REAL OPTIONS The Options on Real Assets. PROJECT APPRAISAL - DCF Evaluation method of capital...

REAL OPTIONS

The Options on Real Assets

PROJECT APPRAISAL - DCFEvaluation method of capital budgeting exercise by discounting the cash flows to find NPV is flawed because values so arrived ignore the value of managerial actions that are available later.

The implied assumption is that nothing would alter after the decision is made.

Conventional project appraisal by DCF method treats the project passive and static i.e. the set of assumptions made now remain valid for times to come.

Financial Management II Rajiv Srivastava

CAPITAL BUDGETINGLimitations

Capital budgeting decisions are seldom routine. They are strategic in nature.

Management has the flexibility to make decisions subsequent to implementation of project.

Managerial interventions have cash flow implications.

Capital budgeting done on the basis of static cash flows ignores the strategic value of the subsequent interventions.


STANDARD CAPITAL BUDGETING Standard techniques to evaluate capital budgeting decisions consider only the present information. It assumes that all managerial actions are absent once the cash flow estimates are prepared.Capital budgeting decisions are not passive and static. Instead they are subject to managerial actions with several options as time progresses.

options to reduce capacity utilisation, undertake intensive advertising campaign if volumes are not picking up. options such as increase production, raise prices, develop more product variants etc.

In fact each capital budgeting decision is a complex set of options.


HOW TO VALUEDo the managerial actions have some value? In NPV we never attached a value to the options that are available.The worth of the project must be evaluated as

Real value of capital budgeting decision = Conventional NPV + Value of the

options


OPTIONS ON REAL ASSETS

The ability of the management to influence the cash flows of the project subsequently is referred as option on real asset.

Options on real assets are many but we confine normally to three types

option to delay,

option to expand and

option to abandon.


OPTION TO DELAY

Option to delay refers to the decision of timing of implementation of project.

Deferment of the project may yield higher NPV than if implemented now.

Higher NPV may result from more clarity on the information as time progresses,

greater reliability of input estimates used, or

use of lower discount rate as uncertainties of cash flows reduce as time progresses.


OPTION TO EXPAND

Option to expand refers to the managerial flexibility to

increase production,

increase price, or

add product variants etc.

These actions based on experience gathered in the interim enhance the cash flows

It is like a call option with exercise price equal to the cost of additional investment required at a later date.


OPTION TO ABANDON

Option to abandon refers to the flexibility of the management to exit the project realising the salvage value.

It is exercised when the cash flows of the project fail to meet the bare minimum expectations.

It is equivalent to a put option with exercise price equal to the salvage value.


VALUING REAL OPTIONSStandard capital budgeting analysis on the discounted cash flow basis treats the situation as now or never.

If the NPV of the project is negative we reject it. Value of embedded options may make a negative NPV project into a positive NPV proposition.

How to valueComparing NPVs of different alternatives

Using binomial approach

Using Black – Scholes modelFinancial Management II Rajiv Srivastava

VALUING REAL OPTIONSDCF Method

One way to value real option is to use DCF approach.

DCF approach compares the NPVs of the same project if implemented at different points of time.

Since option to implement now or later are mutually exclusive we choose the timing of implementation that provides the largest NPV.


VALUING REAL OPTIONSBinomial Method

Many real options situations are apt for valuation by binomial method.

Major advantage of binomial method over DCF method is that binomial does not require the values of the probabilities of the various scenarios.

The current price of the asset is assumed to contain the volatility of the asset.


VALUING REAL OPTIONSBased on Financial Options

Valuation of real options can be done by model developed for financial assets i.e. Black Scholes Model (BSM)

Valuation of real options with BSM would have following limitations:

non-tradability of real options

exercise not being instantaneous

problems of estimating the volatility of the cash flows and

inability to clearly define the option. Financial Management II Rajiv Srivastava

BASIC OPTIONS - CALL & PUT

An OPTION is a right but not an obligation to buy/sell an asset at a predetermined price on or before a given date.

The underlying asset: stock, index, currency, futures, commodity etc.

CALL OPTION

Right to buy an asset

PUT OPTION

Right to sell an asset


FEATURES OF OPTIONS

HOLDER WRITERWho holds the option Who gives the optionWRITER/SELLER of the option is under obligation to perform; HOLDER/BUYER has no such obligation.Option Writer has to be paid a premium upfront. EXERCISE/STRIKE PRICE MATURITY DATEPrice at which the right Time up to which the can be exercised. right is available.AMERICAN EUROPEANExercised on or before Exercised only on maturity maturity


PAY OFF – CALL OPTIONPay Off BUYER WRITER

When S < X - c + cWhen S > X S-X-c - (S-X-c)

Spot Price

c X


PAY OFF – PUT OPTION

Pay Off

X Spot Pricep

BUYER WRITERWhen S < X X-S-p - (X-S-p)When S > X - p + p


BINOMIAL METHODAsset Call

125 25

80%

100

20%

75 0

Probabilities of up and down movement are not required, for no arbitrage argument.Consider a portfolio of

1 Long Share and 2 Short Calls with X = 100 and maturity of 1 year

Value of portfolio at expiryUp move 125 – 2 x 25 = 75Down move 75 – 2 x 0 = 75

Outcome of portfolio is certain, and hence it must yield no more than the risk free rate of return.


VALUING CALL WITH BINOMIAL

Cost of setting the portfolio of 1 long stock and 2 short calls, is 100 – 2c where c is the value of call.Rs 75 is the value after one year and is certain, therefore cost of portfolio must equal the present value of Rs 75 discounted at risk free rate, r = 10% (assumed)With current stock price known this would give the value of the 1 year call with X = 100

100 – 2c = e-rT x 75 = 75 x 0.9048

c = 32.14/2 = Rs 16.07


VALUING CALL ……..

T = 0 At Maturity, TAsset CallΔuS cu

S, c

ΔdS cd

Riskless portfolioΔ long stock and 1 short call; Value of portfolio at expiry is same i.e.

ΔuS – cu = ΔdS - cd

dSuScc du

Value of portfolio at T = 0

ΔS – c = (ΔuS – cu) e-rT

c = [p cu + (1- p)cd] e-rT

WhereFor the example, we have

Δ = ½ and

p =(1.1052 - 0.75)/0.5 = 0.7103

Call value, c

= (0.7103 x 25 – 0.2897 x 0) x 0.9048

= Rs 16.07

dude

prT


RISK NEUTRAL VALUATIONIf the binary state of prices is correct the market as a whole must agree to the same expected price, E(S1) of the stock.

To have universally acceptable E(S1) the expected returns offered by the stock [E(S1) - S0]/S0 can be no greater than the risk free rate of return, r.

Under risk neutral valuation all investors are neutral to risk, i.e. the underlying asset earns the risk free rate of return, i.e. E(S1) = (1+ r) x S0, or with continuous compounding E(S1) = erT x S0 = Futures price, F

While computing futures price therefore we use risk free rate assuming risk neutral world.


RISK NEUTRAL VALUATIONIf p is probability of up move, then expected value of the asset at maturity = [p x 125 + (1 – p) x 75]

Under risk neutrality it must give 10% return therefore,

[p x 125 + (1 – p) x 75 ]= 100 x e0.10 x 1

Therefore p = 0.7103 and 1 – p = 0.2897

Same risk neutral probabilities would apply to the call.

Call value at T = [0.7103 x 25 + 0.2897 x 0]

= Rs 17.7575

The call value today, c

= call value at maturity discounted at risk free rate (10%)

= [0.7103 x 25 + 0.2897 x 0] e-0.10 x 1 = Rs 16.07


REAL WORLD AND RISK NEUTRAL WORLD

If in the real world the expected return from the stock is 20% and not 10% (the risk free rate), then with binary states the probability of up move, p* must be

[p* x 125 + (1 – p*) x 75 ]= 100 x e0.20 x 1

or p* = 0.9428

Then the value of the call at maturity in real world would be

= p* x 25 + (1 – p*) x 0 = = 0.9428 x 25 = Rs 23.57

Actual value of call in risk neutral world is Rs 16.07. The appropriate discount rate would then be 38.31% in the real world (riskier than what applies to asset, 20%).


VALUE A VACANT LAND

A piece of land can be used for making 8 apartments now or after 1 year. The market value of each apartment today is Rs 60 lakh. The cost of building apartments is Rs 360 lakh.The net profit if built today

60 x 8 – 360 = Rs 120 lakhThe firm has an option to delay the project by one yearUncertainty about the value of the apartment a year later. With only two scenarios

Buoyant SluggishMarket Value Rs75 lakh Rs 54 lakh


VALUE A VACANT LAND

Should the builder defer the construction?Conventional capital budgeting process - Construct now with positive NPV of Rs 120 lakh .Additional information available

Cost of construction remains same after 1 year at Rs 360 lakhInterest rate = 12% p.a.Opportunity cost = loss of rental for one year Rs 5 lakh p.a.


BINOMIAL MODEL

Situation Value Payoff

70 70 x 8 – 360 = 200 Buoyant

60

Sluggish

49 49 x 8 – 360 = 32


BINOMIAL MODEL• Probability of rising and falling prices are built in the

current value of the flat. If probability of buoyant condition is p then

p x 70 + (1 - p) x 49 = 60 x 1.12 Gives p = 0.7913

Situation 70 70 x 8 – 360 = 200

BuoyantCall Value = (0.7913 x 200 + 0.2087 x 32)/1.12

60 = 164.94/1.12 = Rs 147.26 lakh

Sluggish

49 49 x 8 – 360 = 32Financial Management II Rajiv Srivastava

VALUE A VACANT LAND

Let us value the option to build 12 flats on the land. The value of each apartment today is Rs 60 lakh. The cost of building apartments is Rs 590 lakh.The net profit if built today

60 x 12 – 590 = Rs 130 lakhThe firm has an option to delay by one yearUncertainty about the value of the apartment a year later. With only two scenarios

Buoyant SluggishMarket Value Rs75 lakh Rs 54 lakh


BINOMIAL MODEL

Situation Value Payoff

70 70 x 12 – 590 = 250 Buoyant

60

Sluggish

49 49 x 12 – 590 = -2


BINOMIAL MODEL• Probability of rising and falling prices are built in the

current value of the flat. If probability of buoyant condition is p then

p x 70 + (1 - p) x 49 = 60 x 1.12 Gives p = 0.7913

Situation 70 70 x 12 – 590 = 250

BuoyantCall Value = (0.7913 x 250 – 0.2087 x 0)/1.12

60 = 197.82/1.12 = Rs 176.63 lakh

Sluggish

49 49 x 12 – 590 = -2 (0)Financial Management II Rajiv Srivastava

OPTION TO DELAY

Now or Never ????

Vs. Now or Later

TIMING DECISION - DCFAssume a software firm SOFTBANK has developed

a new banking product but is uncertain about its demand potential.

Only 2 possible outcomes HIGH DEMAND: Cash flows of Rs 50 lacs for 4 years LOW DEMAND: Cash flows of Rs 30 lacs for 4 years

CAPITAL OUTLAY : Rs. 100 lacs LIFE : 4 years SOFTBANK knows that there is no competitor

emerging in the product developed and it can afford to delay implementation of the project.

The managers at SOFTBANK estimate equal likelihood of the ‘good’ and ‘not so good’ demand scenario.


TIMING DECISION - DCF

The expected annual cash flow would be Rs. 40 lacs (0.50 x 50 + 0.50 x 30).

12% discount rate is considered appropriate for the risk of the cash flows.

The expected NPV of the project if launched now is Rs. 21.49 lacs

With positive NPV the project must be implemented now.

lacs 21.49 Rs.=100-1.12

40+

1.12

40+

1.12

40+

1.1240

=NPV432


OPTION TO DELAY

The decision to implement a year later will depend upon the demand scenario prevailing then.

If the demand remains good SOFTBANK must go ahead with the launch else it must drop altogether.

The above situation can be considered as 2 mutually exclusive options and the decision will be based on the rule of higher NPV.Option I : Launch now

Option II : Launch a year later. Cost of implementing a year later remains same at Rs 100 lacs

Option I and II are mutually exclusive as selection of one precludes the other.


OPTION TO DELAY - NPVs


OPTION TO DELAY FOR 'SOFTBANK' Rs. Lacs OPTION I: LAUNCH NOW Discount Rate 12% Year NPV Prob 'p' p x NPV GOOD 0 1 2 3 4

Cash flow (100.00) 50.00 50.00

50.00

50.00

PV (100.00) 44.64 39.86

35.59

31.78 51.87 0.50 25.93

NOT GOOD

Cash flow (100.00) 30.00 30.00

30.00

30.00

PV (100.00) 26.79 23.92

21.35

19.07 (8.88) 0.50 (4.44)

Expected NPV 21.49 OPTION II : LAUNCH A YEAR LATER Discount Rate 12% Year NPV Prob 'p' p x NPV GOOD 1 2 3 4 5

Cash flow (100.00) 50.00 50.00

50.00

50.00

PV at Year ‘0’

(89.29) 39.86 35.59

31.78

28.37 46.31 0.50 23.16

NOT GOOD Cash flow - - - - - PV - - - - - - 0.50 - Expected NPV 23.16

OPTION TO DELAY - NPVsNPVs need to be compared must coincide in time. Since the expected NPV of Option II is greater the

product must be launched a year later. The value of the option to wait for one year, therefore

is the difference of the two NPVs i.e. Rs. 1.67 lacs. Assumptions:

The firm implements the project if the demand scenario is ‘good’ in Year 1.

Firm abandons the project if the demand scenario is ‘not so good’ in Year 1.

The initial outlay and the cash flows from for next four years remain same. (Should it be discounted at the same rate as that of cash flows??)

The discount rate too remains same at 12%???


NPV – Some Issues

Initial investment must be discounted at much lower rate than WACC – the

applicable rate for discounting the project cash inflows. Some recommend the use of risk free rate.

This will increase the value of initial investment and decrease the NPV of the delay option.

Discount RateUse of same WACC under both the options is fallacious

because of increased certainty of the cash flow in option to delay. Under Option II we do not make investment if low demand is experienced in Year 1. Therefore, discount rate under Option II should be lower than the one used in Option I, not because the rates have fallen or changed but because there is less uncertainty under Option II than under Option I.

This will increase the NPV of the delay option.


OPTION TO DELAY - BINOMIAL


Binomial Presentation

Option to Wait; Binary Option PricingPresent Value% Return

151.87 +51.87%

100

91.92 -8.88%


Option to Delay - Binomial

The firm has option to delay by one year implying thereby that it implements the project with

Exercise price, X = Rs. 100 lacs.

Payoff is like call optionGood demand = Rs. 51.87 lacs.

Low demand = Nil


Option to Delay – A Call OptionUsing risk neural method to value the call option,

the probability of high demand as p, then the payoff of the two branches must yield return equal to risk free rate taken as 9%. Then

p x 51.87% + (1 – p) x (-8.88%) = 9%p = 29.43%

With probability, p of 29.43% the value of the call is computed at Rs. 15.26 lacs.

Value of the call = 0.2943 x 51.87 + 0.7551 x 0 = Rs. 15.26

lacs


OPTION TO DELAYBLACK SCHOLES MODEL


Inputs for BSM

Option to wait resembles a call option on a stock (option to buy at predetermined price within specified time), and we can use BSM to value the option to wait. To value this call option we require following five inputs:

1. The Exercise Price ‘E’2.The Expiration Time ‘t’

3.The Risk free rate ‘rf’4.The Spot Price of the underlying asset ‘S’5.The Variance of return ‘σ2’


Inputs of BSM

Here first three inputs are straight forward .The exercise price ‘E’ = Rs. 100 lacs, the value

of initial investment. The time to expiry of this option, t = one year. Risk free rate can be obtained from yield on the

government securities. Let us assume this at 6%.The underlying asset on the option is the cash

flow of the delayed project. The expected present value of the cash inflows only of the project (not the expected NPV which is the intrinsic value of the option) will be equivalent to the spot price, S.


The Underlying Asset

PRESENT VALUE OF INFLOWS; THE SPOT PRICE Rs lacs

Discount Rate 12%

Year PV Prob 'p' p x PV

1 2 3 4 5

Cash flow -

50.00

50.00

50.00

50.00

PV -

39.86

35.59

31.78

28.37

135.60

0.50

67.80

Cash flow -

30.00

30.00

30.00

30.00

PV -

23.92

21.35

19.07

17.02

81.36

0.50

40.68

Present Value at t = 0 108.48


The Variance

CALCULATING VARIANCE OF OPTIONExpected Price at t

= 1Spot Price

% Return Prob. p x Return

p x dev2

Good 151.87 108.48 40% 0.50 0.20 0.0392

Not Good 91.12 108.48 -16% 0.50 (0.08) 0.0392

Expected Return 12%

Variance 0.0784Standard Deviation 28.00%


BSM – Option to Delay

The values of the input are Spot Price, S= Rs. 108.48 lacs, Exercise Price, X = Rs. 100 lacsTime to expiry, t = 1 year

Interest Rate, rf = 6%Standard Deviation, σ = 28%

Inserting the values, Value of call option = Rs. 19.83 lacs.

tσ-d=d or tσ

/2)tσ-(r+ln(S/X)=d

and ;tσ

/2)tσ+(r+ln(S/X)=d where

)N(dXe-)SN(d=c

12

2

2

2

1

2rt

1-


OPTION TO EXPAND


OPTION TO EXPAND - DCF

Option to expand relates to the flexibility of management to start small and depending upon the outcome set up another big related venture.

This flexibility cannot be exercised unless the initial investment is made.

Most firms start a venture on experimental basis keeping investment small to limit the risk.

Most such projects are likely to be negative NPV projects

With conventional approach of positive NPV or IRR in excess of cost they stand rejected.

Examples of such projects are numerous.


OPTION TO EXPAND – Grow MotorsAn Electric Car may be launched at a cost of Rs 200

crore with expected inflow of Rs 75 crore p.a. for next three years. At 10%, it has NPV of - Rs 13.49 crore.

The launch of Phase I of Electric Car presents an opportunity to improve upon the performance that is likely to expand the market, decrease the price and increase the volumes

and hence improve NPV later.Follow-on investment can be made after 3 years with

Year 3 outlay of Rs 600 crore and present value (Year 3) of inflows is Rs 1,000 crore.


Option to Expand - Grow Motors

GROWMOTORS - LAUNCH OF ELECTRIC CAR - Phase I

Rs crore Discount Rate 10% Year 0 1 2 3

Cash flow

(200.00) 75.00 75.00 75.00 Present Value

(200.00) 68.18 61.98 56.35

Net Present Value (13.49)


OPTION TO EXPAND - DCF


GROWMOTORS – LAUNCH OF ELECTRIC CAR Phase I and Phase II Discount Rate 10% Present Value with High demand Expand Cash flow 0 1 2 3 PV at T = 0 Phase I (200.00) (200.00)

Investment (200.00) Inflows 75.00 75.00 75.00 186.51

Phase II

Investment - - -600.00 (518.30)* Inflows - - 1000.00 751.31

Net Present Value with High demand 219.53 Present Value with Low demand Do not expand

Phase I - -

Investment (200.00) (200.00) Inflows 75.00 75.00 75.00 186.51

Phase II

Investment - - - - Inflows - - - -

Net Present Value with Low demand (13.49) *Being certain discounted at 5%

OPTION TO EXPAND – Grow Motors


NPV GROW MOTORS - with Phase I and Phase II Rs. crore

NPV Prob Exp NPV

219.53 0.60 131.72

Expand

Do not expand

(13.49) 0.40 (5.39)

Expected NPV with Phase I & Phase II 126.32

OPTION TO ABANDON


Option to AbandonOption to abandon relates to the situation where the firm can take a decision to exit the activity to reduce or avoid future losses.Such a right to abandon is valuable as it releases financial resources for

exploring new or more profitable business avenues, or simply help contain future losses that may result due to continuation of the project.

Such an option is analogous to a put option where the holder has option to sell at predetermined price within a predetermined time period.


No “Option to Abandon” - Example Ganga Toll Bridge Company (GANGA) is contemplating to participate in a tender to build a bridge across a river, with following conditions:

The tender stipulates the maximum toll fee that can be charged.

The bridge must be made toll free after 25 years.

The cost of building the bridge is Rs. 10 crore.

Based on traffic estimates GANGA can generate cash flow of Rs 1 crore evenly for next 25 years.

WACC = 12%

NPV of the project

= PVA of Rs. 1.00 crore for 25 years at 12% - 10 crore

= 7.843 – 10.000 = - Rs. 2.157 crore Financial Management II Rajiv Srivastava

Option to Abandon – A Put Option GANGA refuses to accept the tender as NPV is negative.

Govt pursues and offers following information and a proposal to buyback:

The local government is also planning to develop an amusement park and a township on the other side of the river, which is likely to enhance the traffic on the bridge. The estimated time to complete the development is 5 years.

In case the plan does not fructify the government also offered to buyback the bridge at the end of 5 years at Rs. 6 crore if GANGA so chooses.

In the light of new information made available should GANGA reconsider its stand?


Option to Abandon - Ganga The additional information now available has changed the features of the project.

The likely scenario of traffic would change with the amusement park and the new township after 5 years.

It is now a project with a put option (option to sell) at the end of 5 years with GANGA realising Rs. 6 crore.

GANGA estimates that Chances that government’s plan would succeed are 60%. If so it provides cash flows of Rs. 2.50 crore annually for next 20 years.

If developmental plan does not succeed, the expected cash flow would be Rs. 0.50 crore annually for next 20 years and in which case GANGA may abandon the project and handover to government at Rs. 6 crore.


Cashflow of the Bridge Without Option to Abandon


Option to Abandon; GANGA TOLL BRIDGETime (years)

0 5 25

ContinueRs. 2.50 crore p.a.for 20 years at 12%

High = 0.6 PV (at t = 5 yrs) = Rs. 18.674 crore

Rs. 1.00 crore for 5 years

Low = 0.4Abandon

Rs. 0.50 crore p.a. for 20 years at 12%PV (at t = 5 yrs) = Rs. 3.735crore

Value of Bridge Without Option to Abandon


Expected Value & NPV without Put OptionRs. CrorePV (t = 5)

18.674 x 0.6 = 11.204

High (0.6)

1 crore 5 yrs 12%

Low (0.4)

PV (t = 0)

3.605 3.735 x 0.4 = 1.494

7.205 = 12.698

10.810 NPV = 10.810 – 10.000 = 0.810

Value of Bridge With Option to Abandon


Expected Value & NPV without Put OptionRs. CrorePV (t = 5)

18.674 x 0.6 = 11.204

High (0.6)

1 crore 5 yrs 12%

Low (0.4)

PV (t = 0)

3.605 6.000 x 0.4 = 2.400

7.719 = 13.604

11.324 NPV = 11.324 – 10.000 = 1.324

REAL OPTIONS The Options on Real Assets. PROJECT APPRAISAL - DCF Evaluation method of capital...

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Transcript of REAL OPTIONS The Options on Real Assets. PROJECT APPRAISAL - DCF Evaluation method of capital...