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The idea is basically about creating an investment group, Arundel partners, which would purchase the sequel rights associated with films produced by one or more major movie studios before the first films are made. With the sequel right, Arundel could decide whether to make the second film based on the result of the first film. Arundel’s profitability is dependent upon the price it pays for a portfolio of sequel rights. Profitability of the project Arundel would purchase the sequel rights of the entire production of a studio over an extended period of not less than a year.
If a particular film was a hit, it is believed that a sequel would also be profitable, and Arundel would exercise its right to produce the sequel. Alternatively, it can sell the right to the highest bidder. It is of critical importance to Arundel that a number of films and a price per film are agreed upon before either Arundel or the studio knew which films would generate the option of a sequel. In addition, once production started, the studio would inevitably form an opinion about the movie and the likeliness that a sequel would be possible.
This would put Arundel at a disadvantage, because they would then have to negotiate the price for sequel rights on each film produced, while knowing much less than the production studio about the film. Valuation of sequel rights In the following context, we are going to present two approaches to value the per-film value of the portfolio of sequel rights. All the calculations are based on the information given in Exhibit 7. Major results are included in the Appendix. The risk free rate is 6% semiannually as indicated in the case, which is equivalent to an annual rate of 12% with semiannual discounting. 1. NPV approach
In this approach, the difference between the PV of Net Inflows and PV of Negative Cost is used as criteria to determine whether Arundel will exercise the options. If the difference is positive, which means that the hypothetical sequel is profitable, Arundel will exercise the option and thus we would have positive future cash flow from the sequels. We take the average of profits of all the profitable sequels and get the per movie value, which is 4. 43 million/film. The procedure is equivalent to taking the real expectation of terminal payoffs assuming all outcomes are equiprobable and discounting at a risky rate for the underlying. . Black-Scholes approach Since the assumption for original Black-Scholes formula is that the strike price is fixed, while here the PV of negative (analogous to strike price in original BS formula), we are going to adopt the BS formula for exchange option according to Margrabe(1978), Where x1 is average PV of net inflows, x2 is average of PV of negative costs, t*- t= 4, ? is the volatility estimate and ? =? 12+? 22-2??? 1? 2. By plugging all the elements in the formula, the value of the option using BS approach is 14. 8 million/film. Advantages of 2 approaches
For NPV approach: only simple calculation is implemented in this approach and this procedure is equivalent to taking the real expectation of terminal payoffs assuming all outcomes are equally probable and discounting at a risky rate for the underlying. For BS approach: the BS formula for the exchange option is chosen as it would produce more precise result than the basic BS formula in the case of floating strike price. Disadvantages of 2 approaches For both 2 approaches: only pre-tax data are implemented in calculation and Arundel overheads are not included.
For BS approach??: the volatilities of revenue and cost are assumed to be identical, which might be difference from reality, and both volatilities are obtained from calculating volatility of return. However, the correlation between return and cost are obtained from data of revenue and cost, so it may not match the obtained volatility well. Furthermore, we are dealing with a single-period discrete model and BS formula would be more appropriate to be implemented in a continuous-time case. This is may be the reason why the two approach give us quite different result.
If possible, we would like to have some more historical data to implement B-S approach in a better way. The probability of success and information about the willingness of production companies to sell sequel rights at a pre-negotiated price may also help with analysis Disagreements, Contractual terms and provisions For a major studio, it may not be willing to make a sequel film even the first film is successful, due to some artistic judgments. However, the decision would be made by the sequel rights owner, Arundel, thus the studio would probably make less effort on the sequel, which may lead to loss finally.
The Arundel could distribute part of its profit to studio along the increasing number of sequel to encourage it to spend more effort on the production of the film. APPENDIX | | Hypothetical sequel| | | | | PV(Net| PV(Negative| PV(Negative| | PV(Net Inflows)| | | | | Inflows)| Cost)| Cost)| 1-year| discounted back to | (=1) if (2)-(1);0| | | | year 4 (end)| year 3 (end)| percentage ch. | Return| year 3 (end)| (=-1) otherwise| (2)-(1)| | | | (1)| | | (2)| | | 1| PARENTHOOD| 76. 8| 28. 2| | 1. 723404| 68. 35172659| 1| 40. 15173| 2| BORN ON THE FOURTH OF JULY| 56. | 25. 4| -0. 09929078| 1. 23622| 50. 55179779| 1| 25. 1518| 3| FIELD OF DREAMS| 47. 3| 22. 6| -0. 11023622| 1. 09292| 42. 09683161| 1| 19. 49683| 4| UNCLE BUCK| 47| 21. 2| -0. 061946903| 1. 216981| 41. 82983268| 1| 20. 62983| 5| SEA OF LOVE| 44. 4| 35. 3| 0. 66509434| 0. 25779| 39. 51584194| 1| 4. 215842| 6| ALWAYS| 31. 4| 43. 7| 0. 23796034| -0. 28146| 27. 94588822| -1| 0| 7| K-9| 29. 3| 16. 9| -0. 613272311| 0. 733728| 26. 07689569| 1| 9. 176896| 8| THE ‘BURBS| 27. 3| 24| 0. 420118343| 0. 1375| 24. 29690281| 1| 0. 296903| 9| THE DREAM TEAM| 22. | 21. 2| -0. 116666667| 0. 080189| 20. 38091848| -1| 0| 10| DO THE RIGHT THING| 21. 2| 9. 9| -0. 533018868| 1. 141414| 18. 86792453| 1| 8. 967925| 11| DAD| 17. 4| 26. 8| 1. 707070707| -0. 35075| 15. 48593806| -1| 0| 12| SHOCKER| 12. 4| 8. 5| -0. 682835821| 0. 458824| 11. 03595586| 1| 2. 535956| 13| THE WIZARD| 8. 7| 11. 3| 0. 329411765| -0. 23009| 7. 742969028| -1| 0| 14| RENEGADES| 7. 4| 16. 9| 0. 495575221| -0. 56213| 6. 585973656| -1| 0| 15| HARLEM NIGHTS| 51. 1| 42. 3| 1. 50295858| 0. 208038| 45. 47881808| 1| 3. 178818| … | | | | | | | | | 0| DEAD POETS SOCIETY| 74. 4| 28. 2| -0. 090322581| 1. 638298| 66. 21573514| 1| 38. 01574| 91| THE LITTLE MERMAID| 62| 28. 2| 0| 1. 198582| 55. 17977928| 1| 26. 97978| 92| TURNER & HOOTCH| 54. 6| 25. 4| -0. 09929078| 1. 149606| 48. 59380562| 1| 23. 19381| 93| THREE FUGITIVES| 29. 1| 24| -0. 05511811| 0. 2125| 25. 8988964| 1| 1. 898896| 94| AN INNOCENT MAN| 17| 24| 0| -0. 29167| 15. 12993948| -1| 0| 95| BLAZE| 14. 7| 25. 4| 0. 058333333| -0. 42126| 13. 08294767| -1| 0| 96| NEW YORK STORIES| 8. 2| 26. 8| 0. 05511811| -0. 69403| 7. 97970808| -1| 0| 97| GROSS ANATOMY| 8. 1| 16. 9| -0. 369402985| -0. 52071| 7. 208971164| -1| 0| 98| DISORGANIZED CRIME| 7. 1| 15. 5| -0. 082840237| -0. 54194| 6. 318974724| -1| 0| 99| CHEETAH| 7. 1| 9. 9| -0. 361290323| -0. 28283| 6. 318974724| -1| 0| | B-S formula for exchange option| | | NPV valuation| | | | | | correlation | 0. 46394871| | Value of rights| 430. 0157| | | | | x1_0| 19. 19515554| | Permovie (Mio)| 4. 343593| | | | | x2_0| 22. 64242424| | | | | | | | sigma| 1. 256060551| | | | | | | | B-S price| 14. 84168493| | | | | | |