Real Options

Principles of Corporate FinanceBrealey and Myers Sixth Edition

Slides by

Matthew Will Chapter 21

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Topics Covered

Real Options Follow Up Investments Abandon Wait Vary Output or Production

Binomial Model

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Corporate Options

4 types of “Real Options”1 - The opportunity to make follow-up investments.2 - The opportunity to abandon a project3 - The opportunity to “wait” and invest later.4 - The opportunity to vary the firm’s output or production methods.

Value “Real Option” = NPV with option - NPV w/o option

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Intrinsic Value

Option to Wait

Option Price

Stock Price

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Intrinsic Value + Time Premium = Option Value

Time Premium = Vale of being able to wait

Option to Wait

Option Price

Stock Price

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More time = More value

Option to Wait

Option Price

Stock Price

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Example - AbandonMrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option?

Use a discount rate of 10%

Option to Abandon

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Example - AbandonMrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option?

Option to Abandon

Year 0 Year 1 Year 2

120 (.6)

100 (.6)

90 (.4)

NPV = 145

70 (.6)

50 (.4)

40 (.4)

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Option to Abandon

Year 0 Year 1 Year 2

120 (.6)

100 (.6)

90 (.4)

NPV = 162

150 (.4)

Option Value =

162 - 145 =

$17 mil

Example - AbandonMrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option?

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Reality Decision trees for valuing “real options” in a

corporate setting can not be practically done by hand.

We must introduce binomial theory & B-S models

Corporate Options

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Probability Up = p = (a - d) Prob Down = 1 - p

(u - d)

a = ert d =e-[t].5 u =e[t].5

t = time intervals as % of year

Binomial Pricing

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Example

Price = 36= .40 t = 90/365 t = 30/365

Strike = 40 r = 10%

a = 1.0083

u = 1.1215

d = .8917

Pu = .5075

Pd = .4925

Binomial Pricing

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40.37

32.10

36

37.401215.13610

UPUP

Binomial Pricing

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40.37

32.10

36

37.401215.13610

UPUP

10.328917.3610

DPDP

Binomial Pricing

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50.78 = price

40.37

32.10

25.52

45.28

36

28.62

40.37

32.10

36

1 tt PUP

Binomial Pricing

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50.78 = price

10.78 = intrinsic value

40.37

.37

32.10

0

25.52

0

45.28

36

28.62

36

40.37

32.10

Binomial Pricing

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50.78 = price

10.78 = intrinsic value

40.37

.37

32.10

0

25.52

0

45.28

5.60

36

28.62

40.37

32.1036

trdduu ePUPO

The greater of

Binomial Pricing

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50.78 = price

10.78 = intrinsic value

40.37

.37

32.10

0

25.52

0

45.28

5.60

36

.19

28.62

0

40.37

2.91

32.10

.10

36

1.51

trdduu ePUPO

Binomial Pricing

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50.78 = price

10.78 = intrinsic value

40.37

.37

32.10

0

25.52

0

45.28

5.60

36

.19

28.62

0

40.37

2.91

32.10

.10

36

1.51

trdduu ePUPO

Binomial Pricing

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Expanding the binomial model to allow more possible price changes

1 step 2 steps 4 steps

(2 outcomes) (3 outcomes) (5 outcomes)

etc. etc.

Binomial vs. Black Scholes

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How estimated call price changes as number of binomial steps increases

No. of steps Estimated value

1 48.1

2 41.0

3 42.1

5 41.8

10 41.4

50 40.3

100 40.6

Black-Scholes 40.5

Binomial vs. Black Scholes