of output • Define expected (initial) variables • Estimate worse and best case variables• Get NPV’s for expected and also for worst case

and best case situations• Purpose: Determines where you might want to

concentrate your efforts to assure correct forecasts

International Widget Company (IWC)

• The Company is thinking of introducing a new version of widgets designed for the under 30 crowd. To do this requires an initial investment of $150,000 and, at a production level of 10,000 units, it is expected to payoff $20,000 per year for 10 years. At the end of the ten years IWC will be able to sell the fixed assets and equipment for $100,000. If the real Cost of Capital is 4%, is this a good investment? All numbers are in real terms

• The NPV is: ???

Sensitivity Analysis – Initial Investment = $150,000– Output (Q) = 10,000– Life = 10 years– Discount Rate = 4%– Terminal Value = $100,000

• NPV = $79,774.33

• But this is the EXPECTED NPV!. Sensitivity analysis asks what happens in things are worse (better) than predicted

• To answer this you need to know what the production process looks like (“model”).

Sensitivity Analysis The Model• Cost = Fixed Cost + Unit cost X Quantity = $10,000 + $6Q• Revenues = Price X Quantity = $9Q

• Notice at output of 10,000: Cost = $70,000 Revenue = $90,000

Annual Payoff (Net Revenue) $20,000

Our original Scenario

Sensitivity Analysis

• Pessimistic Optimistic – Initial Investment 155 140– Sales price 8 10– Fixed cost 12 8 – Unit Variable Cost 7 5– Output 9 13– Life 8 12– Discount Rate 5% 3%– Scrap Value 95 120– See excel file: International Widget Company

Sensitivity analysis

• What does Sensitivity analysis Tell You?

Scenario Analysis • We have assumed that inflation, over the period will be zero. What

if we assume that the inflation rate is 1% per year• We have to forecast the impact on the variables in the model.

Suppose we forecast that REAL variable costs, and revenues will remain the same. But that the REAL fixed cost will decline by $1,000.

• Then the impact of inflation on annual cash flow will be: – Real CF will increase to $21,000

• Also we forecast that this will impact on the real terminal value of the assets will decline to $90,000, from the original $100,000. .

• What is the new NPV?

Breakeven Analysis

• Breakeven is that level of output for which the investment “breaks even”

• What is meant by “breaks even”– Where NPV = 0

• What is that in terms of output?

Break Even Analysis • Notice that the (real) margin is $2 per unit, and Cash Flow is

the margin times the units sold,– That is CF = (Sale price-Unit cost)*Units sold

= (Margin)*Units sold= (2.00)* 10,000 = $20,000

– What is the minimum units you have to sell to “break even” in PV terms? That is: what is the sales level which will give you a zero NPV.

• The Cash Flow’s PV must equal $150,000• How do you do this? Find the Payments that have a PV of

$150,000• So Breakeven is:

– So quantity must be ???

Monte Carlo Simulation

• Step 1: Modeling the Project• Step 2: Specifying Probabilities• Step 3: Simulate the Cash Flows

Modeling Process

Monte Carlo Simulation

Flexibility & Real OptionsDecision Trees

• Decision Trees - Diagram of sequential decisions and possible outcomes.

• Embedded in a typical project are options which are not adequately dealt with by the standard DCF Analysis.

• These Options are typically contingent on observing new information as time goes by.

• For example, options: – To Expand, – Contract– Cease Operations or abandon

Flexibility & Real Options

• Decision trees help companies determine their Options by showing the various choices and outcomes.

• The ability to create an Option thus has value that should be included in the PV of a project

Classic Analysis

• Search for projects with a positive NPV. • Typically this entails generating a stream of

Expected Cash Flows and appropriately discounting.

• However, this could miss some of the strategic value associated with an investment opportunity.

• That is, the ability to react to new information after the project has begun.

The Strategic Approach

• Views the Firm in a dynamic setting• Firm is searching for and capitalizing on its

comparative advantage• Emphasis on the ability of the firm to react to

complex situations• Emphasis on the firm’s reaction to change and

capitalizing on changing environment

Strategic Approach

• Typically the cash flow from an investment is determined initially with no concept of dynamic reactions.

• The use of Real Options allows us to integrate the two concepts into project analysis.

International Widget Company

• Thinking of expanding into China: the plant will cost $3 million to build and the marketing department tells you that the market will generate the equivalent of about $500,000 per year forever if successful, but may produce as little as $50,000 per year if unsuccessful. the probability of success is 50%. At a 10% discount rate, what is the NPV of the project.

• Accept or Reject this project?

Strategic Approach

• If you develop a pilot project it will only cost $200,000 and if successful, then the pilot project will generate $80,000 if unsuccessful it will only generate $30,000, each outcome equally likely . In either case, the pilot project will not be able to be continued thereafter.

• Note that this is a losing project by itself, but it does allow you to get valuable information about the full scale production

Widget’s China Experiment

• Marketing people tell you that if the pilot project is successful, then there is a 90% chance of the full scale project being successful and generating $500,000 and year, but if the pilot project is unsuccessful then the full scale project will only generate the $500,000 with a probability of 25%.

• Should we (1) undertake the Pilot Project, (2) go immediately into production full scale, or (3) do neither?

Decision Tree Analysis

-200,000

80,000

-3,000,000

5,000,000

500,000

30,000

-3,000,000

5,000,000

500,000

NPV = 0 (stop)

NPV = 0 (stop)

50%

50%

90%

10%

25%

75%

Decision Tree analysis

-200,000

80,000

-3,000,000

5,000,000

500,000

30,000

-3,000,000

5,000,000

500,000

NPV = 0

NPV = 0

50%

50%

90%

10%

25%

75%

Continue

STOP

Continue

STOP

Decision Tree analysis

-200,000

80,000

-3,000,000

5,000,000

500,000

30,000

-3,000,000

5,000,000

500,000

NPV = 0

NPV = 0

50%

50%

90%

10%

25%

75%

Continue

STOP

Continue

STOP

Decision Tree Analysis

-200,000

80,000

30,000NPV = 0

50%

50%

Continue

STOP

NPV(1) = $1,550,000

-200,000

30,000

50%

50%

80,000 + 1,550,000 = $1,630,000

NPV OF Total is: $740,909 + 13,636 -200,000 = 554,545

Decision Tree