7/23/2019 Real Options Theory

1/19

Real Options

7/23/2019 Real Options Theory

2/19

Topics Covered

The Value of Follow-On InvestmentOpportunities

The Timing Option The Abandonment Option

7/23/2019 Real Options Theory

3/19

Corporate Options

3 tpes of !"eal Options#

$ - The opportunit to e%pand and ma&e follow-upinvestments'

( - The opportunit to !wait# and invest later'3 - The opportunit to shrin& or abandon a pro)ect'

Value !"eal Option# * +,V with option - +,V wo option

7/23/2019 Real Options Theory

4/19

.icro computers case /$01(2

ou are Asst' to CFO4 .icro Computers' ou are helping

him evaluate proposed introduction of .ar& I chip'5CF analsis is given below' +,V at hurdle rate is6/782 .n' /Accept"e)ect2'' ou sa !For 9trategicreasons :A;+C

7/23/2019 Real Options Theory

5/19

.icrocomputer ForecastsExample Mark I Microcomputer ($ millions)

7/23/2019 Real Options Theory

6/19

.icrocomputer ForecastsExample Mark II Microcomputer ($ millions)

Forecasted cash flows from 1!"

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

= 467 676

= - $209 million

7/23/2019 Real Options Theory

7/19

.icrocomputer Forecasts

[ ] [ ])()()( 21 EXPVdNPdNOC =

6761.1

900pi!e)e"e!ise(

# ==PV

2

1

2

2 1

1 2

lo% & ' ( )2

(#)lo(467 & 676) (10 )#

2 0.1879# #

.4184

( ) .7408 ( ) .##7844*+ll V+l,e %0.7408 467 %0.##7844 676' $99.11

S X r T d

T

d d t

N d N dmillion

+ +

=

+ +

= =

= =

= =

= =

Example Mark II Microcomputer

7/23/2019 Real Options Theory

8/19

.icrocomputer ForecastsExample Mark II Microcomputer (1!#)

istri%ution of possi%le &resent 'alues

"pe!te/ v+l,e

($807)

e,ie/ investment

($900)

Pesent v+l,e in 198

Po+ilit3

7/23/2019 Real Options Theory

9/19

Intrinsic Value

Option to Dait

OptionPrice

Stock Price

7/23/2019 Real Options Theory

10/19

Intrinsic Value E Time ,remium * Option Value

Time ,remium * Vale of being able to wait

Option to Dait

OptionPrice

Stock Price

7/23/2019 Real Options Theory

11/19

.ore time * .ore value

Option to Dait

OptionPrice

Stock Price

7/23/2019 Real Options Theory

12/19

If ou commit an investment worth 6 $1?.n4 ou have apro)ect worth 6 (?? .n immediatel' If the demandturns out to be low in r' $4 the cash flow will be 6 $8

.n and the value of the pro)ect will fall to 6 $8? .n'ut if the demand is high in ear $4 the cash flow is 6( .n' And the value rises to 6(? .n' 9hould ouinvest immediatel or wait' ;se the ris& free rate of

'+oteG If ou underta&e the investment right awa4 ou

capture the first ears cash flow /6$8 or 6(2' If oudela ou miss out on this'

Option to Dait

7/23/2019 Real Options Theory

13/19

Example - Abandon

.rs' .ulla gives ou a non-retractable offer to bu ourcompan for 6$? mil at antime within the ne%t ear'Biven the following decision tree of possible outcomes4what is the value of the offer /i'e' the put option2 andwhat is the most .rs' .ulla could charge for the optionH

;se a discount rate of $?

Option to Abandon

7/23/2019 Real Options Theory

14/19

Example - Abandon

.rs' .ulla gives ou a non-retractable offer to bu our compan for6$? mil at antime within the ne%t ear' Biven the following decisiontree of possible outcomes4 what is the value of the offer /i'e' the putoption2 and what is the most .rs' .ulla could charge for the optionH

Option to Abandon

ear ? ear $ ear (

$(? /'82

$?? /'82

0? /'72

+,V * $7

@? /'82

? /'72

7? /'72

7/23/2019 Real Options Theory

15/19

Option to Abandon

ear ? ear $ ear (

$(? /'82

$?? /'82

0? /'72

+,V * $8(

$? /'72

Option Value =

162 - 145 =

$17 mil

Example - Abandon

.rs' .ulla gives ou a non-retractable offer to bu our compan for6$? mil at antime within the ne%t ear' Biven the following decisiontree of possible outcomes4 what is the value of the offer /i'e' the putoption2 and what is the most .rs' .ulla could charge for the optionH

7/23/2019 Real Options Theory

16/19

5awn ast4 the chief financial officer of .aine 9ubductorCorp'4 has to decide whether to start production ofJircon subductors' The investment reKuired is 6$( .n'

L 6 ( .n' For roads and site preparation and 6$? .n'For the eKuipment' To operate the eKuipment it costs

6 ?'@ .n' p'a' /a fi%ed cost2' The e%pected life of thepro)ect is $? ears and the depreciation of themachine is done following D5V method M $? p'a'The revenue at todaNs prices is 6$'@ .n and shall

grow M 0 p'a' Also4 the 9'5' of earnings is $7'The ris& free rate is assumed to be 8 p'a'

Option to Abandon

7/23/2019 Real Options Theory

17/19

Option to Abandon

%ample L .s' ast L Value

0.141 1.1

10.87

"pe!te/ et,n 0.1 0.1#(1 ) .06

Po of ,p !5+ne 0.6791Po of /own !5+ne 0.#209

Tu e e

du

p p

= = =

= =

= =

=

=

7/23/2019 Real Options Theory

18/19

Option to Abandon

%ample L .s' ast - "evenues

$'@

$'08

$'71

('(

$'@

$'(0

7/23/2019 Real Options Theory

19/19

Option to Abandon

%ample L .s' ast L Cash Flows

$'?

$'(8

?'@1

$'

$'?

?'0