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Lecture 07 - Real Options

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Real Options 1 AFC 3140 Advanced Corporate Finance
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Page 1: Lecture 07 - Real Options

Real Options

1

AFC 3140 – Advanced Corporate

Finance

Page 2: Lecture 07 - Real Options

Introduction

2

Capital budgeting involves projections of future cash flows.

However, a number of capital budgeting decisions cannot be

made until the future.

Example - If a pilot program trialing a new retail franchise is

successful, additional funds in the future will be committed

to expanding the program, otherwise the program may be

abandoned.

The decision to expand or abandon the program is an

example of a real option which has financial value.

Page 3: Lecture 07 - Real Options

Evolution of capital budgeting concepts

3

DCFSensitivity Analysis

Simulation

Decision Trees

Option Pricing

Real Option

Valuation

Page 4: Lecture 07 - Real Options

Do managers use real options in

practice?

4

Graham and Harvey (2001) surveyed 392 US CFOs and

found that 26.59% of them „always or almost always‟

incorporated real options of a project when evaluating it.

Mature CFOs incorporated real options more than younger

CFOs.

Non-regulated firms evaluated real options more than regulated

firms.

Truong, Partington and Peat (2008) found that 32% of

Australian firms considered real options in project

evaluation but with moderate importance.

Page 5: Lecture 07 - Real Options

Real versus financial options

5

Real options -The right to make a particular business

decision, such as a capital investment

Key distinction between real options and financial

options:

real options, and the underlying assets on which they are

based, are often not traded in competitive markets.

Examples real options:

option to delay an investment opportunity

option to grow (growth options)

option to abandon an investment opportunity

Page 6: Lecture 07 - Real Options

Investment as a Call Option - Example

6

Your company is considering a new project at a startup

cost of $12 million.

The project may begin today or in exactly one year. If

project does not start now or in one year it cannot start

at all because of government regulations.

You expect the project to generate $1,500,000 in free

cash flow the first year if you begin the project today.

Free cash flow is expected to grow at a rate of 3% per

year.

Page 7: Lecture 07 - Real Options

Contd.

7

Furthermore, assume that:

The risk-free rate is 4%.

The cost of capital for this investment is 11%.

The standard deviation (volatility) of the project‟s value is 30%.

Should you begin the project today or wait

one year?

Page 8: Lecture 07 - Real Options

8

Solution PV of CIF if the project starts today:

Thus, the NPV of the project today is:

$18,750,000 − $12,000,000 = $6,750,000

$1,500,000$18,750,000

11% 3%TodayV

Page 9: Lecture 07 - Real Options

Contd.

9

If the project is initiated in one year, investors do not receive

the first year‟s free cash flow ($1,500,000).

However, investors do have an additional year to evaluate the

project and make an investment decision based on more

information.

Page 10: Lecture 07 - Real Options

Contd.

10

If the project does not start now, investors have the right,

but not the obligation, to start the project in one year. That

is, the right to start the project in one year is a European call

option with a strike price of $12,000,000.

If the project starts in one year, investors forego the free

cash flow from the first year. In terms of a financial option,

the free cash flow is equivalent to a dividend paid by a stock.

The holder of a call option does not receive any dividends

until after the option is exercised.

Page 11: Lecture 07 - Real Options

11

Contd. The current value of the project without the “dividend” that

will be missed is:

(This is the stock price)

• The present value of the cost to begin the project in one year is:

(This is the exercise price)

$1,500,000( ) $18,750,000 $17,398,649

1.11

xS S PV Div

462,538,11$04.1

000,000,12XPV

Page 12: Lecture 07 - Real Options

12

Contd. Inputs for Black-Scholes model:

Financial Option Real Option Value

S Stock Price Market value of

asset

$17,398,649

X Exercise Price Upfront investment $11,538,462

σ Stock return

volatility

Asset value

volatility

30%

r Risk free rate Risk free rate 4%

T Time to maturity Time to maturity 1

Div Dividend Free cash flow lost

from delay

$1,500,000

Page 13: Lecture 07 - Real Options

Contd.

13

Given that,

2

)(ln

1

T

T

XPVS

d

Tdd

12

𝑐 = 𝑆 ×𝑁 𝑑1 − 𝑃𝑉 𝑋 × 𝑁 𝑑2

Page 14: Lecture 07 - Real Options

Contd.

5190.12

130.0

130.0

)642,538,11/649,398,17(1

Lnd

2190.1130.05190.12 d

9356.0)5190.1( N

8886.0)2190.1( N

938,024,6$

)8886.0642,538,11()9356.0649,398,17(

C

C

14

Page 15: Lecture 07 - Real Options

Contd.

15

Value of waiting one year to start the project is $ 6,024,938.

NPV of starting the project now is $6,750,000.

Thus, it is optimal to begin the project today rather than

wait.

Page 16: Lecture 07 - Real Options

Factors affecting the decision to wait

16

Volatility

The option to wait is most valuable when there is a great deal of

uncertainty.

Dividends

Absent dividends, it is not optimal to exercise a call option early. In

the real option context, it is always better to wait unless there is a

cost to doing so. The greater the cost, the less attractive the option

to delay becomes.

Page 17: Lecture 07 - Real Options

Growth options

17

A real option to invest in the future

Because these options have value, they contribute to the

value of any firm that has future possible investment

opportunities.

Future growth opportunities can be thought of as a

collection of real call options on potential projects.

This can explain why young firms tend to have higher

returns than older, established firms.

Page 18: Lecture 07 - Real Options

Growth options: Example

18

Sunwaves P/L has the option of investing in the development of a

new rooftop solar cell. Sunwaves management are confident that

a new improved solar cell can be produced; however they are

unclear as to how efficient the new solar cell will be. They

believe that with 35% probability a new highly efficient cell will

be developed. They expect to sell 100,000 of these solar cells

with a net cash flow of $250 per cell in perpetuity. If a less

efficient cell is produced (with 65% probability), they expect to

sell 60,000 solar cells with a net cash flow of $150 over the next

seven years. The start up cost of this venture is $50,000,000.

What is the value of the option to invest in this new project?

Assume aWACC of 20%.

Page 19: Lecture 07 - Real Options

Contd.

19

The NPV of the project if a very efficient solar cell is

produced is as follows.

Annual net cash inflow = 100,000×$250

= $25,000,000

PV of cash inflows =

NPV = -$50,000,000 + $125,000,000 = $75,000,000

000,000,125$20.0

000,000,25$

Page 20: Lecture 07 - Real Options

Contd.

20

The NPV of the project if a less efficient solar cell is

produced is as follows.

Annual net cash inflow = 60,000×$150 = $9,000,000

PV of cash inflows =

NPV = -$50,000,000 + $32,441,326 =-$17,558,674

326,441,32$1

120.0

000,000,9$

2.17

Page 21: Lecture 07 - Real Options

Contd.

21

Weighted NPV of the project (weighted by the

probability of obtaining each outcome) is given by:

=0.35×$75,000,000 + 0.65×-$17,558,674

= $14,836,862

Thus the value of the option to proceed with this project

is $14,836,862.

Note: This is in effect the method of decision tree

analysis used to value a real option.

Page 22: Lecture 07 - Real Options

Abandonment option/option to shutdown

22

An abandonment options is a real option for an investor to

cease making investments in a project.

Abandonment options can add value to a project because a

firm can drop a project if it turns out to be unsuccessful.

Page 23: Lecture 07 - Real Options

Option to shutdown: Example

23

Assume you are the CFO of a chain of gourmet food stores

and you are considering opening a new store in the recently

renovated Ferry Building in New York.

If you do not sign the lease on the store today, someone else

will, so you will not have the opportunity to open a store

later.

There is a clause in the lease that allows you to break the

lease at no cost in two years.

Including the lease payments, the new store will cost

$10,000 per month to operate.

Page 24: Lecture 07 - Real Options

24

Because the building has just reopened, you do not know what the pedestrian traffic will be.

If your customers are mainly limited to morning and evening commuters, you expect to generate $8,000 per month in revenue in perpetuity.

If, however, the building becomes a tourist attraction, you expect to generate $16,000 per month in revenue in perpetuity.

There is a 50% probability that the Ferry Building will become a tourist attraction.

The costs to set up the store will be $400,000.

The risk-free interest rate is constant at 7% per year (or 0.565% per month).

Page 25: Lecture 07 - Real Options

Contd.

25

Note: The number of tourists visiting the New York Ferry

Building represents idiosyncratic uncertainty. Since this is

the kind of uncertainty investors in your company can

costlessly diversify away, the appropriate cost of capital is the

risk-free rate.

Page 26: Lecture 07 - Real Options

Contd.

26

If you were forced to operate the store under

all circumstances, the expected monthly revenue will

be:

($8,000 × 0.5) + ($16,000 × 0.5) = $12,000

The NPV of the investment is:

Given the negative NPV, it would not make sense to open

the store.

12,000 10,000 400,000 $46,018

0.00565 0.00565NPV

Page 27: Lecture 07 - Real Options

Contd.

27

Now consider the option to abandon the project.

In reality, you would not have to keep operating the store.

You have an option to get out of the lease after two years at

no cost.

After the store is open, it will be immediately obvious

whether the Ferry Building is a tourist attraction.

The decision tree is as follows:

Page 28: Lecture 07 - Real Options

Contd.

28

Page 29: Lecture 07 - Real Options

Contd.

29

If the Ferry Building is a tourist attraction, the NPV of the investment opportunity is:

If the Ferry Building does not become a tourist attraction, you will close the store after two years and the NPV of the investment opportunity is:

16,000 10,000 400,000 $661,947

0.00565 0.00565NPV

24 24

8000 1 10,000 1 1 1 400,000

0.00565 1.00565 0.00565 1.00565

$444,770

NPV

Page 30: Lecture 07 - Real Options

Contd.

30

There is an equal probability of each state so the NPV of opening the store is:

By exercising the option to abandon the venture, you limit your losses and the NPV of undertaking the investment becomes positive. The value of the option to abandon is $154,607, the difference between the NPV with and without the option:

NPV = $108,589 – (–46,018) = $154,607

589,108$5.0770,4445.0947,661

Page 31: Lecture 07 - Real Options

Option to expand

31

Firms may undertake projects in order to take on other

projects in the future

In such cases, the initial project is an option that allows the

firm to take other projects and the firm should be willing to

pay a price for such options

A firm may accept a negative NPV on the initial project

because of the possibility of high NPVs on future projects

Page 32: Lecture 07 - Real Options

Option to Expand: Example

32

Consider an investment opportunity with an option to grow that requires a $10 million investment today.

In one year you will find out whether the project is successful.

The risk neutral probability that the project will generate $1 million per year in perpetuity is 50%, otherwise, the project will generate nothing.

At any time we can double the size of the project on the original terms.

Assume a risk free rate of 6%

Page 33: Lecture 07 - Real Options

Contd.

33

Page 34: Lecture 07 - Real Options

Contd.

34

By investing today, the expected annual cash flows are

(ignoring the option to double the size of the project):

$1 million × 0.5 = $500,000

Computing the NPV gives:

without growth option

500,000 10,000,000 $1.667 million

0.06NPV

Page 35: Lecture 07 - Real Options

Contd.

35

• The negative NPV suggests that you should not take on the project

today.

• However, this means you will never find out whether the project is

successful.

Now consider undertaking the project and exercising the

growth option to double the size in a year if the product

takes off.

• The NPV of doubling the size of the project in a year in this state is:

doubling after a year

1,000,000 10,000,000 $6.667 million

0.06NPV

Page 36: Lecture 07 - Real Options

Contd.

36

The risk-neutral probability that this state will occur is 50%,

so the expected value of this growth option is $3.333

million.

6.667 × 0.5 = $3.333

The present value of this amount today is:

millionPV optiongrowth 145.3$06.1

333.3

Page 37: Lecture 07 - Real Options

Contd.

37

You have this option only if you choose to

invest today, so the NPV of undertaking this investment is

the NPV calculated above plus the value of the growth

option we obtain by undertaking the project:

optiongrowthoptiongrowthwithout PVNPVNPV

millionNPV 478.1$145.3667.1

Page 38: Lecture 07 - Real Options

Contd.

38

This analysis shows that the NPV of the investment

opportunity is positive and the firm should undertake it.

It is optimal to undertake the investment today only because

of the existence of the future expansion option.

Page 39: Lecture 07 - Real Options

Past Exam Question (2010 S1) Omega Electricals is an Australian company which produces and sells electrical

appliances. The company intends to enter into the New Zealand market. It plans to

set-up a small store in New Zealand initially, but by doing so will acquire the option

to expand its business in New Zealand market. The small store has an initial cost of

NZ$70 million. It will generate an after-tax cash flow of NZ$4 million in the first

year of its operation which will grow at an annual rate of 3% indefinitely. The

company‟s cost of capital is 10%.

Omega Electricals has an option to build a much larger store in five years. The

initial cost of this expansion will be NZ$300 million. A simulation analysis of the

cash flows of this expansion revealed that the present value of expected cash flows is

NZ$250 million while the variance of these cash flows is 8% p.a. The five-year risk

free rate is 6% p.a.

(i) Evaluate this investment project using the traditional NPV method.

(ii) Calculate the value of the expansion option.

(iii) Explain whether Omega Electricals should invest in this project.

39

Page 40: Lecture 07 - Real Options

Solution

Part (i) - NPV using traditional method

Initial Investment = NZ$70 million

Cash Flow in year 1 = NZ$4 million

Annual growth rate = 3%

Cost of capital = 10%

Therefore,

NPV = -NZ$12.86 million

40

86.127003.010.0

4

NPV

Page 41: Lecture 07 - Real Options

Contd.

Part (ii) –Value of the option

Inputs for the Black-Scholes model:

S = PV of expansion cash flows = NZ$250 million

PV(X) = PV of the Cost of expansion

= 300/(1.06)5=NZ$224.18 million

T = time to expiration of the option = 5 years

Standard deviation of expansion cash flows =

41

2828.008.0

Page 42: Lecture 07 - Real Options

42

4886.02

6324.0

6324.0

1090.0

2

52828.0

52828.0

)18.224/250(

1

1

d

Lnd

1438.0

)6324.04886.0

2

12

d

Tdd

4428.0)(

6874.0)(

2

1

dN

dN

Page 43: Lecture 07 - Real Options

Part (iii) - Omega Electrical should invest in this project

because the NPV of the project with the expansion option is

positive.

The NPV with the expansion option = -12.86 + 72.58 =

NZ$59.72

43

58.72

)4428.018.224()6874.0250(

)(*)()(* 21

C

C

dNXPVdNSC


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