1. Real Options Estimating Volatility Prof. Luiz Brandão brandao@iag.puc-rio.br

2. Estimating Volatility

3. IAG PUC – Rio Brandão 3 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?

4. IAG PUC – Rio Brandão 4 Step 1: DCF Model

5. IAG PUC – Rio Brandão 5 Step 2: Model Uncertainties  In this case the only uncertainty is the future level of sales.  We assume that sales revenues R follow a GBM.  The growth rate is 8.0%  We also assume that the volatility of revenues is σ R = 30%. The model will then be:.xls

6. IAG PUC – Rio Brandão 6 Step 3: Simulation  We model the returns v as: where  Run a simulation on the project returns  The project volatility is the standard deviation of the returns.

7. IAG PUC – Rio Brandão 7 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

8. IAG PUC – Rio Brandão 8 DPL Model  Underlying Asset Model is:

9. IAG PUC – Rio Brandão 9 DPL Model with Options

10. Adding more sources of Uncertainty

11. IAG PUC – Rio Brandão 11 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.

12. IAG PUC – Rio Brandão 12 Setp 1 – Base Case 012345 Sales8.0008.8419.77110.79911.93513.190 Costs(2.000)(2.167)(2.347)(2.542)(2.754)(2.984) Oper Expenses(800) Depreciation(4.000) EBIT 1.8752.6243.4564.3805.406 Tax40%(750)(1.050)(1.383)(1.752)(2.162) Net Income 1.1251.5752.0742.6283.244 Depreciation4.000 CAPEX(20.000) Free Cash Flow (20.000)5.1255.5756.0746.6287.244 V 0 = 20.056 WACC =15%

13. IAG PUC – Rio Brandão 13 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%.

14. IAG PUC – Rio Brandão 14 Sales Uncertainty  The MGB process for Sales is:  The Simulation Model is: where: S t = Sales in the previous year μ S = average growth rate σ S = Volatility

15. IAG PUC – Rio Brandão 15 Cost Uncertainty  The MGB process for the Costs is:  The Simulation Model is:  Where: C t = Costs in the previous year μ S = average growth rate σ C = Volatility

16. IAG PUC – Rio Brandão 16 Step 2 – Simulation Parameters  Sales:  Costs:

17. IAG PUC – Rio Brandão 17 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: V 0 = 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

18. IAG PUC – Rio Brandão 18 Model of the Underlying Project

19. IAG PUC – Rio Brandão 19 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.

20. IAG PUC – Rio Brandão 20 Model with Options