Chapter 22
Principles of
Corporate Finance
Tenth Edition
Real Options
Slides by
Matthew Will
McGraw-Hill/Irwin
Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.
Topics Covered
The Value of Follow-On Investment
Opportunities
The Timing Option
The Abandonment Option
Flexible Production
Aircraft Purchase Options
A Conceptual Problem
22-2
Corporate Options
4 types of “Real Options”
1 - The opportunity to expand and make follow-up
investments.
2 - The opportunity to “wait” and invest later.
3 - The opportunity to shrink or abandon a project.
4 - The opportunity to vary the mix of the firm’s
output or production methods.
Value “Real Option” = NPV with option
- NPV w/o option
22-3
22-4
Microcomputer Forecasts
Example – Mark I Microcomputer ($ millions)
1982
After-tax operating cash flow (1)
Capital investment (2)
Increase in working capital (3)
Net cash flow (1)-(2)-(3)
450
0
-450
NPV at 20% = - $46.45, or about -$46 million
1983
100
0
50
60
Year
1984
159
0
100
59
1985
295
0
100
195
1986
185
0
-125
310
1987
0
0
-125
125
Microcomputer Forecasts
Example – Mark II Microcomputer Option
900
PV (exercise price)  3  676
1.1
OC  N (d1 )  P  N (d 2 )  PV ( EX )
d1  log[ P / PV ( EX )] /  t   t / 2
 log[. 691 / .606]  .606 / 2  .3072
d 2  d1   t  .3072  .606  .9134
N (d1 )  .3793
N (d 2 )  .1805
Call Value  [.3793  467}  [.1805  676]  $55.12million
22-5
22-6
Microcomputer Forecasts
Example – Mark II Microcomputer ($ millions)
Forecasted cash flows from 1982
1982
After-tax operating cash flow
Increase in working capital
Net cash flow
Present Value @ 20%
Investment, PV @ 10%
Forecasted NPV in 1985
……….
467
676
Year
1985
807
900
-93
NPV(1982) =PV(inflows) -PV(investment)
= 467 – 676
= - $209 million
1986
220
100
120
1987
318
200
118
1988
590
200
390
1989
370
-250
620
1990
0
-250
250
Microcomputer Forecasts
Example – Mark II Microcomputer (1985)
Distribution of possible Present Values
Probability
Present value in 1985
Expected value
Required investment
($807)
($900)
22-7
Option to Wait
22-8
Intrinsic Value
Option
Price
Stock Price
22-9
Option to Wait
Intrinsic Value + Time Premium = Option Value
Time Premium = Vale of being able to wait
Option
Price
Stock Price
Option to Wait
22-10
More time = More value
Option
Price
Stock Price
Timing Option Example
Possible cash flows and end-of-period values for the malted
herring project are shown. The project costs $180 million, either
now or later. The figures in parentheses show payoffs from the
option to wait and to invest later if the project is positive-NPV at
year 1. Waiting means loss of the first year’s cash flows. The
problem is to figure out the current value of the option.
22-11
Timing Option Example
High demand generates $25 million and a value of
$250 million at the end of the year. Low demand
generates $16 million and no value.
High Demand
Low Demand
(25  250)
1
200
 .375
Total return 
(16  160)
1
200
 .12
Total return 
Risk neutral return
= 5%
22-12
Timing Option Example
The next step requires the calculation of the probability of there
being a high demand for the malted herring project.
Expected return  (Prob of high demand)  .375  (1  Prob of high demand)  (-.12)
Expected return  .05
Prob of high demand  .343
The option value is now determined as follows.
(.343  70)  (.657  0)
Option Value 
1.05
 $22.9 million
22-13
22-14
Option to Wait
Example – Development option
Cash flow
Office Bldg
Office Bldg
240
NPV>0
Wait
100
NPV<0
100
Hotel NPV>0
240
Cash flow
from hotel
Option to Abandon
22-15
Option to Abandon
Simple Example - Abandon
Mrs. 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%
22-16
Option to Abandon
Simple Example - Abandon
Mrs. 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?
Year 0
Year 1
Year 2
120 (.6)
100 (.6)
90 (.4)
NPV = 145
70 (.6)
50 (.4)
40 (.4)
22-17
22-18
Option to Abandon
Simple Example - Abandon
Mrs. 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?
Year 0
Year 1
Year 2
120 (.6)
100 (.6)
90 (.4)
NPV = 162
Option Value =
162 - 145 =
150 (.4)
$17 mil
Option to Abandon
Example – Ms. East - Revenues
3.73
3.05
2.50
2.50
2.05
1.68
22-19
Option to Abandon
Example – Ms. East – Cash Flows
3.03
2.35
1.80
1.80
1.35
.98
22-20
Option to Abandon
Example – Ms. East – Value
2.5
PV 
 $2.29million
1.09
3.05 p  2.05(1  p )
Expected return 
 .06
2.29
Prob of up change  .382
Prob of down change  .618
APV  -1.108  3.803  $2.695milli on
22-21
22-22
Tanker Example
Value
of
Tanker
Value in
operation
Cost of
reactivating
Mothballing
costs
Value if
mothballed
Tanker
Rates
Aircraft Purchase Option
The option to purchase an aircraft provides the
holder both the ability to obtain a lower price as
well as receive the aircraft sooner. Both have value
to the aircraft buyer, thus the option has value.
22-23
Aircraft Purchase Option
Value of aircraft purchase option—the extra value of the option
versus waiting and possibly negotiating a purchase later. The
purchase option is worth most when NPV of purchase now is about
zero and the forecasted wait for delivery is long.
22-24
Real Option Barriers
 Practical reasons exist why real options are not always
feasible to use.
1.
2.
3.
Valuation of real options can be complex and sometimes it is
impossible to arrive at the “perfect” answer.
Real options do not always have a clear structure their path and
cash flows.
Competitors also have real options, which an alter the value of
your options by altering the underlying assumptions and
environment that serves as the basis of your valuation.
Given these limitations, real options are not always the best
approach when valuing projects.
22-25
Web Resources
Click to access web sites
Internet connection required
http://www.palisade.com/
www.decisioneering.com
22-26