Real Options Analysis
In an Opportunity Constrained
Portfolio
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What is Real Options Analysis?
• Financial Options
– Call option, American and European
– Right without obligation
• Projects = Real Options
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Why Real Options Analysis?
•
•
•
•
•
Active Management Assumption
– Conventional DCF assumes a passive investment strategy
Risk-Neutral Pricing
– Requires risk to be accounted for at source
– Conventional DCF accounts for risk in the net cash flows
Value of Flexibility
– Management has the obligation to respond to uncertainty
– Front End Loading assumes active management and requires
management to respond to uncertainty
– Higher uncertainty = higher value (assuming flexibility to respond)
Computes Project Potential
– Real Options Value is the mean of the positive outcomes from projected
values
– The values in excess of the mean describe project potential - not available
from conventional DCF
– Value at Risk can be quanitifed, therefore project risk can be compared to
risk appetite
Monte Carlo Simulation Well Suited
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Black-Scholes formula
𝑆𝑜 𝑁 𝑑1 − 𝑋𝑒 −𝑟𝑇 𝑁 𝑑2
Where:
𝑆𝑜 is the asset price given by 𝑒 (−𝑅𝑟𝑡) 𝜇
•
𝑒 is the base of the natural logarithm (the constant 2.71828182845904)
•
𝑅𝑟 is the discount rate (or the required rate of return);
•
𝑡 is the time to maturity, and;
•
𝜇 is the mean of the logarithmic rate of return of 𝑆𝑜
𝑋 is the exercise (or strike) price;
𝑟𝑇 is the risk free rate;
𝑁 . is a univariate normal distribution function, and;
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Black-Scholes formula
𝑆𝑜
𝜎2
ln 𝑥 + 𝑟𝑓 + 2 𝑡
𝑑1 =
𝜎 𝑡
𝑑2 = 𝑑1 − 𝜎 𝑡
Where:
•
𝑟𝑓 is the risk free rate;
•
𝜎 is the volatility of the logarithmic rate of return of 𝑆𝑜 , and;
•
𝑡 is the time to maturity of the option
•
𝑥 is the investment
Which can be simplified as:
𝑂𝑝𝑡𝑖𝑜𝑛 𝑉𝑎𝑙𝑢𝑒 = 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦1 ∗ 𝐴𝑠𝑠𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 − 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦2 ∗ 𝑆𝑡𝑟𝑖𝑘𝑒 𝑃𝑟𝑖𝑐𝑒
𝑂𝑣 = 𝑃1 𝐴𝑣 − 𝑃2 𝑆𝑝
In Real Options (projects) we know the option value (option price), can
forecast the asset value (NPV), therefore we need to solve for the strike
price:
𝑃 𝑆𝑝 = 𝑃 𝐴𝑣 − 𝑂𝑣
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Opportunity Constraints
• Territories/ regions
– Whole world, some parts of the world or a single region/territory?
• Mineral Resources
– Multiple commodities or a single mineral
– Finite and becoming more expensive to exploit
• Enterprise resources
– Capital
– Human
– Logistical
• Political and social
– Regulatory framework
– Communities
– Environment
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ROA and Monte Carlo
•
NPV
– Single discount rate
•
•
•
WACC
Risk premiums
Project hurdle rate
– Single cash flow schedule
•
•
•
•
Study and implementation costs
Operational costs
Interest, Depreciation, Tax
ROA
– Separate cash flows
•
•
•
Study costs
Implementation costs
Operational cash flows
– Risk free discount rate
•
Risk priced at source
– Variability modelling
•
Ranges applied to all parameters with variability
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Alpha Uncertainty Parameters
Operational performance parameters
ROM (plant) feed (tons/annum)
Beneficiation yield
Capacity (tons/annum - resultant)
Lump:fines ratio
Lump premium (over fines)
Budget, estimate and cost parameters ('000 000)
Implementation capital
Operating costs (per annum, resultant)
Variable costs - beneficiation
Variable costs - I&S
Fixed costs - Other Overheads
Freight & logistics (per annum, resultant)
Fixed costs - F&L
Variable costs - F&L
Expected
Values
Range
5%
1.89
33.3%
0.63
50%
2.1
35.0%
0.74
95%
2.21
35.9%
0.79
(-)
10.0%
5.0%
14.5%
(+)
5.0%
2.5%
7.6%
17.0%
20.0%
22.0%
15.0%
10.0%
581.3
27.9
30.4
2.0
4.9
70.1
468
20.9
25.2
1.6
4.1
53
551
26.4
28.0
1.8
4.5
65
743
37.9
37.8
2.4
6.1
94
15.0%
20.8%
10.0%
10.0%
10.0%
18.2%
35.0%
43.5%
35.0%
35.0%
35.0%
44.6%
4.9
91.8
4.1
78.3
4.5
82.4
6.1
111.2
10.0%
5.0%
35.0%
35.0%
23
5
2
5
2
2.6
26
5
2
6
2
2.9
30
6
3
8
3
3.4
10.0%
10.0%
20.0%
20.0%
20.0%
11.1%
15.0%
15.0%
25.0%
30.0%
30.0%
16.4%
2.08
0.35
0.72
0.00
19.9%
Project schedule parameters (durations)
Detailed design & construction duration
26
Commissioning duration
5
Handover duration
2
Ramp-up duration
6
Final acceptance testing
2
Project duration (yrs - resultant)
2.9
Deterministic schedule confidence
47.25%
Target schedule confidence
70%
Project duration target (years)
3.01
Target completion 20160404
P80 schedule duration (years)
3.07
P80 completion 20160425
P80 Duraton (months)
1.8
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Schedule Outcomes
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ROA and NPV Financial Models
Project Sigma
Price, volume & time factors
Project Phase Schedule
Ramp-up volume
Production volume
Commodity price, Lump - NPV
Commodity price, Fines - NPV
Commodity price, Lump - ROA
Commodity price, Fines - ROA
Local:USD exchange rate
2013
2014
2015
2016
2017
2018
2019
2020
1
2
3
4
4
6
7
7
0.0
…
2031
-1
0.1
0.5
0.7
0.7
0.7
0.7
0.1
156.0
155.4
139.6
119.0
109.4
103.5
101.7
89.9
97.6
129.9
8.7
129.4
8.7
116.3
8.7
99.1
8.7
91.1
8.7
86.1
8.7
84.6
8.7
74.9
8.7
81.3
8.7
Project costs
Project costs - operational
Project costs - capital
-169
-169
-225
-225
-188
-188
Mining & operational costs
Fixed costs
Variable costs
-
-
-169
-225
-
-
NPV Cash flows
Gross revenue - NPV
Net revenue (EBITDA) - NPV
Depreciation - NPV
Tax - NPV
Net Cash Flow - NPV
ROA Cash flows
Gross revenue
Net revenue (EBITDA)
Depreciation
Tax
Net Cash Flow - ROA
-3
-2
-1
-85
-10
-75
-100
-10
-90
-100
-10
-90
-100
-10
-90
-100
-10
-90
-25
-10
-15
10
8
-180
623
538
538
538
686
586
43
-168
418
649
549
-170
379
638
538
-166
372
564
465
-144
321
118
93
-29
65
9
6
519
434
434
434
571
472
147
-100
371
540
441
-136
304
531
431
-133
298
470
370
-114
256
98
74
-23
51
6
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ROA and NPV Financial Models
NPV Cash flows
Gross revenue - NPV
Net revenue (EBITDA) - NPV
Sum
of discounted
Depreciation
- NPV
(hurdle rate) net cash
Tax - NPV
Net Cash Flowflows
- NPV- @Risk
ROA Cash flows
Gross revenue
Net revenue (EBITDA)
Depreciation
Tax
Net Cash Flow - ROA
12 months
plus any
other
commitments
Dynamic NPV
PV Operating Profit
Option Price
PV Study Costs
PV Capital Costs
PV Project Costs
Net Profit Outcomes
Real Options Value
Project Opportunity Value
P5 Value at Risk
P5 Potential Gain
-169
-225
-
-
-169
622
1 234
-169
-363
-363
871
1 322
1 153
1 073
1 592
-185
-203
10
8
-180
623
538
538
538
686
586
43
-168
418
649
549
-170
379
638
538
-166
372
564
465
-144
321
118
93
-29
65
9
6
6
519
434
434
434
571
472
147
-100
371
540
441
-136
304
531
431
-133
298
470
370
-114
256
98
74
-23
51
-132
352
244
198
173
133
8
5
349
281
218
201
163
17
-
-160
Max(0 or (PV Ops
Profit + PV Project
Cost) - @Risk
Sum of study &
implementation costs
discounted at Risk
Free Rate
Mean (Net Profit
Outcomes)
Sum operational cash flows
discounted at Risk Free Rate @Risk
Real Options Value –
Option Price
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Comparison of Results
Projects
Sigma
Delta
Beta
Zeta
Omega
Theta
Epsilon
Alpha
NPV
3 733
10 130
-1 085
3 187
5 603
-201
1 485
1 459
Opp
Value Difference Percent
8 364
4 631
124%
16 394
6 264
62%
229
1 314
121%
5 026
1 840
58%
9 209
3 606
64%
1 190
1 391
691%
2 290
804
54%
2 082
623
43%
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Risk Neutral Pricing
ROA Price Discount – 15%
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Risk Neutral Pricing
•
•
Problem Statement - Risk
• The geological information has not been acquired to the level
required for an investment commitment, however mining rights
need to be exercised in order to retain them (i.e. investment
commitment is required)
Options
• Take the risk
• Forego the opportunity
• (Can’t apply for an extension)
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NPV
– Compute the NPV of the project by adding a risk premium
to the discount rate
– Positive NPV means the opportunity should be pursued,
i.e. the risk assumed
– How do we determine the risk premium?
• Assume the geologists tell us their confidence in the ROM volume
decreases by 33%
• Add 33% to the project hurdle rate
• 12% becomes 16%
– How do we know the risk premium is right?
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ROA
• Determine where the impact will be realised
– Assume in the ROM volume
• Get new ROM ranges from geologists and mining engineers
– 3 point range estimate applied to P5, P50 and P95 with distribution
function given by geologists
• Re-run Monte Carlo simulation
– Compare new option values to the base case
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Portfolio Composition and Prioritisation
• Risk Appetite and Attitude
– Appetite is the risk capability of the organisation
– Attitude is how the organisation feels about risk
• Risk Threshold
– Threshold is the negative of appetite
– Appetite is typically 1/5th of Equity (Utility Theory)
– Risk threshold can be compared to Project and Portfolio
Value at Risk
• Threshold distance
– Threshold distance is the difference between VaR and the
Risk Threshold
– Risk Ratings follow risk threshold distances, higher
distances mean lower risk (vice versa)
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Risk Rating – Threshold Distance
Threshold
-7 200
Projects
VaR
Portfolio 26 911
Delta 11 076
Sigma 5 766
Omega 5 382
Zeta 2 816
Epsilon 1 886
Alpha 1 772
Theta -2 546
Beta -6 274
Distance
From
To
Rating
-∞
Intolerable
4 000 very high
4 000
8 000
high
8 000 12 000 medium
12 000 16 000
low
16 000
∞
very low
Threshold
Distance
34 111 very low
18 276 very low
12 966
low
12 582
low
10 016 medium
9 086 medium
8 972 medium
4 654
high
926 very high
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Portfolio Risk Profile
Threshold
Rating
Beta
Distance from Threshold
8
12
4
Very High
0.93 -6.27
Theta
High
1.89
9.09
Zeta
2.82
10.02
Omega
5.38
12.58
Sigma
5.77
12.97
Delta
11.08
18.28
34.11
Portfolio
-7.2
Very Low
1.77
8.97
Epsilon
Low
-2.55
4.65
Alpha
Medium
16
-5
0
5
26.91
10
30
Value at Risk
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Portfolio Composition
Projects
Delta
Sigma
Zeta
Omega
Epsilon
Alpha
NPV
Portfolio
10 130
3 733
3 187
3 009
1 485
1 459
Risk
?
?
?
?
?
?
Projects
Delta
Sigma
Omega
Zeta
Epsilon
Alpha
Theta
Beta
ROA
Portfolio
Risk
16 394 very low
8 364
low
9 209
low
5 026 medium
2 290 medium
2 082 medium
1 190
high
229 very high
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ROA and Dynamic NPV
• Some benefits of ROA gained by extending NPV
with Monte Carlo simulation
– Dynamic NPV
• Some issues with Dynamic NPV
– Still applies a single discount rate
– Risk could be double counted (risk premium in discount
rate and in financial parameters)
– NPV understates the present value of costs, Dynamic NPV
does the same
• Level of effort to implement ROA and Dynamic NPV
is similar
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Integration with project risk management
•
•
Framework described is for portfolio management purposes
Project risk management goes into more detail with respect to
discrete and specific project risks and factors.
– Project uncertainty modeled using QRAs should be incorporated into the
ROA parameters on an aggregate level
– Global and portfolio parameters (Global Assumptions) should inform
project risk models
•
•
•
•
•
High level ROA should be conducted IN projects during opportunity
development and concept studies
Detailed ROA should be conducted IN projects during FEL2
Outcomes from ROA in projects should inform portfolio ROA model
Final investment sanction (end of FEL3) should update the ROA
model
ROA model should be re-run whenever new information that informs
uncertainty becomes available
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Implementation implications
• Change management
– New paradigm
– NPV is the 'gold standard'
– Arguments on uncertainty
• Perceived subjectivity
– Communication
• Concept and methodology need to be explained, many (even most)
either don’t get it or don’t accept it
– Expertise
• Financial modelling
• Risk management
– Risk identification
– Risk description
– Risk modelling
• Portfolio management
• Strategic planning
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Questions?
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