Transcript Real Options Valuation - IAG PUC-Rio

Real Options
Estimating Volatility
Prof. Luiz Brandão
[email protected]
Estimating Volatility
Example: InterSom Lda.

InterSom plans to launch a new line of products that will have an
expected life of four years.

Expected cash flows in spreadsheet.

WACC is 10% and risk free rate is 5%.

The project has an option to expand in year 2 and can be abandoned
for a fixed amount in years 2 and 3.

Sales are expected to grow 8% annually.

What is the value of the project considering the options?
IAG PUC – Rio
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Step 1: DCF Model
0
Receitas
Custos Variáveis
Custos Fixos
Depreciação
1.000
LAIR
Impostos
Depreciação
Investimento
(1.200)
Fluxo de Caixa Livre
(1.200)
V0 =
Investimento =
VPL0 =
1.178
(1.200)
(22)
IAG PUC – Rio
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50%
1
2
3
4
1.080
(432)
(280)
(300)
1.166
(467)
(280)
(300)
1.260
(504)
(280)
(300)
1.360
(544)
(280)
(300)
68
(34)
300
120
(60)
300
176
(88)
300
236
(118)
300
334
360
388
418
WACC = 10%
4
Step 2: Model Uncertainties

In this case the only uncertainty is the future level of sales.

We assume that sales revenues

The growth rate is 8.0%

We also assume that the volatility of revenues is σR = 30%.
The model will then be:
Rt 1  Rt e
Rt 1  Rt e
R follow a GBM.


0.302 
RISKNORMAL  0.08
1, 0.30 1 



2 


RISKNORMAL 0.032, 0.30 
.xls
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Step 3: Simulation

We model the returns v as:

v  ln V1 V0

where
 n
 ( i 1) 
V1  C1  E  Ci 1   

 i 2


Run a simulation on the project returns

The project volatility is the standard deviation of the returns.
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Step 4: Model the Project and
Options


PV = 1178

WACC = 10%

Volatility = ?
Assume the project has an option to expand 30% in year 2 at a
cost of $100, and can be abandoned for $350
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DPL Model

Underlying Asset Model is:
D1
D3
u
d
Vol
D2
D4
p
PV
t
r
WACC
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T1
T2
T3
T4
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DPL Model with Options
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Brandão
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Adding more sources of
Uncertainty
DiaGenesis Ltd.

One of the advantages of the Monte Carlo simulation is that one can
use more than one source of uncertainty.

These uncertainties can be of any nature, independent or
correlated.

We will illustrate this through a practical model.

Consider the firm DiaGenesis that has the oportunity to invest
$20.000 in a five year project.

The WACC is 15% a.a. and the risk free rate is 5%.

The DCF analysis indicates that the Expected Present Value of the
project is 20.056.

The project has an optionn to expand in year 2 and can be
abandoned in years 2 and 3.
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Setp 1 – Base Case
0
Sales
Costs
Oper Expenses
Depreciation
EBIT
Tax
Free Cash Flow
V0 =
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3
4
5
8.000
8.841
9.771
10.799
11.935
13.190
(2.000)
(2.167)
(800)
(4.000)
(2.347)
(800)
(4.000)
(2.542)
(800)
(4.000)
(2.754)
(800)
(4.000)
(2.984)
(800)
(4.000)
1.875
(750)
2.624
(1.050)
3.456
(1.383)
4.380
(1.752)
5.406
(2.162)
1.125
1.575
2.074
2.628
3.244
4.000
4.000
4.000
4.000
4.000
5.125
5.575
6.074
6.628
7.244
40%
Net Income
Depreciation
CAPEX
1
(20.000)
(20.000)
20.056
WACC =
15%
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Two Sources of Uncertainty

Assume this project has two independent sources of
uncertainty

Sales (S)




Stochastic Process: Geometric Brownian Motion
Growth (Drift) rate = 10% a.a.
Volatility = 40%.
Costs (C)



Stochastic Process: Geometric Brownian Motion
Growth (Drift) rate = 10% a.a.
Volatility =20%.
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Sales Uncertainty

The MGB process for Sales is:
dS  S Sdt   S Sdz

The Simulation Model is:
St 1  St e


 S2 

RISKNORMAL  S   t ,  S t 


2 


where:
St = Sales in the previous year
 μS = average growth rate


σS = Volatility
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Cost Uncertainty

The MGB process for the Costs is:
dC  C Cdt   C Cdz

The Simulation Model is:
Ct 1  Ct e


 C2
RISKNORMAL  C 

2



 t ,  C t 



Where:
Ct = Costs in the previous year
μS = average growth rate
σC = Volatility
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Step 2 – Simulation Parameters

Sales:
St 1  St e



0.402
RISKNORMAL  0.10 
, 0.40 


2


Costs:
Ct 1  Ct e
IAG PUC – Rio
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

0.202
RISKNORMAL 0.08
, 0.20 


2


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Steps 3 and 4 – Simulation and
Modeling

The BDH simulation provides a volatility of 43.89%

For the binomial model in DPL, we must determine the
dividend rate for each of the five years of the project.

The remaining parameters are:





V0 = 20.056
r = 5%
Volatility = 43,89%
Dividend rate for each year.
Once the underlying project is modeled, we proceed to add
the project options
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Model of the Underlying Project
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Adding the Options

The project can be expanded by 30% at the end of year 2 at a
cost of $5.000.

The project can be abandoned at the end of years 2 and 3, by
receiveing a residual value of $8,000.

With these options, the value of the project increases from
$20.056 to $22.663,42.
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Model with Options
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