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Real Options
Principles of Corporate FinanceBrealey and Myers Sixth Edition
Slides by
Matthew Will Chapter 21
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
21- 2
Topics Covered
Real Options Follow Up Investments Abandon Wait Vary Output or Production
Binomial Model
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
21- 3
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
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
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Intrinsic Value
Option to Wait
Option Price
Stock Price
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
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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
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
21- 6
More time = More value
Option to Wait
Option Price
Stock Price
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
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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
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
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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)
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
21- 9
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?
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
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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
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
21- 11
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
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
21- 12
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
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
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40.37
32.10
36
37.401215.13610
UPUP
Binomial Pricing
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
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40.37
32.10
36
37.401215.13610
UPUP
10.328917.3610
DPDP
Binomial Pricing
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
21- 15
50.78 = price
40.37
32.10
25.52
45.28
36
28.62
40.37
32.10
36
1 tt PUP
Binomial Pricing
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
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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
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
21- 17
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
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
21- 18
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
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
21- 19
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
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
21- 20
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
©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill
21- 21
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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