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21- 1

Chapter 22 Options and Corporate Finance: Extensions and Applications

Real Options Follow Up Investments Abandon Wait Vary Output or Production

Binomial Model Value of the Maximum Price Guarantee

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21- 2

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.

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

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21- 3

Intrinsic Value

Option to Wait

Option Price

Stock Price

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21- 4

Intrinsic Value + Time Premium = Option Value

Time Premium = Value of being able to wait

Option to Wait

Option Price

Stock Price

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21- 5

More time = More value

Option to Wait

Option Price

Stock Price

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21- 6

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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21- 7

Risk-adjusted Probability (pseudo-probability)

Up = p = (a - d) 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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21- 8

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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21- 9

40.37

32.10

36

37.401215.13610

UPUP

10.328917.3610

DPDP

Binomial Pricing

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21- 10

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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21- 11

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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21- 12

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

Binomial Pricing

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21- 13

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

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21- 15 Distribution of Memory Chip Prices

S=$16

S=$10

S=$10

S=$4

S=$13

S=$7

t=0 t=1

t=2

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21- 16 Payoffs of the Maximum Price Guarantee

V=$6

V=$0

V=$0

V=$0

t=0 t=1

t=2

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21- 17 Value of the Maximum Price Guarantee

The risk-adjusted probability is:

q = [($10) (1.03) - $7]/($13 - $7) = .55

The value of the option at t=1 is:

V(S(U),t=1) = [(.55 ) ($6) + (.45) ($0)] / (1.03)

= $3.20 per MB

V(S(D),t=1) = [(.55 ) ($0) + (.45) ($0)] / (1.03)

= $0.00 per MB

The value of the option at t=0 is:

C(t=0) = [(.55 ) ($3.20) + (.45) ($0)] / (1.03) = $1.71 per MB

Therefore the value of the price guarantee = $171 million