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# Chapter 13opciones financieras

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### Transcript of "Chapter 13opciones financieras"

1. 1. Chapter 13 Real-Options Analysis Financial Options 13.1 • u = eσ ∆t = e0.3× 0.75 = 1.2967 1 1 • d= = = 0.7712 u 1.2967 • Risk neutral probability er ∆t − d e0.05×0.75 − 0.7712 q= = = 0.5081 u−d 1.2967 − 0.7712 • Tree valuation 100.88 q Max(0, (100.88-60)) = \$40.88 q 77.80 (\$20.01) 1-q 60 60 9.79 q Max(0, (60-60)) = \$0 1-q 46.27 (\$0.00) 1-q 35.68 Max(0, (35.68-60)) = \$0 ∴ European call option value = \$9.79 13.2 • u = eσ ∆t = e0.4× 1 = 1.4918 1 1 • d= = = 0.6703 u 1.4918 • Risk neutral probability e r ∆t − d e0.05 − 0.6703 q= = = 0.4638 u−d 1.4918 − 0.6703 1 − q = 0.5362 Contemporary Engineering Economics, Fourth Edition, by Chan S. Park. ISBN 0-13-187628-7. © 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should beobtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.
2. 2. • Tree valuation: Note to instructors: No mention is made about the dividend payment in determining the option premium in the text. In financial option, any dividend payment reduces the value of the option. The figures in yellow represent the adjusted share prices after a 3% dividend payment, i.e., (1 – 0.03)(\$124.96) = \$121.21. If there is no dividend payment, we just use the original share prices in determining the option premium. Keep open 124.96 Keep open 86.35 Do not exercise 59.67 121.21 [0] 83.76 57.88 [0] 40 [ 5.34 ] [ 12.04 ] Keep open 56.15 Exercise 38.8 Do not exercise 26.81 54.46 [0] 37.64 26.01 [ 10.47 ] [ 18.99 ] Exercise 25.23 17.43 Exercise 24.47 [ 20.53 ] 16.91 [ 28.09 ] 11.34 Exercise 11.00 [ 34.00 ] ∴ American option value = \$12.04 13.3 Portfolio Premium Payoff at stock price \$60 A long call with X = \$40 \$3 \$20 - \$3 = \$17 A short put with X = \$45 \$4 \$4 – 0 = \$4 Two short call with X = \$35 \$5 (\$5 - \$25)×2 = (\$40) Two short stock at \$40 (\$40 - \$60)×2 = (\$40) Total (\$59) Contemporary Engineering Economics, Fourth Edition, by Chan S. Park. ISBN 0-13-187628-7. © 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be 2obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.
3. 3. 13.4 Note to the instructors – The definitions of intrinsic value as well as time value were not given in the text. In financial option, the option premium is viewed as having two types of value. The intrinsic value is the value if you exercise the option immediately. The time value is the value if you wait. • Intrinsic value = X − S0 = \$2 • Time premium = option premium – intrinsic value = \$2 Real-Options Analysis 13.5 • Define the real option parameters for delaying option. V I T r σ \$1.9 Million \$2 Million 1 year 0.08 0.4 − rf T Ccall = S0 N (d1 ) − Ke N (d 2 ) = 1.9 N (0.2718) − 2e −0.08 N (−0.1283) = \$0.3246M ln( S0 K ) + (rf + σ 2 )T 2 d1 = σ T 0.42 ln(1.9 / 2) + (0.08 + )1 = 2 = 0.2718 0.4 1 d 2 = d1 − σ T = 0.2718 − 0.4 1 = −0.1283 13.6 • Define the real option parameters for license option. V* I T r σ \$30 Million \$40 Million 3 0.06 0.2 * V = (\$340 - \$320) × 1.5M = 30M Contemporary Engineering Economics, Fourth Edition, by Chan S. Park. ISBN 0-13-187628-7. © 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be 3obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.
4. 4. − rf T Ccall = S0 N (d1 ) − Ke N (d 2 ) = 30 N (−0.0165) − 40e −0.18 N (−0.3629) = \$2.8610M ln( S0 K ) + (rf + σ 2 )T 2 d1 = σ T 0.22 ln(30 / 40) + (0.06 + )3 = 2 = −0.0165 0.2 3 d 2 = d1 − σ T = −0.0165 − 0.2 3 = −0.3629 Switching Options 13.7 A switching option is a special case of a put option. • Compute the NPW of project B: NPWB = −\$2 + \$1( P / A,12%,10) = \$3.65M • Define the real option parameters for the switching option and compute the put option premium by using the Black-Scholes model. V I T r σ \$4 Million \$3.65 Million 5 0.06 0.5 Cput = 3.65e −3.0 N (0.2088) − 4 N (−0.9093) = \$0.85M 0.52 ln(4 3.65) + (0.06 + )5 d1 = 2 = 0.9093 0.5 5 d 2 = 0.9093 − 1.118 = −0.2088 Contemporary Engineering Economics, Fourth Edition, by Chan S. Park. ISBN 0-13-187628-7. © 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be 4obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.
5. 5. • Determine the combined option value Combined Option Value = Value of project A + Option to switch to project B \$4 + \$0.85 = \$4.85M R&D Options 13.8 • Assuming MARR = 12%, the cash flow diagram transforms to: \$73.42 0 1 2 3 4 5 6 7 8 9 10 \$14.18 R&D Expenses Manufacturing and Distribution \$80 • Define the real option parameters for R&D option. V I T r σ \$46.66 Million \$80 Million 4 0.06 0.5 − rf T Ccall = S0 N (d1 ) − Ke N (d 2 ) = 46.66 N (0.2009) − 80e −0.08 N (−0.7991) = \$13.70M 0.52 ln(46.66 / 80) + (0.06 + )4 d1 = 2 = 0.2009 0.5 4 d 2 = 0.2009 − 0.5 4 = −0.7991 Contemporary Engineering Economics, Fourth Edition, by Chan S. Park. ISBN 0-13-187628-7. © 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be 5obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.
6. 6. • Therefore, the total value is: Combined option premium = Cost for R&D + Option value = −\$14.18 + \$13.7 = −\$0.48M The maximum amount the firm should spend on R&D for this project is equal to \$13.7M. Abandonment Options 13.9 • Standard NPV approach 0.35 0.35 0.35 0.35 0.35 ... 0 1 2 3 4 . . . ∞ \$3 \$0.35 NPW0 = −\$3 + = −\$0.08M 0.12 • Abandon Option value through the binomial tree - Option parameters V I T r σ \$2.92 Million \$2.2 Million 5 0.06 0.5 - Option valuations Time 0 1 2 3 4 5 2.92 4.81 7.94 13.09 21.58 35.57 1.77 2.92 4.81 7.94 13.09 1.07 1.77 2.92 4.81 Monetary Value 0.65 1.07 1.77 0.40 0.65 0.24 Contemporary Engineering Economics, Fourth Edition, by Chan S. Park. ISBN 0-13-187628-7. © 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be 6obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.
7. 7. 0.50 0.23 0.06 0.00 0.00 0.00 0.77 0.42 0.12 0.00 0.00 1.13 0.69 0.23 0.00 Option value 1.55 1.13 0.43 1.80 1.55 1.96 * Early abandonment decisions could occur in the shaded periods. ∴ Combined option value = -0.08 + 0.50 = 0.42M Scale-Down Options 13.10 • Scale down option parameters V I T r σ \$10 Million \$4 Million 3 0.06 0.3 • Decision tree for a scale-down option through one-year time increment. - u = eσ ∆t = e0.3× 1 = 1.35 1 1 - d= = = 0.74 u 1.35 er ∆t − d e0.06×1 − 0.74 - q= = = 0.53, 1 − q = 0.47 u−d 1.35 − 0.74 Contemporary Engineering Economics, Fourth Edition, by Chan S. Park. ISBN 0-13-187628-7. © 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be 7obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.
8. 8. 24.60 Max(24.60×0.7+4,24.60) 24.60 Do not scale down 18.23 Max(18.23×0.7+4,18.22) 18.22 Do not scale down 13.5 13.5 Max(13.5×0.7+4,13.5) 13.5 Max(13.5×0.7+4,13.94) Do not scale down 13.94 10 Do not scale down 10 Max(10×0.7+4,10.78) 11 11.55 Scale down 7.4 7.4 Max(7.4×0.7+4,7.4) 9.18 Max(7.4×0.7+4,8.94) Scale down 9.18 Scale down 5.48 Max(5.48×0.7+4,7.59) 7.836 Scale down 4.05 Max(4.05×0.7+4,4.05) 6.835 Scale down • From the result of the tree we can get the combined option value as follows: Combined option value = NPW + Option value = \$11.55 ∴ Option value = \$11.55 - \$10 = \$1.55M Expansion-Contraction Options 13.11 (a) Binomial lattice tree • u = eσ ∆t = e0.15× 1 = 1.1618 1 1 • d= = = 0.8007 u 1.1618 Contemporary Engineering Economics, Fourth Edition, by Chan S. Park. ISBN 0-13-187628-7. © 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be 8obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.
9. 9. • Tree with a one-year incremental period 134.99 116.18 100 100 86.07 74.08 (b) Option valuation • Risk neutral probability e r ∆t − d e0.05×1 − 0.8007 q= = = 0.6328 , 1 − q = 0.3672 u−d 1.1618 − 0.8007 134.99 Max(134.99×0.9+25,134.99×1.3-20,134.99) 155.48 Expand 116.8 Max(116.8×0.9+25,116.8×1.3-20,133.76) 133.76 Keep option open 100 Max(100×0.9+25,100×1.3-20,100) 100 115 116.31 Contract 86.07 Max(86.07×0.9+25,86.07×1.3-20,101.24) 102.46 74.08 Contract Max(74.08×0.9+25,74.08×1.3-20,74.08) 91.67 Contract ∴ Option value = \$116.31 - \$100 = \$16.31M Contemporary Engineering Economics, Fourth Edition, by Chan S. Park. ISBN 0-13-187628-7. © 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be 9obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.
10. 10. Compound Options 13.12 • Compound option parameters V0 I1 I2 T1 T2 r σ \$32.43 \$10 \$30 1 3 0.06 0.5 • Decision tree for a scale-down option with a one-year time increment. - u = eσ ∆t = e0.5× 1 = 1.6487 1 1 -d= = = 0.6065 u 1.6487 e r ∆t − d e0.06×1 − 0.6065 - q= = = 0.4369 u−d 1.6487 − 0.6065 145.34 Combined OP = NPV + Option value Max(145.34 - 30, 0) = -\$5 + \$8.13 = \$3.13 115.34 Invest \$30 88.15 59.90 Keep option open 53.47 53.47 Max(53.47 - 30, 0) 23.47 Max(29.77 - 10, 0) Invest \$30 19.77 Invest \$10 32.43 32.43 9.66 Keep option open 8.13 19.67 19.67 Max(19.67 - 30, 0) 0 Max(3.97 - 10, 0) Do not invest 0 Do not invest 11.93 0 Do not invest 7.24 Max(7.24 -30, 0) 0 Do not invest First Option Second Option Contemporary Engineering Economics, Fourth Edition, by Chan S. Park. ISBN 0-13-187628-7. © 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be 10obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.
11. 11. Short Case Studies ST 13.1 (a) American option value • Option parameters S K T ∆t r σ \$150 \$100 5 1 year 0.05 0.3 • u = eσ ∆t = e0.3× 1 = 1.3499 1 1 • d= = = 0.7408 u 1.3499 • Risk neutral probability e r ∆t − d e0.05×1 − 0.7408 q= = = 0.5097 , 1 − q = 0.4903 u−d 1.3499 − 0.7408 672.25 ∴ American Option value = \$6.64 4 ax(100-672.25, 0) M 0 498.02 Do not terminate 0 Keep option open 368.94 368.94 Max(100-368.94, 0) 0 0 Keep option open 273.32 Do not terminate 0 273.32 Keep option open 0 202.48 Keep option open 202.48 Max(100-202.48, 0) 202.48 0 0 Max(100-202.48, 1.85) Keep option open 150 Do not terminate 0 1.85 150 Keep option open 111.12 Keep option open Max(100-150, 3.96) 150 Max(100-111.12, 0) 3.96 111.12 6.64 Keep option open Max(100-111.12, 8.48) 0 111.12 Do not terminate 8.48 82.32 Max(100 -111.12, 12.32) Keep option open Max(100-82.32, 18.19) 12.32 82.32 18.19 Keep option open Max(82.32-100, 22.31) Keep option open 60.99 22.31 60.99 Max(100-60.99, 0) Keep option open Max(100-60.99, 34.39) 39.01 31.09 Terminate Terminate 45.18 Max(100-45.18, 49.94) 33.47 54.82 Max(100-33.47, 0) Terminate 66.53 Terminate Contemporary Engineering Economics, Fourth Edition, by Chan S. Park. ISBN 0-13-187628-7. © 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be 11obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.
12. 12. (b) European option value is \$6.09 by B-S equation ST 13.2 (a) Since \$4 M is lower than the option price, it is a good investment for Merck. • To give a range for the option value, first use one period lattice. V K T ∆t r σ \$36M \$72M 3 3 years 0.06 0.5 (\$30×1.2M) (\$60×1.2M) • u = eσ ∆t = e0.5× 3 = 2.3774 1 1 • d= = = 0.4206 u 2.3774 • Risk neutral probability er ∆t − d e0.06×3 − 0.4206 q= = = 0.3969 , 1 − q = 0.6031 u−d 2.3774 − 0.4206 • One period lattice and option price: \$5.17M 85.59 Max(85.59 - 72, 0) 15.59 Buy the stock 36 5.17 15.14 Max(15.14 - 72, 0) 0 Do not buy the stock • Through the B-S model, the option price should be \$6.54M. Contemporary Engineering Economics, Fourth Edition, by Chan S. Park. ISBN 0-13-187628-7. © 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be 12obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.