Lec Real Option 110

8/2/2019 Lec Real Option 110

1/16

Real Options

Decision Tree Analysis

Decisions and uncertainty resolution

Assume you purchase goods on eBay andresell them in Sunda market.

You are charged $500 by market in advance toset up your booth. Ignoring the cost of the booth,

your average profit is $1100 per week.

NPV of setting up a booth is $600 and is optimal

2

$1100 - $500 = $600

Go to market

Stay home

$0


2/16

Mapping Uncertainties on a Decision Tree Market attendance is weather dependent.

In good weather you profits $1500, bad weather youlose $100. There is a 25% chance of bad weather.

Sunshine (75%) $1500

Go to market -$500Rain (25%)

-$100

3

Stay home 0

You pay for the booth in advance, regardless ofweather, however you can stay home if weather isbad and save $100.

Real Options Option to wait until you find out what the weather is

like before you decide to go to market is a real option. Assume you are weather risk neutral.

between exp. profit without real option to wait until theweather is revealed to the value with the option to wait.

If you decide to go to market regardless:0.75 $1500 + 0.25 ($100) = $1100

If you go when weather is good:0.75 $1500 + 0.25 $0 = $1125

4

Option value = $1125 -$1100 = $25

If you pay for the booth the day before, (Saturday)NPV = $1125 $500 = $625 (always pay for booth)


3/16

Real Options Corporations face similar options.

The option to delay, the option to grow, or abandon.

, ,there is no cost to wait, in the real world, thereis often a cost to delay.

By choosing to wait, a firm gives up any profitsthe project might generate.

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,develop a competing product.

The decision involves a trade-off between these

costs and the benefit of remaining flexible.

Investment as a Call Option

Assume you have negotiated a deal with adining chain to open one in your hometown.

ccor ng o e con rac you mus open erestaurant either immediately or in exactly one year.

If you do neither, you lose the right to open restaurant.

How much you should pay for this opportunity?

Cost to open now or in a year is 5m, capital cost 12%.

6

If you open the restaurant immediately, you expectit to generate $600,000 in free cash flow first year.

Future cash flows are expected to grow 2% per year.


4/16

Restaurant Investment Opportunity

7

The value of opening restaurant today is:

$600,000V = = $6m, with NPV = $6m -$5m= $1m

12% - 2%


Given the flexibility you have to delay openingfor one year, what should you be willing to pay?

e ld e e e Payoff if you delay is equivalent to payoff of

one-year Eup. call on with a strike price of $5m.

Assume: The risk-free interest rate is 5%, volatility is 40%.

If you wait to open the restaurant you have an opportunity

8

cos o , n e rs year . In terms of a financial option, the FCF is equivalent to a

dividend paid by a stock. The holder of a call option does notreceive the dividend until the option is exercised.

Use B-S model to evaluate this real option.


5/16


The current value of the asset without the dividendsthat will be missed is:

x $0.6 million

The present value of the cost to open the restaurant inone year is: 5/1.05 = $4.76

= - v = m on - = . m on1.12

x

1

ln[S / PV(K)] T ln(5.46 / 4.76)d = + = + 0.20 = 0.543

2 0.40 T

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2 1d = d - T = 0.543 - 0.40 = 0.143

x 1 2C = S N(d ) - PV(K)N(d )= ($5.46 million) (0.706) - ($4.76 million) (0.557)

= $1.20 million

Investment as a Call Option The value today from waiting to invest in the

restaurant next year (and only opening it ifit is profitable to do so) is $1.20 million.

This exceeds the NPV of $1 million from openingthe restaurant today. Thus, you are better offwaiting to invest, and the value of the contract is$1.20m.

Whether it is optimal to invest today or in

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one year w epen on e magn u e o anylost profits from the first year, comparedto the benefit of preserving your right tochange your decision.


6/16

Valuing the Growth Potential of a Firm

Assume StartUp Inc is a new company whoseonly asset is a patent on a new medicine. If produced, the medicine will generate certain

profits of $1 million per year for 17 years (afterthen, competition will drive profits to zero).

It will cost $10 million today to produce .

Yield on a 17-year risk-free annuity is 8% per year.

What is the value NPV of the atent?

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Given todays interest rates, it does not make senseto invest in the medicine today.

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1m 1NPV = 1 - - 10m = - $878,362

0.08 1.08

Valuing the Growth Potential of a Firm Lets use binomial model and risk-neutral

probabiliy to solve this problem.

T e pro a i ity t at set t e va ue o a inanciaasset today equal to the PV of its future cashflows at risk free rate.

Todays value of a 17-year risk-free annuitythat a s $1000 er ear is:

12

17

10 0 0 1S = 1 - = $ 9 12 2

0 .0 8 1 .0 8


7/16


If interest rates rise to 10%, or fall to 5% in one year,the value of the annuity will be:

To calculate risk-neutral prob. of interest rate change,

d 16

10 0 0 1S = 10 0 0 + 1 - = $ 11 , 8 3 8

0 .0 5 1 .0 5

u 16

1000 1S = 1000 + 1 - = $8824

0.1 1.1

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, .annuity, which is assumed to be 6%.

f d

u d

(1 + r )S - S 1.06 9122 - 11,838 = = = 71.95%

S - S 8824 - 11,838


The value today of the investment opportunity is thepresent value of the expected cash flows (using risk-

neutral probabilities) discounted at the risk-freerate:

837, 770 (1 - 0.7195) + 0 0.7195PV = = $221, 693

1.06

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,project are known with certainty, the uncertaintyregarding future interest rates creates substantialoption value for the firm.


8/16

The Option to Expand

An investment opportunity with an option togrow requires a $10 million investment today.

n one year you w n ou w e er e pro ecis successful.

The risk neutral probability that the project willgenerate $1 million per year in perpetuity is 50%,otherwise, the project will generate nothing.

At any time we can double the size of the project on theori inal terms.

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By investing today, the exp. annual cash flows

are $0.5m (ignoring option to double the size) $1 million 0.5 = $500,000


16


9/16


Computing the NPV gives:

500,000- -

Now consider undertaking the project and exercisingthe growth option to double the size in a year.

The NPV of doubling the size of the project in a year is:

without growth option , , .0.06

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doubling after a year

1,000,000NPV = - 10,000,000 = $6.667 million

0.06

The Option to Expand The risk-neutral prob. of this state is 50%, so the exp.

value of this growth option is 6.667 0.5 = $3.333m

Total NPV of this investment is the NPV without option,plus the value of growth option:

growth option

.PV = = $3.145 m illion

1.06

w ithout grow th option growth optionNPV = NPV + PV

18

It is optimal to undertake the investment today, onlybecause of the future expansion option.

= - 1.667 + 3.145 = 1.478 million


10/16

The Option to Shutdown

Assume you are the manager of a souvenirstore, considering opening a new branch inRoc s.

If you do not sign the lease on the store today,someone else will, so you will not have theopportunity to open a store later.

There is a clause in the lease that allows you to

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rea e ease a no cos n wo years.

Including the lease payments, the new store will cost$10,000 per month to operate.

The Option to Shutdown Because the building has just reopened, you do not

know what the pedestrian traffic will be.

If your customers are limited to commuters, you expect togenerate $8000 per month in revenue in perpetuity.

If, however, the area becomes a tourist attraction, you expectto generate $16000 per month in perpetuity.

There is a 50% probability that area become a tourist

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.

The costs to set up the store will be $400,000.

Risk-free = 7% per year (or 0.565% per month).


11/16

The Option to Shutdown

The number of tourists visiting Rocks representuncertainty. Since this is the kind ofuncertainty you can cost ess y iversi y away,the appropriate cost of capital is the risk-freerate.

If you were forced to operate the store underall circumstances, the expected revenue will be

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.

$8000

0.5 + $16,000

0.5 = $12,00012, 000 10, 000NPV = - - 400, 000 = - $46, 018

0.00565 0.00565

The Option to Shutdown In reality, you would not have to keep

operating the store. You have an option to getou o e ease a er wo years a no cos .

After the store is open, it will be immediatelyobvious whether the area is a tourist attraction.The decision tree is shown on the next slide.

If the Rocks is a tourist attraction, the NPV

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16,000 10,000

NPV = - - 400,000 = $661,9470.00565 0.00565


12/16

The Decision Tree

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The Option to Shutdown If the area does not become a tourist attraction, you

will close the store after two years with NPV of theinvestment o ortunit :

The NPV of opening the store is (equal Prob.):

24 24

8000 1 10,000 1NPV = 1 - - 1 - - 400,000

0.00565 1.00565 0.00565 1.00565

= -$444,770

$661, 947 0.5 - $444, 770 0.5 = $108 ,5 89

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By exercising the option to abandon the venture, you limit yourlosses and the NPV of investment becomes positive.

Option value = $108,589 (46,018) = $154,607


13/16

The Option to Prepay

An important real world abandonment optionis the option to prepay or refinance a mortgage.

repaymen op on An abandonment option that allows mortgage holders to pay

off a mortgage before the end of the scheduled term.

Refinance Repaying an existing loan, and taking out a new loan at a lower

rate.

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Mortgage interest rates are higher than Treasuryrates because mortgages have the abandonmentoptions of prepayment and refinancing .

The Option to Prepay Corporate bonds also often contain

embedded abandonment o tions.

The issuing firm may issue callable bonds,bonds that have an option that allows theissuer to repurchase (or call) the bonds at apredetermined price (usually at face value).

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onver e on s are corpora e on sthat give the holders the option toconvert the bond into equity.


14/16

Deciding Between Mutually ExclusiveInvestments of Different Lengths

An engineering firm was asked to design a newmachine for use in production.

The firm has produced two designs The cheaper design cost is $10m, last five years.

More expensive design cost is $17m and last 10 years.

In both cases, the machines are expected to save thecompany $3 million per year.

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,should be approved?

5

3 1N PV = 1 - - 10 = $1.37 m illion

0 .1 1 .1

NPV of Each Design The NPV of adopting the longer-lived design is:

3 1

If the cost of the machine in the shorter-lived designwill either increase by 3% or decrease by 3% and thatthe risk-neutral prob. of each state is 50%.

What is the optimal decision?

10- - .0.1 1.1

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, ,but will use the original technology instead.

If costs fall, then the machine will cost $8.9 million. 10 (1 0.03)5 = $8.59


15/16

NPV if Future Costs Are Uncertain

At that point, the NPV of replacing themachine is:

The NPV of adopting the five-year design istherefore the NPV of using the machine for

5

3 1NPV = 1 - - 8.59 = $2.78 million

0.1 1.1

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five years plus the NPV of optimally replacing

the machine in five years, as shown in thefollowing decision tree:

NPV if Future Costs Are Uncertain

5

0.50 2.78NPV = 1.37 + = $2.23 million

1.1

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NPV of adopting the five-year design andoptimally replacing it in five years exceeds theNPV of adopting the ten-year design, so thefive-year design is the superior investment.


16/16

Equivalent Annual Benefit (EAB) Method

NPV of shorter-lived design is $1.37 million.

Let xbe the e uivalent annual benefit.

The present value of the equivalent annual benefiteach year equals the NPV today.

The EAB of the shorter-lived design is given by:

x 1= -

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5

5

.0.1 1.1

1.37 0.1x = = $0.361 million11 -

1.1

EAB Method

Repeating the process for the longer-liveddesi n ives:

10

10

x 11.43 = 1 -

0.1 1.1

1.43 0.1x = = $0.233 million

11 -

1.1

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Based on EAB method, the analyst should select theshorter-lived design.

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Lec Real Option 110