Case ID: 292140     Solution ID: 9     Words: 1145 Price \$ 75

# Arundel Partners The Sequel Project Case Solution

## Abstract

Arundel Partners is a monetary organization that is thinking about a surprising venture extend. The organization is hoping to purchase rights to conceivable spin-offs for forthcoming motion pictures and benefit by really making the continuations for motion pictures that get to be distinctly business achievement. The organization has as of now started converses with a few studios and ventures that it can purchase an arrangement of film rights for \$2 million for each motion picture. The valuation of the venture is dubious on account of the questionable way of incomes in the motion picture industry. So as to esteem the venture, we propose the utilization of net present esteem approach with an unequivocal change for the alternative implanted in the proposition. It is assessed that the organization may think that its productive to buy motion picture rights from specific studios, yet the unverifiable way of the estimation warrant assist examination with extra information.

We next needed to answer the question of how much Arundel should be willing to pay for these sequel production rights. If they are interested in creating a broad portfolio encompassing all six major studios, we can use several different approaches: We could calculate an NPV of the proposed portfolio, we could use decision trees to calculate an NPV, or we could use an option pricing formula and apply it to our situation. To calculate the Net Present Value for all sequels, we needed to calculate the individual NPV of each hypothetical sequel first.

We found these values by taking the Present Value of the negative cost incurred and then adding the PV of the inflows the next year divided by the discount rate, which was given to us as 12%. Once NPVs were found for each individual sequel, we took the sum and divided it by the number of sequels, which is 99. This calculation led us to an NPV of -\$3.38. Then we had to discount these values back 2 years to get an average NPV per sequel of -\$2.69. We need to discount back 2 years because the NPV for our years 3 and 4 (for the film sequel) give us years 2 and 3, but we want years 0 and 1, so we need to discount again. This is also the year when Arundel would make the purchase. With a negative NPV, it would not make sense for Arundel to purchase sequel rights. Of course this calculation method doesn't account for the fact that Arundel would in reality only take on sequel production in cases where the original was successful enough to warrant it; it simply assumes that we would take on all projects, when we already know that statistically speaking, the majority of movies are not popular enough to create a successful sequel from. We need a way to model this, and eliminate superfluous negative cash flows from our evaluation. This is where a decision tree method is helpful. Using this approach, we created an inequality, stating if the NPV of a sequel is greater than 0, then take it, but it the NPV of a sequel is not greater than 0, then don't take it. If the NPV was greater than 0, we had the inequality output the NPV value; if the NPV was not greater than 0, we had it output 0 (no gains or losses from forgoing the purchase of sequel rights). We then summed up all the values and divided them by 99 to get an average NPV of a sequel if the project was taken or not. Our newly calculated NPV is for all the sequels is 6.965981241, but when discounted back 2 years becomes 5.553237596. This value reflects a situation where Arundel would purchase sequel rights for a positive NPV project, but not for a negative NPV project.

To model a likely state in which we (and studios) are working with a limited budget, we have also made an estimation of a proposed portfolio NPV using the decision tree approach and a constraint limiting us to only ten sequels that can be produced. We took the top ten sequels because if we could only choose ten, these are clearly the ones we would wish to produce. The top ten net present value films in descending order are: Batman, Look Who's Talking, Honey I shrunk the Kids, Driving This Daisy, Parenthood, Dead Poet's Society, When Harry Met Sally, The Little Mermaid, Born on 4th of July and Steel Magnolias. The sum of the net present value for these top grossing sequels is \$526.46, giving them an average NPV of \$52.646. The NPV and decision tree calculations may be seen in Exhibits A and B. LACK-SHOLES MODEL AND SENSITIVITY ANALYSIS

Another, very different approach to valuing this investment is to treat it just like any option on a security, and apply the Black-Scholes Model. We would be buying the rights to produce the movie for a certain cost, with a strong expectation of returns on the sequel that would make this expenditure profitable. There are certain factors needed to conduct this calculation, and the Black-Scholes Table requires two inputs to find the corresponding value: A and B. In order to calculate A and B to look up a value in the Black-Scholes Table, we need Asset Value (So), Exercise Price (X), The Volatility of Asset Returns (?), Time to Expiration, and a Risk-free Rate.

To calculate the proper underlying asset value, we used the average cost of producing a film sequel, as given in Exhibit 7 of the case, giving us \$22.6; however, it represents the cost incurred for the sequel in year 3. The reason it is for year 3 is because the decision to produce a sequel usually isn't made until about 3 years after the initial film is released, and 3 years is our proposed time limit by which Arundel would have to make such a declaration. Therefore, we needed to discount this number back 2 years to get an Asset Value (So) of 17.21938776. To calculate the correct exercise price, we used the average first year inflows of producing a film sequel. This number is \$21.6; however, it represents the present value of inflows in year 4. Therefore, it is necessary to discount this number back 2 years, to get an Exercise Price (X) of \$18.02. We used the standard deviation of the averaged one-year returns for a sequel, which came out to be 1.21. Some of the 99 films had negative NPVs while others had positive NPVs. Therefore, the standard deviation associated with the averaged NPVs accurately reflects the volatility of asset returns because it takes into account all 99 hypothetical sequels and their respective outcomes. For our time to expiration, we chose the period of one year. This reflects when uncertainty is resolved because it shows the process from cost outflows to the first inflows after release. At this point in time, we can calculate if there is a positive or negative NPV. Finally, the risk-free rate has been given to us as 6.0%. With these numbers, we found the value of A to be 1.013097 and B to be 1.21, giving us 45.15%. This number represents the value of this call option, expressed as a percentage of the assets being acquired (average cost of sequel production). In other words, we'd should be willing to pay a total of [\$17.22 * 0.451] or \$7.77 for the option. These calculations are found in Exhibit C. We then conducted a sensitivity analysis on our Black-Scholes data, based on changes in Asset value, Exercise Price, and volatility. We chose an asset value range of 10 to 25 (approximately surrounding \$17.22 calculated value), and as expected, concluded that as asset value increased, the Black-Scholes % values (option value) increased.

Conversely, we found that as exercise price increased, using the same range, the value decreased. Using a volatility range of .5 to 2, we found that volatility and option price, like asset value, also have a positive correlation. The sensitivity analyses can be found in Exhibit D.

### Excel Calculations

Discount Rate, Average PV of Inflows at Year 4, Average PV of Outflows at Year 3,  Total No of Movies, Average NPV at Year 0, Maximum Payment per Sequel Rights

### Questions Covered

1. Why do the principals of Arundel Partners think they can make money buying movie sequel rights? Why do the partners want to buy a portfolio of rights in advance rather than negotiating film-by-film to buy them?
2. Estimate the per-film value of a portfolio of sequel rights such as Arundel proposes to buy. [There are several ways to approach this problem, all of which require some part of the dataset in Exhibit 6-9. You may find it helpful to consult the Appendix, which explains how these figures were prepared.]
3. What are the primary advantages and disadvantages of the approach you took to valuing rights? What further assistance or data would you require to refine your estimate of the rights’ value?
4. What problems or disagreements would you expect Arundel and a major studio to encounter in the course of a relationship like that described in the case? What contractual terms and provisions should Arundel insist on?