Chapter 23 PrinciplesPrinciples

ofof

CorporateCorporate

FinanceFinance

Ninth Edition

Real Options

Slides by

Matthew Will

Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved

McGraw Hill/Irwin

23-2

Topics Covered

The Value of Follow-On Investment Opportunities

The Timing OptionThe Abandonment OptionFlexible ProductionAircraft Purchase OptionsA Conceptual Problem

23-3

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

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Microcomputer Forecasts

1982 1983 1984 1985 1986 1987

After-tax operating cash flow (1) 100 159 295 185 0Capital investment (2) 450 0 0 0 0 0Increase in working capital (3) 0 50 100 100 -125 -125Net cash flow (1)-(2)-(3) -450 60 59 195 310 125

NPV at 20% = - $46.45, or about -$46 million

Year

Example – Mark I Microcomputer ($ millions)

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Microcomputer Forecasts

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12.55$]6761805[.}4673793[. Value Call

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12

1

Example – Mark II Microcomputer Option

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Microcomputer Forecasts

1982 ………. 1985 1986 1987 1988 1989 1990After-tax operating cash flow 220 318 590 370 0Increase in working capital 100 200 200 -250 -250Net cash flow 120 118 390 620 250Present Value @ 20% 467 807Investment, PV @ 10% 676 900Forecasted NPV in 1985 -93

Year

Example – Mark II Microcomputer ($ millions)

Forecasted cash flows from 1982

NPV(1982) =PV(inflows) -PV(investment)

= 467 – 676

= - $209 million

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Microcomputer Forecasts

Example – Mark II Microcomputer (1985)

Distribution of possible Present Values

Expected value

($807)

Required investment

($900)

Present value in 1985

Probability

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Option to Wait

Intrinsic Value

Option Price

Stock Price

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Option to Wait

Intrinsic Value + Time Premium = Option Value

Time Premium = Vale of being able to wait

Option Price

Stock Price

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Option to Wait

More time = More value

Option Price

Stock Price

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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.

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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.

375.

1200

)25025(return Total

12.

1200

)16016(return Total

High Demand Low Demand

Risk neutral return = 5%

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Timing Option Example

The next step requires the calculation of the probability of there being a high demand for the malted herring project.

The option value is now determined as follows.

343. demandhigh of Prob

05.return Expected

(-.12)demand)high of Prob1(375.demand)high of Prob(return Expected

million 9.22$05.1

)0657(.)70343(. ValueOption

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Option to Wait

Example – Development option

Wait

NPV<0 100 240

Hotel NPV>0

Cash flow from hotel

Cash flow Office Bldg

Office Bldg

NPV>0

240

100

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Option to Abandon

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%

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Option to AbandonExample - 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)

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Option to AbandonExample - 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

150 (.4)

Option Value =

162 - 145 =

$17 mil

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Option to Abandon

Example – Ms. East - Revenues

2.50

3.05

2.05

3.73

2.50

1.68

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Option to Abandon

Example – Ms. East – Cash Flows

1.80

2.35

1.35

3.03

1.80

.98

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Option to Abandon

Example – Ms. East – Value

on2.695milli$3.803-1.108APV

.618change down of Prob

.382change up of Prob

06.29.2

)1(05.205.3return Expected

29.2$09.1

5.2

pp

millionPV

23-21

Tanker Example

Mothballing costs

Value if mothballed

Cost of reactivating

Value in operation

Tanker Rates

Value of Tanker

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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.

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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.

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Real Option Barriers

Practical reasons exist why real options are not always feasible to use.

1. Valuation of real options can be complex and sometimes it is impossible to arrive at the “perfect” answer.

2. Real options do not always have a clear structure their path and cash flows.

3. 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.

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Web Resources

www.puc-rio.br/

www.decisioneering.com

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