Lecture 4

MIN 100Investment Analysis

Roy Endré DahlUniversity of Stavanger

E-mail: [email protected]

1

mailto:[email protected]

Early dialogue• We need to elect a student representative who will help

organize the early dialogue in this course. • The early dialogue will answer 5 questions:

1. Teaching and assesment methods2. Curriculum3. Use of it’s learning4. Working conditions5. Other conditions that could be improved

• You will be given 10 minutes during this lecture to discuss these questions, and the representative will fill out a form reporting on the 5 questions.

2

0-3

MIN 100 – Investment AnalysisWeek / date Chapters / Topic Note

35 – 29.08.2012 1-3 / Introduction and basic concepts.

Part 1: Overview

37 – 12.09.2012 4-5 / Net present value, bonds, markets

Part 2: Valuation and Capital budgeting

38 – 19.09.2012 6-7 / Stocks, NPV and other investment rules

39 – 26.09.2012 8-9 / Cash flow and capital budgeting, decision tree, sensitivity, Monte Carlo

40 – 03.10.2012 10-11 / Return and Risk, expected return, CAPM

Part 3: Risk and Return

41 Mandatory assignment

42 – 17.10.2012 11-12 / CAPM, Risk, Cost of Capital

43 – 24.10.2012 13-14 / Financing, capital structure, Modigliani & Miller

Part 4: Capital Structure and Dividend Policy

44 – 31.10.2012 15-16 / Use of debt, leverage, dividends

45 – 07.11.2012 17 / Financial and Real Options. Part 5: Special topics

Making Capital Investment Decisions

Chapter 8

McGraw-Hill/Irwin

• Determine the relevant cash flows for various types of capital investments

• Compute depreciation expense for tax purposes

• Incorporate inflation into capital budgeting

• Employ the various methods for computing operating cash flow

• Apply the Equivalent Annual Cost approach

Key Concepts and Skills

8.1 Incremental Cash Flows

8.2 The Baldwin Company: An Example

8.3 Inflation and Capital Budgeting

8.4 Alternative Definitions of Cash Flow

8.5 Investments of Unequal Lives: The Equivalent Annual Cost Method

Chapter Outline

Opening CaseLas Vegas hotel – it’s all about cash flows

7

Cash flows matter—not accounting earnings. Sunk costs don’t matter. Incremental cash flows matter. Opportunity costs matter. Side effects like synergy, cannibalism and

erosion matter. Taxes matter: we want incremental after-tax

cash flows. Inflation matters.

8.1 Incremental Cash Flows

• When performing capital budgeting analysis:

– Always base calculations on cash flow, not income• Earnings ≠ Cash• Need cash for capital spending• Need cash for rewarding shareholders• Therefore, capital expenditure analysis must be

based on cash

Cash Flow: The Basis of Capital Budgeting Decisions

Much of the work in evaluating a project lies in converting accounting income to cash flow

Examples:◦ Depreciation (most common example)

You never write a check made out to “depreciation.”

◦ Amortization◦ Deferrals and Accruals

Cash Flows ≠ Accounting Income

• Remember: Incremental cash flows arise as a consequence of selecting a project

• Seems like a simple task– Not so, there are many pitfalls in identifying

incremental cash flow

Incremental Cash Flows

• Sunk costs are not relevant– Just because “we have come this far” does not mean

that we should continue to throw good money after bad.

• Opportunity costs do matter. Just because a project has a positive NPV, that does not mean that it should also have automatic acceptance. Specifically, if another project with a higher NPV would have to be passed up, then we should not proceed.


Side effects matter.◦Erosion and cannibalism are both bad

things. If our new product causes existing customers to demand less of current products, we need to recognize that.

◦ If, however, synergies result that create increased demand of existing products, we also need to recognize that.


Allocations◦ Overhead may be allocated to the new project◦ Allocations are only relevant if the project increases or

decreases the cash outlay of the entire firm Salvage Value

◦ Don’t forget to treat salvage value (after tax, of course) as a cash inflow at the end of the project

Changes in Net Working Capital◦ Many projects require an increase in NWC (inventory,

receivables, and other current assets) when initiated; this is a cash outlay at the beginning of the project

◦ Don’t forget: To reduce NWC at the end of a project requiring increased NWC; this is a cash inflow at the end of the project


Later chapters will deal with the impact that the amount of debt that a firm has in its capital structure has on firm value.

For now, it’s enough to assume that the firm’s level of debt (and, hence, interest expense) is independent of the project at hand.

Interest Expense

• Will invest in a new bowling ball machine. Cost: $100,000 (depreciated according to MACRS 5-year)

• Costs of test marketing (already spent): $250,000

• Current market value of proposed factory site (which we own): $150,000

• Increase in net working capital: $10,000

8.2 The Baldwin Company

• Production (in units) by year during 5-year life of the machine: 5 000, 8 000, 12 000, 10 000, 6 000

• Price during first year is $20; price increases 2% per year thereafter.

• Production costs during first year are $10 per unit and increase 10% per year thereafter.

• Annual inflation rate: 5%• Working Capital: initial $10 000 changes with

sales

The Baldwin Company

The Baldwin Company($ thousands) (All cash flows occur at the end of the year.)

The Baldwin Company

At the end of the project, the warehouse is unencumbered, so we can sell it if we want to.

The Baldwin Company

Recall that production (in units) by year during the 5-year life of the machine is given by: (5 000, 8 000, 12 000, 10 000, 6 000).

Price during the first year is $20 and increases 2% per year thereafter.

Sales revenue in year 3 = 12 000×[$20×(1.02)2] = 12 000×$20.81 = $249 720.

The Baldwin Company

Again, production (in units) by year during 5-year life of the machine is given by:

(5 000, 8 000, 12 000, 10 000, 6 000).Production costs during the first year (per unit) are $10, and they increase 10% per year thereafter.Production costs in year 2 = 8 000×[$10×(1.10)1] = $88 000

The Baldwin Company

Depreciation is calculated using the Accelerated Cost Recovery System (shown at right).Our cost basis is $100,000.Depreciation charge in year 4 = $100,000×(.1152) = $11.52.

Year ACRS %

1 20.00%

2 32.00%

3 19.20%

4 11.52%

5 11.52%

6 5.76%

Total 100.00%

The Baldwin Company

What cash flows are relevant for an investment project?

Incremental After Tax Cash Flows

588.51$

)10.1(

66.224$

)10.1(

87.59$

)10.1(

86.66$

)10.1(

19.54$

)10.1(

80.39$260$

5432

NPV

NPV

• Inflation is an important fact of economic life and might be considered in capital budgeting.

• Consider the relationship between interest rates and inflation, often referred to as the Fisher equation:

(1 + Nominal Rate) = (1 + Real Rate) × (1 + Inflation Rate)

• A nominal cash flow refers to the actual dollars to be received (or paid out).

• A real cash flow refers to the cash flow’s purchasing power (thus equal to the nominal cash flow adjusted by inflation)

8.3 Inflation and Capital Budgeting

• For low rates of inflation, this is often approximated: Real Rate Nominal Rate – Inflation Rate

• While the nominal rate in the U.S. has fluctuated with inflation, the real rate has generally exhibited far less variance than the nominal rate.

• In capital budgeting, one must compare real cash flows discounted at real rates or nominal cash flows discounted at nominal rates.

Inflation and Capital Budgeting

Example 8.6• A company selling books is considering publishing a new novel 4

years from now. • Today’s price is $10.00 per book and the company assumes an

inflation of 6% over the next four years. • The company anticipates its books to outgrow this inflation by an

additional increase in price of 2% per year.• A new novel will therefore be sold at $13.60 four years from now

($10 * 1.084), and sales are estimated at 100 000 copies.

• Their nominal cash flow 4 years from now is:$13.60 * 100 000 = $1.36 million

• By deflating the nominal cash flow at 6% per year, we get the real cash flow (or the actual purchasing power):

$1.36 / (1.064) = $1.08 million 27

When discounting it is important to be consistent between cash flows and discount rates:• Nominal cash flows must be discounted at the nominal

rate.• Real cash flows must be discounted at the real rate.

Net Present Value will be equal if you use the correct discounting rate. Generally, if the cash flow is given in nominal (real) rate, use nominal (real) discount rates.

Discounting: Nominal or Real ?

• Cash Flow from Operations can be found as:– OCF = EBIT + Depreciation – Taxes

(EBIT = Earnings before interest and taxes)

• Bottom-Up Approach– Works only when there is no interest expense– OCF = Net Income + depreciation

• Top-Down Approach– OCF = Sales – Costs – Taxes– Don’t subtract non-cash deductions

• Tax Shield Approach– OCF = (Sales – Costs)(1 – T) + Depreciation*T

8.4 Alternative Methods for Computing OCF

• There are times when application of the NPV rule can lead to the wrong decision.

• Consider a factory that must have an air cleaner that is mandated by law. There are two choices:– The “Cadillac cleaner” costs $4,000 today, has annual

operating costs of $100, and lasts 10 years.– The “Cheapskate cleaner” costs $1,000 today, has

annual operating costs of $500, and lasts 5 years.• Assuming a 10% discount rate, which one

should we choose?

8.5 Investments of Unequal Lives

• Since the lifespan of these two investments are unequal, we must compare them by looking at their annual cost over an equal period.

• There are two methods used to achieve this:1. Using a Replacement Chain, where the projects are repeated

until they start and end at the same time. Then you can compute the NPV for the repeated projects.

2. Calculate their Equivalent Annual Cost.• By repeating the purchase of the cheap air cleaner we

have 2 cash flows over 10 years:

8.5 Investments of Unequal Lives

Year 0 1 2 3 4 5 6 7 8 9 10Cadillac 4000 100 100 100 100 100 100 100 100 100 100Cheapskate 1000 500 500 500 500 1500 500 500 500 500 500

Net Present Value(Replacement Chain)

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0.0 %2.5 %

5.0 %7.5 %

10.0 %12.5 %

15.0 %17.5 %

20.0 %22.5 %

25.0 %27.5 %

30.0 %32.5 %

35.0 %37.5 %

40.0 %42.5 %

45.0 %47.5 %

50.0 % -

1,000.00

2,000.00

3,000.00

4,000.00

5,000.00

6,000.00

7,000.00

8,000.00

The Cadillac cleanerThe Cheapskate cleaner

Crossover rate = 10.60%

NPV Cheap > NPV Cadillac

NPV Cheap < NPV Cadillac

• EAC is the annual annuity payment implied by a project’s NPV:

• This time we know NPV and need to find C, and by rearranging we find:

• The EAC for the Cadillac filter is $750.98• The EAC for the Cheapskate filter is $763.98• In general, select the EAC with the lower cost. • Suggests a decision to reject the Cheapskate filter.• (However, we are still dependent on discount rate.)

Equivalent Annual Cost (EAC)

Closing CaseExpansion at East Coast Yachts

• East Coast Yachts are considering expanding their production with a new manufacturing plant. A preliminary analysis has been conducted at a cost of 1.2 mill. for market research and investment costs.

• Investments will be carried out over 2 years: 50 mill. in year 0 and 25 mill. in year 1.

• Income for the first years is as follows:

• From year 6, income will grow indefinitely at 2% per year.• Variable costs = 60% of sales.• Fixed costs = 2 mill. per year.• Net working capital requirement = 8% of sales.• Tax rate = 40 %• Required return = 11 %• Depreciation rate = 1/20• Value of the land is disregarded, as it will go unused for ever if not used.• Consider the cash flows and calculate NPV, profitability index and IRR. 34

Year 2 Year 3 Year 4 Year 5 Year 6Sales 15 000 000 27 000 000 35 000 000 40 000 000 42 000 000

Operating Cash Flow Year 0 Year 1 Year 2 Year 3 Year 4 Year 5Revenue 15 000 000 27 000 000 35 000 000 40 000 000 Variable costs -9 000 000 -16 200 000 -21 000 000 -24 000 000 Fixed costs -2 000 000 -2 000 000 -2 000 000 -2 000 000 Depreciation -2 500 000 -3 875 000 -4 068 750 -4 272 188 -4 485 797

EBIT -2 500 000 125 000 4 731 250 7 727 813 9 514 203 Tax -1 000 000 50 000 1 892 500 3 091 125 3 805 681 Net income -1 500 000 75 000 2 838 750 4 636 688 5 708 522 OCF 1 000 000 3 950 000 6 907 500 8 908 875 10 194 319

Net working capital Year 0 Year 1 Year 2 Year 3 Year 4 Year 5Beginning 1 200 000 2 160 000 2 800 000 3 200 000 Ending 1 200 000 2 160 000 2 800 000 3 200 000 3 360 000 NWC Cash Flow -1 200 000 -960 000 -640 000 -400 000 -160 000

Value of perpetuity after year 5 113 722 279

Cash flow Year 0 Year 1 Year 2 Year 3 Year 4 Year 5Operating cash flow - 1 000 000 3 950 000 6 907 500 8 908 875 10 194 319 Capital Spending -50 000 000 -25 000 000 - - - - Net working capital - -1 200 000 -960 000 -640 000 -400 000 -160 000 Terminal value - - - - - 113 722 279 Total Cash Flow -50 000 000 -25 200 000 2 990 000 6 267 500 8 508 875 123 756 598

Discounted Cash Flow -50 000 000 -22 702 703 2 426 751 4 582 742 5 605 060 73 443 517

NPV 13 355 367 > 0 Profitability Index 1,267 > 1IRR 15 % > 11 %

35

First calculate operating cash flow.Then calculate net working capitalAdd perpetuity for indefinite cash flow.Finally calculate total cash flow, and discount it.

Should invest since NPV is positive, and profitability index is greater than 1 and the Internal Rate of Return is higher than the required rate of return.

Early dialogue• We need to elect a student representative who will help

organize the early dialogue in this course. • The early dialogue will answer 5 questions:

1. Teaching and assesment methods2. Curriculum3. Use of it’s learning4. Working conditions5. Other conditions that could be improved

• You will be given 10 minutes during this lecture to discuss these questions, and the representative will fill out a form reporting on the 5 questions.

36

Risk Analysis, Real Options, and Capital Budgeting

Chapter 9

McGraw-Hill/Irwin

• Grasp and execute decision trees• Apply scenario and sensitivity analysis• Comprehend and utilize the various forms

of break-even analysis• Conceptualize Monte Carlo simulation• Practically apply real options in capital

budgeting

Key Concepts and Skills

9.1 Decision Trees

9.2 Sensitivity Analysis, Scenario Analysis, and Break-Even Analysis

9.3 Monte Carlo Simulation

9.4 Real Options

Chapter Outline

Opening CaseOil fund real estate investments

40

Opening CaseOil investments

41

Decisions are often made in several stages. Decision tree analysis is a graphical representation of the

alternatives available in each period and the likely consequences of our choices.

It estimates what is expected net present value when it is conditional on decisions and outcomes of stochastic variables during earlier stages of the project. Decisions: E.g., investment level, technology choice Stochastic variables: E.g., sales.

This graphical representation helps identify the best course of action.

9.1 Decision Trees

Notation

Decisionnode

Decisionbranches

Decision tree:Decision A

Decision B

The first decision node is called the root node

Chancenode

Chancebranches

Chance tree:State of nature 1

State of nature 2

“Study”

”Do not study”

”E”

Example of a Decision Tree

Squares represent decisions to be made.

Circles represent receipt of information, e.g., a test score.

The lines leading away from the squares represent the alternatives.”D”

”B”

”C”

”A”

Stewart Pharmaceuticals Corporation is considering investing in the development of a drug that cures the common cold.

A corporate planning group, including representatives from production, marketing, and engineering, has recommended that the firm go ahead with the test and development phase.

This preliminary phase will last one year and cost $1 billion. Furthermore, the group believes that there is a 60% chance that tests will prove successful.

If the initial tests are successful, Stewart Pharmaceuticals can go ahead with full-scale production. This investment phase will cost $1.6 billion. Production will occur over the following 4 years.

Stewart Pharmaceuticals

Note that the NPV is calculated as of date 1, the date at which the investment of $1,600 million is made. Later we bring this number back to date 0. Assume a cost of capital of 10%.

NPV Following Successful Test

75.433,3$

)10.1(

588,1$600,1$

1

4

1

1

NPV

NPVt

t

Investment Year 1 Years 2-5Revenues $7,000 Variable Costs (3,000)Fixed Costs (1,800)Depreciation (400)Pretax profit $1,800 Tax (34%) (612)Net Profit $1,188 Cash Flow -$1,600 $1,588

Remember that Operating Cash Flow can be calculated using bottom-up approach when there is no interest:OCF = Net income + depreciation

NPV Following Unsuccessful Test

461.91$

)10.1(

90.475$600,1$

1

4

1

1

NPV

NPVt

t

Investment Year 1 Years 2-5Revenues $4,050 Variable Costs (1,735)Fixed Costs (1,800)Depreciation (400)Pretax profit $115Tax (34%) (39.10)Net Profit $75.90Cash Flow -$1,600 $475.90

Note that the NPV is calculated as of date 1, the date at which the investment of $1,600 million is made. Later we bring this number back to date 0. Assume a cost of capital of 10%.

Decision Tree for Stewart

Do not test

Test

Failure

Success

Do not invest

Invest

Invest

The firm has two decisions to make:1. To test or not to test.2. To invest or not to invest.

0$NPV

NPV = $3.4 b

NPV = $0

NPV = –$91.46 m

Let’s move back to the first stage, where the decision boils down to the simple question: should we invest?

The expected payoff evaluated at date 1 is:

Decision to Test

failuregiven

Payoff

failure

Prob.

successgiven

Payoff

sucess

Prob.

payoff

Expected

25.060,2$0$40.75.433,3$60.payoff

Expected

95.872$10.1

25.060,2$000,1$ NPV

The NPV evaluated at date 0 is:

So, we should test.

• Sensitivity Analysis:– Also called “What if” analysis

• Allows the calculation of a range of NPV based on the probability of changes in NPV variables

• TIP: When working with spreadsheets:– build the model so variables can be adjusted in a

single cell;– And the NPV calculations update automatically.

9.2 Sensitivity, Scenario, and Break-Even

Algorithm for sensitivity analysis

1. Specify the NPV equation, including cash flow equation

2. Specify base values for stochastic variables in the NPV equation (base assumptions)

3. Calculate NPV using base values

4. For each stochastic variable:1. Decide upon alternative outcomes for the variable2. Calculate the NPV under alternative outcomes

5. Analyze the effect of alternative outcomes on NPV– Find which variables have the greatest effect, e.g. by using a ”spider” (also

called “star”) diagram

Janus example • The company

– The Janus plant was established in 1895 and is now one of Europe’s leading manufacturers of underwear. The factory at Espeland in Bergen has around 100 employees producing underwear and socks for children and adults.

• Janus considering investment in a new brand of underwear– Perform a sensitivity analysis on this investment

1. Specify the NPV equation, including cash flow equation

• Net present value (NPV):

• Cash flow (CF):

• Remember: depreciation cost should not be included in the cash flow

T

ttr

INPV1

t

1

flowCash

cost Fixed - Sold Unitscost unit Variabl. - Sold Unitsprice Sales

Outflow -Inflow

CF

CF

2. Specify base values for stochastic variables in the NPV equation

Sales price 200 NOK/unitVariable unit cost 100 NOK/unitFixed cost 120 000 NOK/yearDepreciation cost 250 000 NOK/yearUnits sold 5 000 units/yearInvestment 1 250 000 NOKTime horizon 5 YearsDiscount rate 3 %

Janus example - Base assumptions:• The company does not incur taxes• No working capital• All amounts are in real NOK

3. Calculate NPV using base values

• Positive NPV → accept project• Or isn’t this all that is to say about the venture?

(in 1000 real NOKs)

4902865797.43800001250000

flowcash Annual

1

flowCash

%3,5

1

t

NPV

AINPV

rINPV

year

T

tt

År 0 1 2 3 4 5Sales revenue 1000 1000 1000 1000 1000- Variable costs 500 500 500 500 500- Fixed cost 120 120 120 120 120- Investment 1250 = Cash Flow -1250 380 380 380 380 380

56

• The present value of a persistent cash-flow:

• Multiply by (1+r) on both sides:

• Subtraction of the first expression from the last now yields

Recall: The present value of an annuity

nr

C

r

C

r

C

r

CPV

)1()1()1()1( 32

12 )1()1()1()1(

nr

C

r

C

r

CCPVr

nr

CCPVr

)1(

57

• Division by r on both sides yields for the PV:

• The fraction is called the annuity factor (a), and represents the ratio between present value and annual cash-flow in an annuity

• Observe that the annuity factor depends only on interest rate level and duration/maturity

Recall: The present value of an annuity

n

n

rr

rCPV

)1(

1)1(

)(, 1 PVa

PVCaCPV a

4.1 Decide upon alternative outcomes for each stochastic variable

Change from base value

-20,00% -10,00% 0,00% 10,00% 20,00%

Sales price 160 180 200 220 240

Variable unit cost 80 90 100 110 120

Fixed costs 96 000 108 000 120 000 132 000 144 000

Units sold 4 000 4 500 5 000 5 500 6 000

Investment 1 000 000 1 125 000 1 250 000 1 375 000 1 500 000

Life span 4 4,5 5 5,5 6

Risk free interest rate

2,4 2,7 3 3,3 3,6

4.2 Sensitivity analysis on one variable – sales price

Sales price 160 180 200 220 240

Annual CF 180 000 280 000 380 000 480 000 580 000

NPV -425 653 32 318 490 289 948 259 1 406 230

-1000

-500

0

500

1000

1500

160 180 200 220 240

NP

V (1

000

NO

K)

Sales price

Under sensitivity analysis, one input is varied at a time while all other inputs are assumed to meet their expectations (base assumption)

5. Spider diagram from Janus example

-1000000

-500000

0

500000

1000000

1500000

-20 % -10 % 0 % 10 % 20 %

NP

V

Change from base

Sales price

Variable unit costFixed costs

Units sold

Investment

Life span

Risk free interest rate

Note: The spider diagram does not say how likely these outcomes are!

Advantages of sensitivity analysis

• Recognizes the uncertainty associated with the variables• Shows how significant any variable is in determining a

project’s NPV• Help in anticipating and preparing for the ”what if”

questions that are asked in presenting and defending a project

• Does not depend on probabilities associated with outcomes of variables

• Can be used when there is little information, resources and time for more sophisticated techniques

Disadvantage of sensitivity analysis

• Variables are often interrelated • Sensitivity analysis provides no explicit probabilistic

measure of risk exposure How likely is a pessimistic or expected or optimistic

value and how likely is the corresponding outcome value?

• In other words, sensitivity analysis provides information on the effects of different outcomes of variables on project NPV, but not on the likelihood of these outcomes, and the associated probability distribution of NPV

Scenario analysis

• Scenario analysis examine different scenarios, where each scenario involves a confluence of factors

• Scenario analysis allow us to look at different but consistent combination of variables

• What happened if Janus biggest competitor starts to make a similar type of underwear?– Sales drop by 10%– Price drop by 10%– NPV: -151 872

• Common tool for analyzing the relationship between sales volume and profitability. The focus is on how far sale could fall before the project begins to lose money

• Is break-even analysis important?o Very much so: All corporate executives fear losses. Break-even analysis determines

how far down sales can fall before the project is losing money

There are three common break-even measures◦ Accounting break-even: sales volume at which net income = 0◦ Cash break-even: sales volume at which operating cash flow = 0◦ Financial break-even: sales volume at which net present value = 0

We will look at accounting break-even and financial break-even.

Break-Even Analysis

Janus example – base assumptions

Sales price 200 NOK/unitVariable unit cost 100 NOK/unitFixed cost 120 000 NOK/yearDepreciation cost 250 000 NOK/yearUnits sold 5 000 units/yearInvestment 1 250 000 NOKTime horizon 5 YearsDiscount rate 3 %

• The company does not incur taxes• No working capital• All amounts are in real NOK

Break-even analysisAccounting Profit Break even Point

0500

10001500

20002500

30003500

40004500

50005500

0

200000

400000

600000

800000

1000000

1200000

3700100-200

250000120000

costunit Var. - price Sales

onDepreciaticost Fixed :Pointeven Break Accounting

Accounting Profit Break even Point

Revenue = Sales price × units sold

Total cost= Var. unit cost× units sold+Fixed cost +Depreciation

Unit sold

NOK

Is a project that breaks even in accounting term an acceptable investment?

• Would you be happy about investing in a stock that after 5 years gave you a total rate of return of zero? – A zero return does not compensate you for the time value of

money or the risk you have taken. – A project that simply breaks even on accounting basis gives you

your money back, but does not cover the opportunity cost of capital tied up in the project

• A project that just breaks even in accounting terms will surely have a negative NPV.– Have just seen that accounting break-even point is 3 700.– In order to include the time value and risk, the net present

value break-even must be higher than this.

A project that just breaks even in accounting terms will surely have a negative NPV

• Yearly sale: 3700 units• Yearly CF: NOK 250 000• Initial investment: NOK 1 250 000

• Total cash flow from operations = 5 years × NOK 250 000 = NOK 1 250 000= initial investment

• Revenues are not sufficient to repay the opportunity cost of that NOK 1 250 000 investment

1050755797.42500001250000

flowcash Annual %3,5

NPV

AINPV year

Break-even analysis Present Value Break-even Point

0500

10001500

20002500

30003500

40004500

50005500

-1000000

-500000

0

500000

1000000

1500000

2000000

2500000

NPV of CFInvestment

Present Value Break even Point

3929100-200

272943 120000

costunit Var.- price Sales

EACcost Fixed :Pointeven Break PV

Accounting Profit Break even Point vsPresent Value Break-even Point

3929100-200

272943 120000 Units


/AInvestmentcost FixedUnits

InvestmentCost Fixed- UnitsCostunit Var -price Sales

Investmentflow)PV(cash

:Pointeven Break PV

5years,3%

%3,5

yearA

3700100-200

250000120000Units


onDepreciaticost FixedUnits

Cost TotalRevenue

:Pointeven Break Accounting

Investment /Time horizon=1 250 000/5 = 250 000

EAC: Investment/A5years,3%

=1 250 000/4.5797= 272 944

• Monte Carlo simulation is a further attempt to model real-world uncertainty.

• Approach takes its name from the famous European casino– analyzes projects the way one might analyze gambling

strategies.

9.3 Monte Carlo Simulation

• Monte Carlo simulation of capital budgeting projects– Highly probabilistic seen as a step beyond either

sensitivity analysis or scenario analysis.• Interactions between the variables are explicitly

specified in Monte Carlo simulation, – Theoretically provides a more complete analysis.

• Pharmaceutical industry has pioneered applications of this methodology– Use in other industries is far from widespread.

Monte Carlo Simulation

• Imagine a serious blackjack player who wants to know if she should take the third card whenever her first two cards total sixteen.– She could play thousands of

hands for real money to find out.

– This could be hazardous to her wealth.

– Or, she could play thousands of practice hands.

• Monte Carlo simulation of capital budgeting projects is in this spirit.

Monte Carlo Simulation

Monte Carlo simulationSample Results (4 Decks)

Iterations BlackJack Bust 17 18 19 20 21100 9,00 % 44,00 % 22,00 % 12,00 % 16,00 % 21,00 % 10,00 %

1 000 0,90 % 21,30 % 12,80 % 16,90 % 14,40 % 23,70 % 11,10 %10 000 4,70 % 27,62 % 15,62 % 15,46 % 12,86 % 16,51 % 7,60 %

100 000 4,97 % 26,99 % 14,89 % 14,38 % 13,50 % 17,89 % 7,45 %1 Million 4,98 % 27,68 % 14,48 % 14,11 % 13,53 % 18,00 % 7,23 %

10 Million 4,90 % 27,62 % 14,45 % 14,13 % 13,52 % 18,19 % 7,19 %Win chance* 95,10 % - 27,62 % 42,07 % 56,20 % 69,72 % 87,91 %

74

Converges to appr. 12% chance for the dealer to get either blackjack or 21.

* Gives your chance of winning with a hand equal or better than the column header.

Monte Carlo simulation can provide us with even more information:- Probability of winning with different dealer’s card showing.- Probability of winning with a counted card deck

(equal to the plot in the movie 21).

Monte Carlo simulation

75

The dealer is more likely to bust if she gets 2 – 6 (average bust rate = 38 %).

With this table you can calculate more accurate odds since you know your hand and see the dealer’s top card. E.g.:• If you have 18 and the dealer is dealt:

• a 4, you will win by a likelihood of 54 %.• an 8, you will win by a likelihood of 36 %.• a 10 or face, win by a likelihood of 28 %.

• If you have 20, and the dealer is dealt:• a 4, you will win by a likelihood of 81 %.• an 8, you will win by a likelihood of 92 %.• a 10 or face, win by a likelihood of 53 %.

Simulation Results (percent of hands with dealer card showing)Dealer Up Card BlackJack Bust 17 18 19 20 21

Ace 28 % 13 % 14 % 15 % 16 % 10 % 5 %2 0 % 32 % 15 % 17 % 10 % 13 % 13 %3 0 % 40 % 11 % 13 % 12 % 11 % 13 %4 0 % 34 % 18 % 13 % 15 % 10 % 9 %5 0 % 37 % 12 % 12 % 12 % 13 % 14 %6 0 % 47 % 16 % 10 % 8 % 9 % 10 %7 0 % 25 % 40 % 13 % 6 % 8 % 7 %8 0 % 24 % 15 % 40 % 13 % 3 % 5 %9 0 % 17 % 12 % 11 % 43 % 12 % 4 %

10 or Face 8 % 23 % 9 % 10 % 10 % 36 % 3 %

Algorithm for simulation analysis

1. Specify the basic model2. Estimate or assume a probability distribution of stochastic

variables, e.g. a normal, uniform, lognormal3. Draw a number from each probability distribution4. Calculate NPV (or other measures) using the values from step 35. Replicate step 3 and 4 many times, e.g. 10000 times.6. Sort the estimated NPVs and construct the simulated probability

distribution.• If there are 10000 draws, then each value will represent 1/10000 =

0.0001 of the simulated probability distribution

Simulation analysis - Janus case

• What is the mean value of NPV? • What is the 50% (median) value of the distribution? • What are the 10% and 90% percentile values?• What is the probability that the project will have a

negative NPV?

• Can do more sophisticated analyses using more dedicated software, e.g. @risk, Crystal Ball

1. Base assumptions:Sales price 200 NOK/unitVariable unit cost 100 NOK/unitFixed cost 120 000 NOK/yearUnits sold 5000 units/yearInvestment 1 250 000 NOKTime horizon 5 YearsDiscount rate 3 %

289 490 4,5797000 380 000 250 1 - NPV

flowCash %3,5

yearAINPV

000 380kr 000 kr120 -5000kr100 -5000200kr CF

cost Fixed - sold unitscost unit Variabl - Sold Unitsprice Sales

CF

2. Estimate or assume a probability distribution of stochastic variables

Probability distribution

2. Estimate or assume a probability distribution of stochastic variables

Probability 20% 20% 20% 20% 20%

Sales price 180 190 200 210 220


Fixed costs 100000 110000 120000 130000 140000

Units sold 4000 4500 5000 5500 6000

• We assume a discrete uniform distribution • The variable values all have the same probability of

occurring (20%)

Probability distribution for sales price

180 190 200 210 2200%

5%

10%

15%

20%

25%

Probability

Sales price

3. Draw a number from each probability distribution4. Calculate NPV using the values from step 3

• My random numbers: 3, 4, 3, 5 Number 1 2 3 4 5

Probability 20% 20% 20% 20% 20%

Sales price 180 190 200 210 220Variable unit cost 90 95 100 105 110

Fixed costs 100000 110000 120000 130000 140000

Units sold 4000 4500 5000 5500 6000

000 450kr 000 kr120 -units 6000105kr -units 6000200kr CF

cost Fixed - sold Unitscost unit Variabl - Sold Unitsprice Sales

CF

868 8104,5797 000 450 000 250 1 - NPV

flowCash %3,5

yearAINPV

• Draw you own random numbers:Probability 20% 20% 20% 20% 20%

Sales price 180 190 200 210 220


Fixed costs 100000 110000 120000 130000 140000

Units sold 4000 4500 5000 5500 6000

cost Fixed - sold Unitscost unit Variabl - Sold Unitsprice Sales CF

%3,5flowCash yearAINPV

5. Replicate step 2 and 3 many times, e.g. 10000 times

Generate random numbers in Excel

• If you want to generate random numbers in Excel, use the RANDBETWEEN (TILFELDIGMELLOM) function. This function allows you to specify the range of numbers it is to pick from. RANDBETWEEN returns only integers.

• The syntax for the RANDBETWEEN function is: = RANDBETWEEN(Bottom;Top) – Bottom - the lowest number the function is to use. – Top - the highest number the function is to use.

http://spreadsheets.about.com/od/excelfunctions/qt/080218_randbetw.htm

http://spreadsheets.about.com/od/excelfunctions/qt/080218_randbetw.htm

Random variables for sales price

• A random integer between 180 and 220, where all values have the same probability of occurring:

=RANDBETWEEN(180;220)

• A discrete uniform distribution of the values 180, 190, 200, 220, 220, where each value has equal probability of occurring:

=180+RANDBETWEEN(0;4)*10

Probability 20% 20% 20% 20% 20%

Sales price 180 190 200 210 220

Can you answer the questions?

• What is the mean value of NPV? • What is the 50% (median) value of the

distribution? • What are the 10% and 90% percentile

values?• What is the probability that the project

will have a negative NPV?

6. Cumulative probability distribution from Janus example

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-600000 -400000 -200000 0 200000 400000 600000 800000 1000000 1200000 1400000 1600000 1800000

NPV

Cum

ulat

ive

prob

abili

ty d

istr

ibut

ion

Median

10% percentile

90% percentile

Probability of negative NPV = 0.145

Mean NPV = 482160 (must be calculated)

Pros and Cons Simulation analysis

• A simulation model that attempts to be realistic will also be complex– Difficult to model the underlying probability distribution of each

variable– Difficult to model the interactions between variables

• Simulation analysis is sensitive to assumption affecting the input parameters

• GIGO principle: “Garbage in, garbage out”

• Simulation can provide useful information that sensitivity- or scenario analysis cannot give us

• One of the fundamental insights of modern finance theory is that options have value.

• The phrase “We are out of options” is surely a sign of trouble.

• Corporations make decisions in a dynamic environment – Choice of options should be considered in

project valuation.

9.4 Real Options

• The Option to Expand– Has value if demand turns out to be higher

than expected• The Option to Abandon

– Has value if demand turns out to be lower than expected

• The Option to Delay– Has value if the underlying variables are

changing with a favorable trend

Real Options

Real Option = Flexibility

• The investment flexibility is equal to a call/put option on a stock

• It gives the right, but not the obligation, to make an investment expenditure/abandon the investment

• What is this option worth?– First we study an example without flexibility– Afterwards with flexibility

Example: Buying jet or propeller• Standard investment problem: • Buy large capacity jet or smaller or cheaper propeller?

• The opportunity cost of capital for this venture is 10%

• Price jet: 400• Price propeller: 200

• The demand is uncertain: – The probability for high demand the first year is 0.6, and for low demand

0.4. – The probabilities for the second year depend on the first period

outcomes

Payoff and probability matrix

Decision State of natureYear 1

Outcome (probability)

State of natureYear 2

Outcome1 (probability)

Jet -400

High demand 200 (0.6) High demandLow demand

1000 (0.8)50 (0.2)

Low demand -100(0.4) High demandLow demand

500 (0.3)-500 (0.7)

Propeller-200

High demand 100 (0.6) High demandLow demand

400 (0.8)200 (0.2)

Low demand 0 (0.4) High demandLow demand

300 (0.3)0 (0.7)

• The demand is uncertain• The probabilities for the second year depend on the first period

outcomes

1 You can interpret the outcome in year 2 as the present value at the end of year 2 of the cash flow for that and all the subsequent years

Example: Buying jet or propeller

• Which plane should be bought?

• What is the optimal investment level without flexibility for the risk neutral firm?

Standard investment problem

Buy jet or propeller?

Jet-400

Propeller-200

High demand(p=0.6) 200

Low demand(p=0.4) -100


Low demand(p=0.4) 0





Low demand(p=0.7) 0

Low demand(p=0.2) 200



Year 0 Year 1 Year 2

Expected NPV as decision criterion leads us to invest in a propeller

E(NPV) if buying a jet:

E(NPV) if buying a propeller:

26.8

1.1

-500×0.7+500×0.30.4+50×0.2+1000×0.80.61.1

-100×0.4+200×0.6+400 -=NPVE

2

Jet

81.621.1

0×0.7+300×0.30.4+200×0.2+400×0.80.61.1

0×0.4+100×0.6+200 -=NPVE

2

Propeller

Flexibility

1. Investment problem with call option on a used propeller two years from now

2. Investment problem with call option on a used propeller two years from now, and a put option on the first propeller two years from now

3. Investment problem with call- and put option on both propeller and jet in two years.

Flexibility: The option to expand

• Start out with one propeller

• High demand - buy another one– Price secondhand propeller: 100

• Low demand - sit tight with one smal relative inexpensive aircraft

• What is the optimal investment choice if we have this flexibility?

Call option on a used propeller

Jet-400

Propeller-200




Low demand(p=0.4) 0





Low demand(p=0.7) 0






Expand-100

Do not exp0

What are we willing to pay for a used propeller in year 1?

Flexibility: The option to Abandon

• If we can buy a used propeller for 100, there should be possible to also sell it for 100

• When do we want to sell?– When demand is low.

Allow for the possiblity of selling the propeller

Jet-400

Propeller-200




Low demand(p=0.4) 0





Low demand(p=0.7) 0




Expand-100

Sell propeller100

Do not sell propeller

Flexibility: The option to Abandon

• If the business in the first year is poor, it may pay to sell the jet and abandon the venture

• Assume that the used jet could be sold next year for 300

Should we sell the jet if the demand is low the first year?• What is the value of this option to abandon? • What is the optimal investment choice if we have this

flexibility?

Allow for the possiblity of selling the jet

Jet-400

Propeller-200




Low demand(p=0.4) 0





Expand-200

Sell Jet 300

Sell Propeller 100

Do not sell Jet



Expected NPV as decision criterion leads us to invest in a propeller

Without real options the expected NPV for buying a propeller was higher than when buying a jet (62.81 > 8.26).E(NPV) if buying a jet w/real options:

(Real option value = 173.55 – 8.26 = 165.29)

E(NPV) if buying a propeller w/real options:

(Real option value = 115.71 – 62.81 = 52.90)With real options accounted for, you should choose to buy the jet.

• Consider the above project, which can be undertaken in any of the next 4 years. The discount rate is 10 percent. The present value of the benefits at the time the project is launched remains constant at $25,000, but since costs are declining, the NPV at the time of launch steadily rises.

• The best time to launch the project is in year 2—this schedule yields the highest NPV when judged today.

The Option to Delay: Example

Year Cost PV NPV t NPV 0

0 20,000$ 25,000$ 5,000$ 5,000$ 1 18,000$ 25,000$ 7,000$ 6,364$ 2 17,100$ 25,000$ 7,900$ 6,529$ 3 16,929$ 25,000$ 8,071$ 6,064$ 4 16,760$ 25,000$ 8,240$ 5,628$

What is the value of flexibility?• The value of flexibility is equal to the increase in expected NPV

(cash flow) compared to the alternative without flexibility

Expected NPV with flexibility – Expected NPV without flexibility

= Value of flexibility

• Expansion value = value of option to make an investment expenditure

• Abandonment value = value of option to bail out• Delay value = value of option to delay investment

• Simple idea with broad implications

Real Options

• Land sites with resources have often a real option concerning the timing of the extraction.

• Tar sand in Canada and gold at Finnmarksvidda in Norway are both highly dependent on high prices for the resource to make production profitable.

108

Opening case revisitedOil field investment

109

Revenues Investment Operational cost Tariffs Exploration cost

Reduced exploration costs

Reducedinvestments

Reduced tariffs

Reduced operational costs

Swift decision-makingFast-track developments

Accelerated ramp-upof production

Improved regularity and capacity utilisationExtension of plateau production

Higher prices

Increased recovery

Extended tailend production

Opening case revisited Oil Field Investment

• Statoil is considering exploring a new oil field at the Loki field in the North Sea. The initial exploration at 10 mill. NOK has indicated findings of 250 (p = ½), 600 (p = ¼) and 1250 (p = ¼) mill. barrels of oil equivalents (mboe). Further explorations can make the estimates more accurate but will cost another 10 mill. over 3 years and will delay production by 3 years. You need to evaluate if this is necessary before concluding on the size of the investment.

• There are several uncertain factors in this project:– Size of oil field (deciding lifespan in years and barrels per year)– Oil price– Operating cost– Technical progress increasing recovery– Discount rate

110


The following base assumptions are used:• Field size

– Large = 1 200 mboe– Medium = 600 mboe– Small = 250 mboe

• Oil rig investment– Large 50 mboe per year, cost = 25 000 mill. NOK, operating cost = 1 800 MNOK– Medium 35 mboe per year, cost = 14 000 mill. NOK , operating cost = 850 MNOK– Small 25 mboe per year, cost = 8 000 mill. NOK , operating cost = 500 MNOK

• Oil price = 100 USD / bbl = 550 NOK / bbl• Discount rate = 22 % (remember Statoil’s implied required rate of

return = 25.3 %)• Tax rate = 78 %• Depreciation rate = 1/40 per year• Calculate NPV and IRR for the options.

111

Oil field decision tree

112

Further Exploreation

Results

Small

Medium

Large

Investment

Large inv.

Large field

Medium field

Small field

Medium inv.

Large field

Medium field

Smalle field

Small inv.

Large field

Medium field

Small field

Yes

No

NPV = 3 691.97

NPV = 3 233.49

NPV =2 215.81 NPV = 11 272.80

NPV = 9 860.02

NPV = 5 157.04

NPV = 8 847.84

NPV = 8 465.92

NPV = 5 975.67

NPV = 6 698.49

NPV = 6 627.53

NPV = 5 541.05

NPV (Yes) = 0.25 * 3 691.97 + 0.25 * 3 233.49 + 0.5 * 2 215.81 = 2 839.27

NPV (No) = MAX(NPV Large, NPV Medium, NPV Small) = 7 861.72 = NPV Large

Since NPV (No) > NPV (Yes), we should not do any further exploration. The best option is to do a large investment with no exploration.


• Real option: The Loki field is close to existing findings at the Laufey field, and if investments at Loki is set to large, the findings of 150 mboe can be connected through an extra investment of 400 mill. NOK.

• This investment would produce 10 mboe per year at an operating cost of only 200 mill NOK per year.

• The investment is depreciated at 1/40 per year.

• Calculate the value of this real option.

113


• NPV of real option = NPV investment with option – NPV investment without option

• NPV investment with option can easily be calculated by adding the extra production, investment and operating cost to alternative Large, since there are no uncertainty to this real option.

• Provides us with an NPV of 9 341.91, and the real option is worth:

NPV of real option = 9 341.91 - 7 861.72 = 1 480.19 MNOK

114

Lecture summary

• Chapter 8 – Making Capital Investment Decisions– Incremental Cash Flows– Inflation and Capital Budgeting– Investments of Unequal Lives

• Chapter 9 – Risk Analysis, Real Options, and Capital Budgeting– Decision trees– Sensitivity, scenario and break-even analysis– Monte Carlo simulation– Real options

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Lecture 4

Documents

Transcript of Lecture 4