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Trading real options analysis course - business cases and software applic - Mun P.D.

Mun P.D. Trading real options analysis course - business cases and software applic - Wiley publishing , 2003. - 318 p.
ISBN 047-43001-3
Download (direct link): tradingohnathan2003.pdf
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_JH|8
Exercise Solutions
Solutions for DCF Model
Discounted Cash Flow Analysis
Discount Rate 20%
Discrete Discounting
Year 2002 2003 2004 2005 2006 2007
Revenues $100 $200 $300 $400 $500
Operating Expenses $10 $20 $30 $40 $50
Net Income $90 $180 $270 $360 $450
Investment Costs ($450)
Free Cash Flow ($450) $90 $180 $270 $360 $450
Present Value of Cash Flow ($450) $75 1 $125 1 $156 1 $174 $181
Net Present Value $261
Continuous Discounting
Year 2002 2003 2004 2005 2006 2007
Revenues $100 $200 $300 $400 $500
Operating Expenses $10 $20 $30 $40 $50
Net Income $90 $180 $270 $360 $450
Investment Costs ($450)
Free Cash Flow ($450) $90 $180 $270 $360 $450
Present Value of Cash Flow ($450) $74 1 $121 CO $162 $166
Net Present Value
$220
213
214
EXERCISE SOLUTIONS
Solutions for Simulation I (Simulating a DCF Model)
Monte Carlo Simulation
|- Input Parameters------------
Discount Rate (Cash Flow) Discount Rate (Impl. Cost) Tax Rate
Revenue Cost of Revenue Gross Profit Operating Expenses Depreciation Expense Interest Expense Income Before Taxes Taxes
Income After Taxes Non-Cash Expenses Cash Flow
Implementation Cost
15.00%
7.00%
40.00%
$20.00
i- Results ------------------------
Present Value (Cash Flow) Present Value (Impl. Cost) Net Present Value
$40.00
$60.00
$80.00
$334.72
$234.94
$99.79
2002 2003 2004 2005 2006
$100.00 $200.00 $300.00 $400.00 $500.00
$25.00 $50.00 $75.00 $100.00 $125.00
$75.00 $150.00 $225.00 $300.00 $375.00
$10.00 $20.00 $30.00 $40.00 $50.00
$5.00 $10.00 $15.00 $20.00 $25.00
$5.00 $10.00 $15.00 $20.00 $25.00
$55.00 $110.00 $165.00 $220.00 $275.00
$22.00 $44.00 $66.00 $88.00 $110.00
$33.00 $66.00 $99.00 $132.00 $165.00
$10.00 $10.00 $10.00 $10.00 $10.00
$43.00 $76.00 $109.00 $142.00 $175.00
$100.00
Solutions for Simulation II (Simulating a Stock Price Path)
Simulated Stock Price Path
Stock returns annualized volatility Annualized mean growth of returns Starting stock price at time 0 Calculated periodic volatility
100.00% 8.00% $100.00 13.87%
Simulate Date Value
01-Jan-01 $100.00
-0.8962 08-Jan-01 $87.73
0.6556 15-Jan-01 $95.84
0.8031 22-Jan-01 $106.66
-0.3144 29-Jan-01 $102.17
0.7859 05-Feb-01 $113.46
-0.8904 12-Feb-01 $99.63
-1.1061 19-Feb-01 $84.50
-0.0203 26-Feb-01 $84.39
-0.4653 05-Mar-01 $79.08
-0.4988 12-Mar-01 $73.73
-0.2829 19-Mar-01 $70.95
2.2697 26-Mar-01 $93.39
-1.0476 02-Apr-01 $79.96
1.0232 09-Apr-01 $91.43
0.1844 16-Apr-01 $93.91
-0.8955 23-Apr-01 $82.29
0.3269 30-Apr-01 $86.26
-1.5852 7-May-01 $67.43
0.4027 14-May-01 $71.30
1.3701 21-May-01 $84.95
Exercise Solutions
215
Solutions for Volatility Estimates
Solutions for Creating and Solving Lattices
Creating and Solving Lattices
Assumptions Intermediate Calculations
Asset Value ($) $100.00 Stepping-Time (dt) 1.0000
Implementation Cost ($) $80.00 Up Step-Size (up) 1.2840
Maturity (Years) 5.00 Down Step-Size (down) 0.7788
Risk-free Rate (%) 5.00% Risk-neutral Probability (prob) 53.93%
Dividends (%) 0.00% óD i
Volatility (%) 25.00%
Lattice Steps 5 Lattice Results $42.09 I
Underlying Asset Lattice 349.03 |
271.83
211.70 211.70 |
164.87 164.87
128.40 128.40 128.40 |
100.00 100.00 100.00
77.88 77.88 77.88 |
60.65 60.65
47.24 47.24 |
36.79
28.65 |

Option Valuation Lattice 269.03 |
195.73
139.31 131.70 |
96.19 88.77
64.48 56.42 48.40 I
42.09 34.53 24.83
20.58 12.74 0.00 I
6.53 0.00
0.00 0.00 I
0.00
0.00 I
216
EXERCISE SOLUTIONS
Solutions for Granularity in Lattice
Granularity in Lattices
? Assumptions-----------------
Asset Value ($) Implementation Cost ($) Maturity (Years)
Risk-free Rate (%) Dividends (%)
Volatility (%)
Small Lattice Steps Large Lattice Steps
$100.00
$90.00
5.00
5.00%
0.00%
20.00%
5
10
? Intermediate Calculations -
Stepping-Time (dt)
Up Step-Size (up)
Down Step-Size (down) Risk-neutral Probability (prob)
1.0000 0.5000
1.2214 1.1519
0.8187 0.8881
57.75% 55.39%
Underlying Asset Lattice 271.83 |
222.55
182.21 182.21 |
149.18 149.18
122.14 122.14 122.14 |
I 100.00 100.00 100.00
81.87 81.87 81.86 |
67.03 67.03
54.88 54.88 |
44.93
36.79 |
ng Asset Lattice (10 Steps) 411.33 I
357.08
309.99 309.99 I
269.11 269.11
233.62 233.62 233.62 I
202.81 202.81 202.81
176.07 176.07 176.07 176.07 |
152.85 152.85 152.85 152.85
132.85 132.69 132.69 132.69 132.69 |
115.19 115.19 115.19 115.19 115.19
100.00 100.00 100.00 100.00 100.00 |
86.81 86.81 86.81 86.81 86.81
75.36 75.36 75.36 75.36 75.36 |
65.43 65.43 65.43 65.43
56.80 56.80 56.80 56.80 |
49.31 49.31 49.31
42.80 42.80 42.80 |
37.16 37.16
32.26 32.26 |
28.00
24.31 |
100.00
Exercise Solutions
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