Case Write-Up: Arundel Partners 15. 415 Finance Theory Section B, Oysters Arundel Partners: The Sequel Project With the purchase of sequel rights, what Arundel is achieving is to have a call option on the revenue that each movie brings. This helps to remove the uncertainty and risks associated with producing a movie, especially with regard to moviegoers’ taste. With the sequel right, Arundel will only exercise this option to produce a sequel if the first movie proved to be popular and the sequel is hence predicted to bring in profits.This provides downside protection, as huge losses (due to high production costs) associated with a failed movie will be avoided. Arundel plans to agree on the number of films and price per film before either the studio or itself knows which films would be produced. This prevents the studio from increasing the price of the sequel right if it predicts that a particular movie will be a hit. Thus, Arundel is aiming to earn handsome profits from movies that eventually turn out to be a hit, since it would have paid a relatively low price for the call option on the movie.This is an important point as Arundel’s profitability heavily relies on how much it has to pay for the sequel rights. Although most of the movies will not have profitable sequels (hence rendering the option’s payoff as zero), the few hit movies will bring about a huge payoff such that overall, Arundel predicts to profit from this idea. If we use straight PV analysis of all the movies, by using the PV of Inflow at Yr4 and PV of Negative cost at Yr3, we can calculate the NPV of each movie at Yr0.Since the total NPV for all 6 studios is negative, we will not purchase all the sequel rights if we use this simple NPV analysis. However, MCA Universal and TCFOX have positive NPV’s and hence we are willing to pay up to $4. 47M for each sequel of MCA Universal and $6. 08M for each sequel of The Walt Disney Company. Sl. | Studio| PV Inflow @ T=4| PV Negative Cost @ T=3| NPV @Yr 0| Number of Movies| Cost of each Sequel Right| 1| MCA Universal| 450. 3| 311. 9| 62. 65| 14| 4. 47| 2| Paramount Pictures| 202. 7| 246. 7| (46. 74)| 10| (4. 67)| 3| Sony Pictures Entertainment| 444. 1| 764. | (260. 38)| 34| (7. 66)| 4| Twentieth Century FOX| 186. 2| 241. 1| (53. 14)| 11| (4. 83)| 5| Warner Brothers| 458. 4| 421. 7| (9. 68)| 19| (0. 51)| 6| The Walt Disney Company| 393. 5| 255. 3| 66. 91| 11| 6. 08| | Total| 2135. 2| 2241. 3| (240. 38)| 99| | However if we consider that Arundel has the choice whether to exercise the right, we realise that Arundel will only produce the sequels with positive NPV. With this analysis, the idea of buying the sequels can be profitable for the industry as a whole and for each studio (the level at which the contract will be negotiated).The cost of each sequel rights for each studio is provided in the below table: Sl| Studio/Movie Title| PV Inflow @ T=4| PV Negative Cost @ T=3| NPV of +ive Return Projects @ Yr0| Number of Movies| Cost of each Sequel Right| 1| MCA Universal| 450. 3| 311. 9| 92. 08| 14| 6. 58| 2| Paramount Pictures| 202. 7| 246. 7| 26. 33| 10| 2. 63| 3| Sony Pictures Entertainment| 444. 1| 764. 6| 96. 92| 34| 2. 85| 4| Twentieth Century FOX| 186. 2| 241. 1| 19. 20| 11| 1. 75| 5| Warner Brothers| 458. 4| 421. 7| 137. 21| 19| 7. 22| 6| The Walt Disney Company| 393. 5| 255. 3| 111. 42| 11| 10. 13| | Total| 2135. | 2241. 3| 483. 17| 99| | Black-Scholes Option Value | | | | Input Data| | | Stock Price now (P)| | 13. 55| Exercise Price of Option (EX)| | 22. 6| Number of periods to Exercise in years (t)| | 3| Compounded Risk-Free Interest Rate (rf)| | 12. 36%| Standard Deviation (annualized ?? | | 121. 00%| Output Data| | | Present Value of Exercise Price (PV(EX))| | 15. 5981| ?*t^. 5| | 2. 0958| d1| | 0. 9808| d2| | -1. 1150| Delta N(d1) Normal Cumulative Density Function| | 0. 8367| Bank Loan N(d2)*PV(EX)| | 2. 0656| Value of Call| | 9. 2728| To price the sequel right, we can treat it as a call option.The company will not exercise the sequel right if they predict that the sequel will not be profitable based on the first movies’ performances. The downside of the investment is removed when we purchase the sequel right. To get an estimate of the call price, we use the average of PV of net inflows as the underlying asset, PV of negative costs as exercise price, standard deviation of return as volatility, and 1992 T-bill rate as the risk free rate. After plugging in these numbers into the Black-Scholes formula, we calculated that the average cost for a sequel option should be 9. 728. The main assumption we are making here is that our call option (sequel right) is for an average movie (i. e. if we decide to buy the right, we are willing to pay an average call option price of 9. 2728 for each movie regardless of the studio it is produced from). However, in reality, the company will be negotiating the prices of the sequel rights with each studio. Thus, the quoted price we will get from each studio can be quite different from the overall average price we calculated since each studio’s expected performance is different from one another.The volatility we used is the industry volatility approximated from the standard deviation of returns from 99 movies’ sequel. When we are evaluating a quoted price of a sequel right, 9. 2728 will be a good bench mark. According to our simple NPV analysis, we would reject the idea of purchasing sequel rights since the NPV value is negative overall. However, if we consider the sequel right as a call option, we see that there is a fair price for each sequel rights. Hence, on average, for any studio quoting less than or equals to 9. 2728 per movie, it is profitable to enter the sequel deal with the studio.