Real Options
1
AFC 3140 – Advanced Corporate
Finance
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.
Evolution of capital budgeting concepts
3
DCFSensitivity Analysis
Simulation
Decision Trees
Option Pricing
Real Option
Valuation
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.
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
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.
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?
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
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.
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.
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
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
$1,500,000
Contd.
13
Given that,
2
)(ln
1
T
T
XPVS
d
Tdd
12
𝑐 = 𝑆 ×𝑁 𝑑1 − 𝑃𝑉 𝑋 × 𝑁 𝑑2
Contd.
5190.12
130.0
130.0
)642,538,11/649,398,17(1
Lnd
2190.1130.05190.12 d
9356.0)5190.1( N
8886.0)2190.1( N
938,024,6$
)8886.0642,538,11()9356.0649,398,17(
C
C
14
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.
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.
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.
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%.
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$20.0
000,000,25$
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
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.
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.
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.
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).
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.
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
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:
Contd.
28
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
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
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
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%
Contd.
33
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
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
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
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
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.
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
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
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
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
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