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CHAPTER. 8. Risk Analysis, Real Options, and Capital Budgeting. Chapter Outline. 8.1 Decision Trees 8.2 Sensitivity Analysis, 8.3Break-Even Analysis 8.4Scenario Analysis, Options 8.5 Monte Carlo Simulation 8.6Summary and Conclusions. 8.1 Decision Trees.

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Chapter

CHAPTER

8

Risk Analysis, Real Options, and Capital Budgeting


Chapter outline

Chapter Outline

8.1 Decision Trees

8.2 Sensitivity Analysis,

8.3Break-Even Analysis

8.4Scenario Analysis, Options

8.5 Monte Carlo Simulation

8.6Summary and Conclusions


8 1 decision trees

8.1 Decision Trees

  • Allow us to graphically represent the alternatives available to us in each period and the likely consequences of our actions.

  • This graphical representation helps to identify the best course of action.


Example of decision tree

“A”

“B”

“C”

“D”

“F”

Example of Decision Tree

Squares represent decisions to be made.

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

Study finance

The lines leading away from the squares represent the alternatives.

Do not study


Capital investment decision sec

Capital Investment Decision: (SEC)

  • Solar Electronics Corporation (SEC) has recently developed the technology for solar powered jet engines and presently is considering test marketing of the engine. 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 $100 million. Furthermore, the group believes that there is a 75% chance that tests will prove successful.

  • Cost of capital is 15%.

  • If the initial tests are successful, Solar Electronics Corporation can go ahead with full-scale production. This investment phase will cost $1500 million. Production will occur over the next 5 years. Annual sales would be 30% of the market of 10,000. Sales price is $2 million per unit.

  • If the initial tests are not successful, and Solar Electronics Corporation still goes ahead with full-scale production; the investment will cost $1500 million, and annual sales would then be 682 units over the next 5 years.


Sec npv of full scale production following successful test

SEC: NPV of Full-Scale ProductionFollowing Successful Test


Sec npv of full scale production following failure of test

SEC: NPV of Full-Scale ProductionFollowing Failure of Test


Decision tree for sec

Invest

=

NPV

$

0

Decision Tree for SEC

The firm has two decisions to make:

Invest

To test or not to test.

To invest or not to invest.

NPV = $1,517

Success

75% prob.

Test

Do not invest

NPV = $0

Failure

NPV = –$3,612 (Sales units=682)

25% prob.

Do not test


Npv of the project

NPV of the project

Expected payoff at date 1=(Prob. of success x Payoff if successful) +(Prob. Of failure x Payoff if failure)

=(.75x$1,517)+(.25x0)

=$1,138 million

The NPV of the testing computed at date 0 (in million) is

Since NPV is positive, so we should test.


Calculation of accounting bep

Calculation of accounting BEP

BEPQ=Net Fixed charges/Net Contribution

=(Fixed cost + Depreciation) *(1-Tc)/(Sales Price-Variable cost)*(1-Tc)

=[(1791+300)*(1-.34)]/[(2-1)*(1-.34)]

=1380/.66=2,091 engines is the break-even point for an accounting profit


Sensitivity analysis sec

Sensitivity Analysis: SEC

  • We can see that NPV is very sensitive to changes in revenues. For example, when sales drop from 4,000 units to 3,000, a 25% drop in revenue leads to a 59% drop in NPV.

For every 1% drop in revenue, we can expect roughly a 2.4% drop in NPV:

Similarly, when sales drop from 3,000 to 2,500 units then 1% drop in revenue makes 4.4% drop in NPV.


Figure accounting bep

Figure: Accounting BEP

$ in million

Total Revenue

Total Cost

$4,182

Fixed cost (including depreciation)=$2,091

2,091

Output (sales units)


Present value bep q

Present Value BEPQ

  • The Equivalent Annual Cost (EAC) of the investment of $1,500 (in million) is:

After tax fixed charges: =EAC + (Fixed costs x(1-Tc))-(Depreciation*Tc)

=$447.5 +($1,791*.66 - $300*.34)=$1,528

So, present value BEPQ=After tax fixed charges/After tax contribution


Break even revenue sec

+ TVC

+D

+FC

$147.5

0.66

Break-Even Revenue SEC

Work backwards from OCFBE to Break-Even Revenue

Total Revenue

$4,630

Total Variable cost

$2,315

Fixed cost

$1,791

Depreciation

$300

EBIT

$223.5

Tax (34%)

$76.0

Net Income

$147.5

OCF =

$147.5+ $300

$447.5


Sec npv of full scale production following successful test1

SEC: NPV of Full-Scale ProductionFollowing Successful Test


Financial break even

Financial Break-even

  • Expected pay-off at date 1=(.75*0)+(.25*0)=0

  • We fail to finance the test of $100.

  • For that we need a pay-off of $115 at date 1

  • Thus the NPV needed at date 1 is 115/.75=$153million

  • The cost of investment becomes=$1,500+$153=$1,653m

  • EAC=1653/3.352155=$493

  • Net profit required is ($493-$300(dep))=$193

  • Before tax profit is (net profit/(1-T))=$193/.66=$292.75

  • Total contribution needed=$292.75+$300+$1,791=$2,383.75

  • So, (P-VC)Q=2,383.75

  • (2-1)2,383=2,383.75


Sec financial bep of full scale production following successful test

SEC: Financial BEP of Full-Scale ProductionFollowing Successful Test


Sensitivity analysis

Sensitivity Analysis


Example 2 stewart pharmaceuticals

Example 2: Stewart Pharmaceuticals

  • 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.


Npv following successful test

NPV Following Successful Test

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%.

PVIFA=3.1699


Npv following unsuccessful test

NPV Following Unsuccessful Test

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 pharmaceutical

Invest

=

NPV

$

0

Decision Tree for Stewart Pharmaceutical

The firm has two decisions to make:

Invest

To test or not to test.

To invest or not to invest.

NPV = $3.4 b

Success

Test

Do not invest

NPV = $0

Failure

NPV = –$91.46 m

Do not test


Decision to test

Decision to Test

  • 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:

The NPV evaluated at date 0 is:

So, we should test.


Sensitivity analysis stewart

Sensitivity Analysis: Stewart

  • We can see that NPV is very sensitive to changes in revenues. In the Stewart Pharmaceuticals example, a 14% drop in revenue leads to a 61% drop in NPV.

For every 1% drop in revenue, we can expect roughly a 4.26% drop in NPV:


Scenario analysis stewart

Scenario Analysis: Stewart

  • A variation on sensitivity analysis is scenario analysis.

  • For example, the following three scenarios could apply to Stewart Pharmaceuticals:

    • The next years each have heavy cold seasons, and sales exceed expectations, but labor costs skyrocket.

    • The next years are normal, and sales meet expectations.

    • The next years each have lighter than normal cold seasons, so sales fail to meet expectations.

  • For each scenario, calculate the NPV.


Break even analysis

Break-Even Analysis

  • Common tool for analyzing the relationship between sales volume and profitability

  • There are two common break-even measures

    • Accounting break-even: sales volume at which net income = 0

    • Financial break-even: sales volume at which net present value = 0


Break even analysis stewart

Break-Even Analysis: Stewart

  • Another way to examine variability in our forecasts is break-even analysis.

  • In the Stewart Pharmaceuticals example, we could be concerned with break-even revenue, break-even sales volume, or break-even price.

  • To find zero NPV, we start with the break-even operating cash flow.

    • EAC=1600/3.1699=504


Accounting bep q

Accounting BEPQ

  • BEP=(1,800+200)*(.66)/($10-($3,000/700))*(.66)=385

TR

TC

$3,850

385

Quantity of sales


Break even revenue stewart

+ VC

+D

+FC

$104.75

0.66

Break-Even Revenue: Stewart

  • Work backwards from OCFBE to Break-Even Revenue

Revenue

$5,358.71

Variable cost

$3,000

Fixed cost

$1,800

Depreciation

$400

EBIT

$158.71

Tax (34%)

$53.96

Net Income

$104.75

OCF =

$104.75+ $400

$504.75


Break even analysis p be

$5,358.71

PBE

=

= $7.66 / dose

700

Break-Even Analysis: PBE

  • Now that we have break-even revenue of $5,358.71 million, we can calculate break-even price.

  • The original plan was to generate revenues of $7 billion by selling the cold cure at $10 per dose and selling 700 million doses per year,

  • We can reach break-even revenue with a price of only:

    $5,358.71 million = 700 million × PBE


Dorm beds example

Dorm Beds Example

  • Consider a project to supply the University of Missouri with 10,000 dormitory beds annually for each of the next 3 years.

  • Your firm has half of the woodworking equipment to get the project started; it was bought years ago for $200,000: is fully depreciated and has a market value of $60,000. The remaining $100,000 worth of equipment will have to be purchased.

  • The engineering department estimates that you will need an initial net working capital investment of $10,000.

  • The project will last for 3 years. Annual fixed costs will be $25,000 and variable costs should be $90 per bed.

  • The initial fixed investment will be depreciated straight line to zero over 3 years. It also estimates a (pre-tax) salvage value of $10,000 (for all of the equipment).

  • The marketing department estimates that the selling price will be $200 per bed.

  • You require an 8% return and face a marginal tax rate of 34%.


Dorm beds ocf 0

Dorm Beds OCF0

What is the OCF in year zero for this project?

Cost of New Equipment$100,000

Net Working Capital Investment $10,000

Opportunity Cost of Old Equipment* $39,600

$149,600

*Calculation of Opportunity Cost of Old Equipment:

Market value$60,000

Book value 0

Profit (Loss)$60,000

Tax (34%) ($20,400)

Net salvage value$39,600


Dorm beds ocf 1 2

Dorm Beds OCF1,2

What is the OCF in years 1 and 2 for this project?

Revenue

10,000× $200 =

$2,000,000

Variable cost

10,000 × $90 =

$900,000

Fixed cost

$25,000

Depreciation

100,000 ÷ 3 =

$33,333

EBIT

$1,041,666.67

Tax (34%)

$354,166.67

Net Income

$687,500

OCF =

$687,500 + $33,333

$720,833.33


Dorm beds ocf 3

Dorm Beds OCF3

Revenue

10,000× $200 =

$2,000,000

10,000 × $90 =

Variable cost

$900,000

$25,000

Fixed cost

100,000÷ 3 =

Depreciation

$33,333

$1,041,666.67

EBIT

$354,166.67

Tax (34%)

$687,500

Net Income

$720,833.33

OCF =$687,500 + $33,333 =

We get our NWC back and sell the equipment. Since the book value and market value of net working capital is same, so there is no tax effect. Thus, and net cash flow becomes $10,000. The salvage value of equipment $10,000 and the book value is zero. So the capital gain of $10,000 is taxable. Thus, the after-tax salvage value is $6,600 = $10,000 × (1 – .34)

Thus, OCF3 = $720,833.33 + $10,000 + $6,600 = $737,433.33


Npv of dorm beds

NPV of Dorm Beds


Dorm beds break even analysis

Dorm Beds Break-Even Analysis

  • In this example, we should be concerned with break-even price.

  • Let’s start by finding the revenue that gives us a zero NPV.

  • To find the break-even revenue, let’s start by finding the break-even operating cash flow (OCFBE) and work backwards through the income statement.


Dorm beds break even analysis1

Dorm Beds Break-Even Analysis

The PV of the cost of this project is the sum of $149,600 today less $6,600 of net salvage value and $10,000 as return of NWC in year 3.

Let us find out the Equivalent Annual Cost (EAC) of the investment:


Break even revenue

$19,603.13

0.66

Break-Even Revenue

Work backwards from OCFBE to Break-Even Revenue

Revenue

10,000× $PBE =

$988,035.04

Variable cost

10,000 × $90 =

$900,000

Fixed cost

$25,000

Depreciation

100,000 ÷ 3 =

$33,333

EBIT

$29,701.71

Tax (34%)

$10,098.58

Net Income

$19,603.13

OCF =

$19,603.13 + $33,333

$52,936.46


Break even analysis1

Break-Even Analysis

  • Now that we have break-even revenue we can calculate break-even price

  • If we sell 10,000 beds, we can reach break-even revenue with a price of only:

PBE× 10,000 = $988,035.34

PBE= $98.80


Common mistake in break even

$

988

,

035

.

04

=

=

Break

-

even

sales

volume

4

,

941

beds

$

200

Common Mistake in Break-Even

  • What’s wrong with this line of reasoning?

  • With a price of $200 per bed, we can reach break-even revenue with a sales volume of only:

As a check, you can plug 4,941 beds into the problem and see if the result is a zero NPV.


Don t forget that variable cost varies

$19,603.13

0.66

Don’t Forget that Variable Cost Varies

Revenue

QBE× $200 =

$88,035.04 + QBE×$110

Variable cost

QBE× $90 =

$?

Fixed cost

$25,000

Depreciation

100,000 ÷ 3 =

$33,333

EBIT

$29,701.71

Tax (34%)

$10,098.58

Net Income

$19,603.13

OCF =

$19,603.13 + $33,333

$52,936.46


Break even analysis2

$88,035.04

QBE

=

= 801 beds

$110

Break-Even Analysis

  • With a contribution margin of $110 per bed, we can reach break-even revenue with a sales volume of only:

  • If we sell 10,000 beds, we can reach break-even gross profit with a contribution margin of only $8.80:

    CMBE ×10,000 = $88,035.04

    CMBE = $8.80

  • If variable cost = $90, then break-even price (PBE) = $98.80


8 4 options

8.4 Options

  • 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. Because corporations make decisions in a dynamic environment, they have options that should be considered in project valuation.

  • 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.


The option to expand

The Option to Expand

  • Imagine a start-up firm, Campusteria, Inc. which plans to open private (for-profit) dining clubs on college campuses.

  • The test market will be your campus, and if the concept proves successful, expansion will follow.

  • The start-up cost of the test dining club is only $30,000 (this covers leaseholder improvements and other expenses for a vacant restaurant near campus).


Campusteria pro forma income statement

4

$

2

,

550

å

=

-

+

=

-

NPV

$

30

,

000

$

21

,

916

.

84

t

(

1

.

10

)

=

t

1

Campusteria pro forma Income Statement

We plan to sell 25 meal plans at $200 per month with a 12-month contract.

Variable costs are projected to be $3,500 per month.

Fixed costs (the lease payment) are projected to be $1,500 per month.

We can depreciate our capitalized leaseholder improvements.


The option to expand1

The Option to Expand:

  • Note that while the Campusteria test site has a negative NPV, we now evaluate the possibility of expansion of sales. If sales grows at the rate 40% annually over the next 4 years, and the investment has the excess capacity to produce the higher level of sales, Then cost benefit takes following form. Find out the value of the expansion option.


The option to expand2

The Option to Expand:

NPV is $4,730 which is positive

Value of the managerial option=21,916+4,730=$26,646


Discounted cash flows and options

Discounted Cash Flows and Options

  • We can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial options implicit in the project.

    M = NPV + Opt

  • A good example would be comparing the desirability of a specialized machine versus a more versatile machine. If they both cost about the same and last the same amount of time the more versatile machine is more valuable because it comes with options.


The option to abandon example

The Option to Abandon: Example

  • Suppose that we are drilling an oil well. The drilling rig costs $300 today and in one year the well is either a success or a failure.

  • The outcomes are equally likely. The discount rate is 10%.

  • The PV of the successful payoff at time one is $575.

  • The PV of the unsuccessful payoff at time one is $0.


The option to abandon example1

Expected Payoff

Prob. Success

Successful Payoff

Prob. Failure

Failure Payoff

=

×

+

×

$287.50

= –$38.64

NPV =

Expected Payoff

–$300 +

= (0.50×$575) + (0.50×$0) = $287.50

1.10

The Option to Abandon: Example

Traditional NPV analysis would indicate rejection of the project.


The option to abandon example2

Success: PV = $575

Sit on rig; stare at empty hole: PV = $0.

Drill

-

$

300

Failure

Sell the rig; salvage value = $250

Do not drill

=

NPV

$

0

The Option to Abandon: Example

Traditional NPV analysis overlooks the option to abandon.

The firm has two decisions to make: drill or not, abandon or stay.


The option to abandon example3

Expected Payoff

Prob. Success

Successful Payoff

Prob. Failure

Failure Payoff

=

×

+

×

$412.50

= $75.00

NPV =

Expected Payoff

–$300 +

= (0.50×$575) + (0.50×$250) = $412.50

1.10

The Option to Abandon: Example

When we include the value of the option to abandon, the drilling project should proceed:


Valuation of the option to abandon

Valuation of the Option to Abandon

  • Recall that we can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial options implicit in the project.

    M = NPV + Opt

    $75.00 = –$38.61 + Opt

    $75.00 + $38.61 = Opt

    Opt = $113.64


The option to delay example

$

7

,

900

=

$

6

,

529

2

(

1

.

10

)

The Option to Delay: Example

  • 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 remain 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.


Option to delay

Option to delay

  • When should we make the investment if annual sales revenue is Tk.8,000, variable cost 40% of sales, fixed costs Tk.1500 and project life 4 years. The cost of capital is 10%. The investment has zero salvage value and follows straight line depreciation. The amount of investment varies as following:


Calculation of npv t investment tk 10 00

Calculation of NPVt(Investment=Tk.10,00)


Calculation of npv t investment tk 8 600

Calculation of NPVt(Investment=Tk.8,600)


Delay option

Delay option

We should delay the investment. We should make the investment in 2013.


Option to delay with salvage value

Option to delay (with salvage value)

  • When should we make the investment if annual sales revenue is Tk.8,000, variable cost 40% of sales, fixed costs Tk.1500 and project life 4 years. The cost of capital is 10%. The investment has 10 year life and will fetch 25% salvage value at the end of the project, and follows straight line depreciation. The amount of investment varies as following:


Option to delay with salvage value1

Option to delay (with salvage value)

Taking net salvage value under consideration, we should make the investment in 2010 rather than 2011.


Option to delay with 65 salvage value

Option to delay (with 65% salvage value)

  • When should we make the investment if annual sales revenue is Tk.8,000, variable cost 40% of sales, fixed costs Tk.1500 and project life 4 years. The cost of capital is 10%. The investment has 10 year life and will fetch 65% salvage value at the end of the project, and follows straight line depreciation. The amount of investment varies as following:


Option to delay with 65 salvage value1

Option to delay (with 65% salvage value)

Taken 65% terminal market value of investment, the project should be started in 2010.


Option to delay with 65 salvage value2

Option to delay (with 65% salvage value)

Taken 65% terminal market value of investment, the project should be started in 2010.


8 5 summary and conclusions

8.5 Summary and Conclusions

  • This chapter discusses a number of practical applications of capital budgeting.

  • We ask about the sources of positive net present value and explain what managers can do to create positive net present value.

  • Sensitivity analysis gives managers a better feel for a project’s risks.

  • Scenario analysis considers the joint movement of several different factors to give a richer sense of a project’s risk.

  • Break-even analysis, calculated on a net present value basis, gives managers minimum targets.

  • The hidden options in capital budgeting, such as the option to expand, the option to abandon, and timing options were discussed.


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