Real Options
The Right to do Something Real
Introduction
• The classical DCF valuation method involves a
comparison between the cost of an investment
project and the present value of the cash flows
the project will generate.
• The application of the formula is made possible
by two more or less tacit assumptions or
conventions:
– Uncertain future cash flows can be replaced by their
expected values.
– The discount rate is known and depends solely upon
the risk of the project.
DCF Limitations
• The classical approach presupposes a
static approach to investment decisionmaking.
• The investment decision does not take into
account the possibility of new information
arriving during the life of a project.
– No need to throw good money after bad.
– Can invest more after good news.
Good
News
Cash Flow
Good
News
Bad
News
Cash Flow
Investment
Decision
Cash Flow
Good
News
Bad
News
Bad
News
Cash Flow
Discounting with Information Flows
• The only way of accounting for interim
information is by using scenarios.
– But then what is the probability of each scenario
occurring?
• Even more fundamentally, the degree of
managerial discretion in making future operating
decisions will tend to affect the risk of the project
under consideration.
– A project that can be abandoned under adverse
circumstances will be less risky than one that cannot.
• The WACC does not allow for this.
Example: Trigeorgis
• Trigeorgis wishes to value an opportunity
to invest in research and development for
a new drug. One year later:
– If the research goes well sales will generate
cash flows of $180.
– If the research goes poorly, sales will equal
$60.
– Each scenario is equally likely.
Trigeorgis Continued
• The government, wishing to support this project,
offers a guarantee (or insurance policy) to buy
the entire output for $180 million if the research
goes poorly.
• Without the guarantee the project’s cash flows
have a risk-adjusted discount rate of r=20%.
• The risk-free rate is rf=8%.
• What is the PV of this project (V) and of the
abandonment put option provided by the
guarantee (P)?
Trigeorgis: Traditional DCF Solution
• Using traditional DCF techniques, the PV
of the project without the guarantee is:
pChigh +(1-p)Clow 0.5×180+0.5×60
PV =
=
= 100.
1+r
1+0.20
• PV without the guarantee:
0.5×180+0.5×  60+120 
PV =
= 150.
1+0.20
• Implies the guarantee’s put option is worth
150-100 = 50.
DCF Calculation: An Error
• The traditional DCF calculation is clearly
wrong, as the flexibility to abandon the
project for a guaranteed price should alter
the project’s risk and its discount rate.
• The government’s guarantee makes the
project riskless.
Valuing Trigeorgis with the Option
• Since the cash flows are riskless with the
guarantee:
0.5×180+0.5×  60+120 
PV =
= 166.
1+0.08
*
• The put option is thus worth 166-100=66.
Guarantee Option: Risk Neutral
Probabilities
• If we price the put option using risk-neutral
probabilities we obtain the same result.
• Since the PV of the project is 100 using
the risk-adjusted discount rate, then:
180
60
u=
= 1.8, and d =
= 0.6.
100
100
Option Value Continued
• Now use the formula:
1+rf -d 1+0.08-0.6
q=
=
= 0.4.
u-d
1.8-0.6
• The put’s value is thus:
0.4×0+0.6×120
P=
= 66.7.
1+0.08
Comments about Trigeorgis
• This is a very stylized example, since with the
abandonment option, the risk of the project
completely disappear.
• In most cases, a firm has different options
available that reduce the risk of the investments
it makes.
• Measuring that risk, that is, adjusting the
discount rate accordingly, is an almost
impossible task.
• That is why we use real options.
Real Options in Real Life
• Option to build.
– Firm owns a lot on which it can build an office complex.
• Option to abandon.
– Firm can abandon a project that is going poorly.
• Scale option.
– Firm can increase or reduce the size of a project.
• Option to switch.
– Firm can alter a plant’s product mix.
• Growth options.
– Need to complete on stage of a project successfully before
proceeding to the next.
Incorporating Real Options Into the Capital
Budgeting Process: An Example
• Monsters Inc. proposes a phased
expansion of its facilities. They plan to
build a new, state-of-the-art screaming
factory.
• Three years from now, though, they
anticipate further investments to face new
research challenges.
• The volatility of the project’s cash flow is
40%. The riskless interest rate is 8%.
MONSTERS Inc. -- INITIAL CALCULATIONS FOR A
PROPOSED EXPANSION
Year
0
1
2
3
4
5
6
455
551
800
1080
1195
1255
Operating Projections
Revenues
-COGS
322.3 393.9
575 764.8 845.8 891.3
Gross Profit
132.7 157.1
225 315.2 349.2 363.7
-SG&A Expense
110.4
130
-Depreciation
19
21
21
46.3
48.1
50
Operating Profit
3.3
6.1
-15.2
17.3
20.8
26.3
EBIT (1-tax rate)
2.2
4
-10
11.4
13.7
17.4
+Depreciation
19
21
21
46.3
48.1
50
100
8.1
9.5
307
16
16.3
17
25
4.1
5.5
75
7.1
8
9.7
-125
9
10
-371
34.6
37.5
40.7
219.2 251.6 280.3 287.4
Cash Flow Calculation
-CAPEX
-Increase in WCR
=FCF
+Terminal Value (perpetuity value
at 5% per year)
609.9
MONSTERS Inc. -- INITIAL CALCULATIONS FOR A
PROPOSED EXPANSION
=FCF
-125
9
10
-371
34.6
37.5
+Terminal Value (perpetuity
value at 5% per year)
PV discount factor
(12%)
40.7
610.5
1
0.89
0.80
0.71
=PV (by year)
-125
8.04
7.97
-264.07
NPV
0.12
0.64
0.57
0.51
21.99 21.28
329.61
Monster Analysis
• Based on DCF calculations, the project’s NPV is
slightly positive.
• The project incorporates an option not to invest
in the third year if the NPV of the additional
investment becomes negative.
– Since cash flows are volatile, three years from now
the company will have more accurate information
regarding the project’s profitability.
• The next exhibit separates the initial investment
cash flows from those in year 3.
MONSTERS Inc. -- PROJECTIONS
REARRANGED Year
0
1
2
3
4
5
6
0
9
10
11
11.6
12.1
12.7
Phase 1
Cash Flow
+Terminal Value
-Investment
x discount factor (12%)
=PV (by year)
NPV
190.5
-125
1 0.893 0.797
-125
8.0
8.0
0.712 0.636 0.567
0.507
7.8
7.4
6.9
102.9
0
23.1
25.4
28
16.02
Phase 2
Cash Flow
+Terminal Value
420
-Investment
-382
x discount factor (12%)
0.712 0.636 0.567
=PV (by year)
NPV
-271.9
-15.84
14.7
14.4
0.507
227.0
MONSTERS Inc. -- PROJECTIONS
Phase 1 + Phase 2
Cash Flow
0
9
10
11
34.6
37.5
+Terminal Value
-Investment
x discount factor
(12%)
=PV (by year)
NPV
40.7
610.5
-125
1
-125.0
0.12
-382
0.893 0.797
8.04
0.712 0.636
0.567
0.507
7.97 -264.07 21.99
21.28
329.92
Monster Inc.: Phase 2 Value
• Cash flows from Phase 2 are also
expected, and in PV terms (as of year 0)
are:
23.1 25.4 28.0 420
PV(Phase 2 Cash Flows) =



4
5
6
1.12 1.12 1.12 1.126
 256.1.
Monster Option
• Therefore, the company has the option to invest
in a project whose expected cashflow (as of year
0) is 256.1, and whose cost is 382 (in year 3).
• This looks like an option!
• Cash flows are volatile (volatility=40%), and the
company will exercise the option if in year 3, the
expected cash flows are larger than the cost of
the project. That is:
NPV(Expansion, Year 3) =
max [PV(Cash Flows,Year 3)-382,0]
Monster Option Value
• Option value in year 0 can be calculated using standard
option valuation techniques. The inputs are:
–
–
–
–
–
S=256.1
X=382
σ=40%
rf=8%
Time to Maturity: 3 years
• From the Black-Scholes formula: c = 55.12
– This is the Phase 2 NPV.
• The project’s NPV 55.12+16.3 = 71.82
– Why is it higher once we incorporate the option to expand?
Measuring the Future Asset Prices
and Volatility
• The asset price in real options analysis is
the present value of future cash flows
associated with the assets when using
passive present value analysis.
• Volatility is harder to estimate.
– The reason is that it is not constant during the
life of the option.
– Usually the firm’s stock volatility or a historical
standard deviation based on cash flow
estimates is employed.