Decision Tree Questions

8/8/2019 Decision Tree Questions

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y Make better strategic decisions usingand evaluating statistical information

produced by a simulation model.

y Apply simulation techniques to valuereal options facing new ventures.

2003, Entrepreneurial Finance , Smith and Kiholm Smith

Chapter 5

Applications of Simulationy Strategy formulation y Deal structuring y Risk allocation y Contingent claims analysis y Cash needs assessment y Staging of investments y Valuation


Chapter 5

Essentialsof Simulation: A Simple Exa


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mple - Estimating

Space Needs

y A model -The amount of warehouse space neede

d for storage of boxes: o Volume per box = Height x Width x

Depthy Specification of assumptions anddescription of uncertainties

o 5000 boxes per day o Sizes: 1 x 1 x 1, 2 x 1.5 x 1.5, and 3

x 2 x 2 o Sizes are equally likely.

y Run the simulation (Excel file). 2003, Entrepreneurial Finance , Smith and Kiholm Smith

Chapter 5

UsingSimulation to Study Options

y A model


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o Calls and Puts on an underlyingshare of stock

o

Terminal value of Call = Stock price -Exercise price y Specification of assumptions and

description of uncertainties o Stock sells today for $118 o Exercise price for call or put is $125 o Expected monthly appreciation of

stock = 1%,

+ or - 4% per month

o Risk-free rate is 0.3% per month y

Run the simulation (Excel file).


Chapter 5

EvaluatingStrategic Alternatives by Sim

ulation


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y Step1: Identify the strategic alternatives.

y

Step 2: Determine evaluation criteria.

y Step 3: Construct a model of thestrategic decisions.

y Step 4: Specify assumptions anddescribe uncertainties.

y Step 5: Run the simulation and evaluatethe results.


Chapter 5

Identification

of Strategic Alternatives: TheRestaurant ExampleContinued

y Build a large restaurant o Without option to convert (abandon

restaurant business) o With option to convert

y Build a small restaurant


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o Without option to expand o With option to expand o

Without option to convert

o With option to convert y Do not invest

o Without future consideration o With option to delay


Chapter 5

Evaluation Criteria y Maximum NPV for the entrepreneur y Other?


Chapter 5

Modelof the Large Restaurant

y PV Ca sh Flow = PV(Revenue - CashExpenses - Depreciation) x (1 - tax rate)+ PV Depreciation


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y S imp lify - Private corporation with noeffective tax liability. PV Ca sh Flow =

PV Revenues - PV Cash Expenses

y PV R evenues = PV Unit Price x UnitSales (over life of restaurant)

y U nit S al es = Lesser of DemandQuantity or Capacity

y D em a nd Qu a ntity = Market Size xMarket Share

y Ca p a city = An assumed maximumvalue

y PV Ca sh Ex penses = PV Unit Cost xUnit Sales + PV Fixed Costs

y Result is PV of restaurant 2003, Entrepreneurial Finance , Smith and Kiholm Smith

Chapter 5

Modelof Restaurant, Continued: Re

turn to the Entrepreneur


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y PV Entrepreneur Interest = PV Cash Flows - PV Outside

Investor Interest

y PV Outside Investor Interest = (TotalInvestment - Entrepreneur Investment) xPercent Equity Per Dollar Invested x PVCash Flows

y NPV Entrepreneur Interest = PVEntrepreneur Interest - Entrepreneur Investment

y Model the small restaurant in a similar way

y Build in various options by modifying themodel.`


Chapter 5

Assumptionsand Statistical Processes of the Large Restaurant Model


Chapter 5


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Simulation Statistics -

300 Trials

F igure 5-3 2003, Entrepreneurial Finance , Smith and Kiholm Smith

Chapter 5

MarketSize Simulation Results F igure 5-4(a)

Ma rket S ize ( in thousands of meals)

N ote: The figure represents a simulation of market size with 300 iterations. 2003, Entrepreneurial Finance , Smith and Kiholm Smith

Chapter 5

Market

Size Simulation Results

F igure 5-4(b)

Ma rket S ize ( in thousands of meals)


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Small

Restaurant NPV to Entrepreneur F igure 5-7

N ote: The figure shows the sample distribution of the entrepreneur's NPVfrom 600 iterations of the simulation model for investing in the smallrestaurant. The effect of the abandonment option is reflected in the figure bythe limitation of negative NPVs.


Chapter 5

Option

Structure of Small Restaurant NPV to Entrepreneur F igure 5-8


Chapter 5


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Chapter 5

End of Chapter Questions

Note: Please Be Familiar WithVenture .SIMTM Before

Attempting These Problems.2003, Entrepreneurial Finance , Smith and Kiholm Smith

Chapter 5

Question 5-1

You have spentlast 6 months developing a new product

for treatment of arthritis and believe that a breakthroughcould occur

any time inthe next 8 months and that thereis a 10% chance of


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success inany given month. You have decided to

abandon theproject if you do not succeed within that period.

y In the event of success, clinical testingrequired for FDA approval will take 6 to10 months. Based on experience, if developmental efforts are successful,there is a 80% chance that approval willbe granted. Approval or disapproval inany month is equally likely.

y Your venture consumes cash at anaverage rate of $30,000 per month.

y You estimate that in any given month,there is a 30% chance that the cost willbe $20,000 and 20% chance that it willbe $45,000.

y The cost of financing will be lower onceapproval is obtained. The problem isthat you need additional financing rightnow.


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Chapter 5


Chapter 5

Question 5-1 (Contd)

o Suppose

you want to provide enough financing for the worst case outcome. How muchmoney should you raise?

o Using a simulation model,determinehow much you should raise now sothat the probability of running out of money before the FDA acts is 25%.

o Suppose the cost of financing wouldalso be lower after development wascompleted. How could you usesimulation to determine the best wayto stage the financing of the venture?What factors would affect your


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choice of when and how muchcapital to raise?


Chapter 5


Chapter 5

Question 5-2 An entrepreneur who would like to open a restauranthas approached you. By coincidence, itis the same entrepreneur whose decision

you have been studying in this chapter.He is offering 1% of equity for every$10,000 and will contribute $400,000.Suppose you agree with entrepreneurs assumption as outlined in Fig 5-2 for the largerestaurant, and elsewhere in the Chapter for the small restaurant, including thePV assumptions. Use simulation to examine


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the opportunity from your perspective instead of the entrepreneur s .

o What is the NPV of your investmentin the large restaurant if there nooptions and investment isimmediate?

o What is the NPV of your investment

in the small restaurant if there are nooptions and investment isimmediate?

o How do abandonment options withexercise values of $600,000 and$300,000 for the large and smallrestaurant respectively, affect theNPVs of your prospectiveinvestments?


Chapter 5


Chapter 5


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Question 5-2 (Contd)

o Suppose,to acquire an abandonment option for either restaurant, the expected cost is $20,000higher (which you would pay in exch

angefor an additional 2% of the equity).Would you want the entrepreneur toacquire the option?

o The entrepreneur proposes to build asmall restaurant initially, and if expected demand turns out to bemore than 300,00 meals, to expandthe capacity to the same as the largerestaurant. The cost of expanding is$300,00 and the entrepreneur proposes that you contribute thatamount in exchange for an additional15% of equity. Based on thesimulation, would you accept the


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proposal? Why or why not? Is thereanother alternative under which the

entrepreneur could exercise theexpansion option, that you would findmore attractive?


Chapter 5


Chapter 5

Question 5-3 The monthly standard deviation of the S&P 500index is 6.8%. The expected return

for investing in the index is 1% per month

o Suppose you invest $100 in the index today Use simulation to estimate the expected

value and standard deviation of theinvestment at the end of 3 months

What is the estimated expected value andstandard deviation at the end of 9 months?

o Suppose, instead of investing $100 in the index,you are interested in a call option on the $100claim on the index


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What are the expected value and standarddeviation of a 3 month call in 3 months withan exercise price of $100?

What are the expected value and standarddeviation of a 9 month call in 9 months withand exercise price of $100?

What is the expected value in 9 months of a9 month call on an index value of $100 if theexercise price is $90?


Chapter 5


Chapter 5

Question 5-4

Think aboutan aspect of your current situation (possibly

related to

your career, education, or personal life).

y What are the most important decisionsyou will have to make as you goforward?


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y Try describing the alternatives in termsof a decision tree .

y

What real options are reflected in thechoices you will have to make? y The outcomes of the branches should

be describable in terms such as dollars,utility, and happiness. See, if you canwrite a model, similar to the one in thechapter, that describes how outcomesrelate to your possible choices.

y Now, supposing that you wanted tosimulate the results of your decisions,how might you go about specifying theassumptions of your model?

y If you feel ambitious, try setting up themodel in an Excel spreadsheet and usesimulation to evaluate the choices.


Chapter 5


Chapter 5


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Question 5-5

Refer to therestaurant example in the chapter. If the investor is astute, the terms of deal will be different for the largerestaurant than for the small one.Why and how do you think they might

be different?


Chapter 5


Chapter 5

Question 5-6The originof the term r eal options is traceable toProfessor Stewart Myers ( D eterminants of Capital Borrowing, 5 Jo urnal of Financial Ec o n om ics

, 1977), who noted that manycorporate real assets can be viewed as calloptions.

o What do you think he means?


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o Estimate the size that would besufficient 95% of the days.

o

How does this compare to theestimate in the text, of the size thatwould be sufficient 95% of the days?

o What do you think accounts for thedifferences in size?


Chapter 5


Chapter 5

Question 5-8

The commonstock of Unron is selling today for $50 per share. The stock is expectedto appreciate at a rate of 1% per month with a standard deviation of 15%per month. As an Unron employee,you have just been awarded executive stock options to acquire 1000 shares: Exerciseprice = $50. Cannot be sold or


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exercised for 5 years (60 months).Monthly risk free rate is 0.3%.

o Simulate the price of Unron stock atthe end of five years and the value of the call option at expiration.

o What is the likelihood for the optionto be in the money at expiration?

o

What are the expected stock priceand expected value of the call optionin 5 years?

o As you cannot trade the options, youcannot use conventional optionpricing models to determine their value. What is the present value of the options if you discount their expiration date value by 1% per month?

o What is the present value if youdiscount their expiration date valueby the risk free rate?


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Chapter 5


Chapter 5

Question 5-9

Download the Black-Scholes Option value Template from the

text Web site and use it to valuethe following options on Unron stock (Seeproblem 8).

o 1 year calls with exercise price of $50

o

1 year calls with exercise price of $40 o 1 year puts with exercise price of

$50, $40 o Six month calls and puts with

exercise price of $50, $40 o For 1 year puts and calls with

exercise price of $50, how does thevalue change if the risk free rateincreases to 0.5% per month?


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o For 1 year puts and calls withexercise price of $50, how does the

value change if the monthly standarddeviation decreases to 10%?

Discuss theconsistency of your findings with theprinciples of option valuation.

2003, Entrepreneurial Finance , Smith and Kiholm Smith Chapter 5


Chapter 5

Question 5-10

For the restaurantexample in the chapter, evaluate the combinedeffects of the following assumption changes

on the values of large and small

restaurants and the effects on the variousoptions on value

o The standard deviation of mealprices is $2.


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o The preliminary market size estimatehas a triangular distribution with

(8,2.6 and 0.5 million units).

o The preliminary estimate of marketshare has a standard deviation of 2%.

How do these

assumptions of increased risk affect optimalstrategy? Why do you think the effectsare as you find them to be? 2003, Entrepreneurial Finance , Smith and Kiholm Smith

Chapter 5


Chapter 5

Question 5-11

For the restaurantexample in the chapter, evaluate the combi

nedeffects of the following assumption changeson the values of large and small


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restaurants and the effects on the variousoptions on value

o The expected variable cost per mealis $4

o Expected fixed cost of the largerestaurant is $750,000

o Expected cost of the small restaurant

is $600,000

How do theseassumptions about the variable and fixedcost structures affect optimal strategy?

Why do youthink the effects are as you findthem to be? 2003, Entrepreneurial Finance , Smith and Kiholm Smith

Chapter 5

Decision Tree Questions

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