The median start of a sequel production amounts three years after the production-start of the first movie. This is also a point were Arundel Partner have cost to produce the sequel or alternatively they can sell the rights to the highest bidder. Another year later, in year five, the sequel starts gaining revenues.
In the following paragraphs, I am going to make several calculations to determine the value of the rights of a hypothetical sequel.
The first calculation I have made is the net present value of for a sequel in year 0 given the average PV of net inflows in year 4 and the average PV of negative costs in year 3 for the hypothetical sequels in exhibit 7 as well the cost of capital of 12% in the appendix.
(1)
Given this formula and the data in exhibit 7, I had to calculate and fill in the average present value of net inflows in year 4 and the average present value of negative costs in year 3. The arithmetic average of the present value of net inflows in year 4 of 99 movies is 21.6 millions US-Dollar and the arithmetic average of the present value of negative costs in year 3 of 99 movies is 22.6 millions US-Dollar. By discounting these values for 4 respectively 3 years with the cost of capital of 12%, I got a net present value of -2.36 millions US-Dollar.
(2)
A net present value of -2.36 million US-Dollar is strongly negative on a average of 99 sequels of movies. Based on this calculation, I would recommend dropping this project. But this calculations based on the assumption, that all hypothetical sequels will be released, no matter if they will earn a return of 12% or not. Of course Arundel Partners will only exercise the rights at a time it will have learned from the performance of the first film to go on. Selecting the 26 movies from exhibit 7 the hypothetical sequels, which expect to earn a return at least of the cost of capital, I was able to did another net present value calculation, which is more realistic. The method I have used is the same as above, with same formula (1). But this time I have calculated the average (26 movies) present value of net inflows at year 4 of all 26 sequels were estimated to be 57.2 millions US-Dollar and the average (26 movies) present value of negative cost at year 3 were 24.5 millions US-Dollar.
(3)
Therefore the average net present value of the hypothetical sequels with a return at least of 12% is 18.9 million US-Dollar and would be strongly positive. In this case I would highly recommend continuing with the sequel project.
As shown in calculation (2) and calculation (3) the outcome depends highly of the chosen hypothetical sequel rights. I also could have chosen the top 5 hypothetical sequels to get an even better net present value for a sequel. Therefore picking randomly assumptions can be foolish. We know that projects with a high degree of uncertainty can be seen as an option. Of course the outcome of the actual project can be positive and negative, but just having the opportunity to profit from the potential positive outcome as a value. The time will show how the project really turns out. I am going to use the Black Scholes Formula (4) to value this project. The auxiliary conditions are stated in equations (5) and (6).
(4)
(5)
(6)
To be able to calculate the auxiliary conditions first and then the value of the sequel project with the Black Scholes Formula (4), I have to determine five parameters. These are:
The exercise price X can be calculated through exhibit 7. The average of all present values of negative costs equals the exercise price X and this is 22.6 millions US-Dollar.
The present value of the underlying asset can also be calculated with exhibit 7. I took the average of all present values of net inflows in 4 years and discounted it to 1.124, because the cost of capital was given as 12%. Therefore the present value of the underlying asset is 13.7 millions US-Dollar.
The number of periods T to the exercise date of the option is in this case 3, because as it was described in the case and we can also see in the timeline above, Arundel Partners had three years time to exercise the option or not.
The next parameter σ, standard deviation, given in exhibit 7 is estimated from the one-year return in year 3. I assume that the sequel depends highly on the performance of the first film the given standard deviation already equals σ multiplied with the square root of T. Therefore we have to calculate the standard deviation simple be dividing 1.21 with the root of 3 (year).
(7)
In the end I assume the last parameter rf as 6% and the five parameters are completed to calculate the value of each sequel using the Black Scholes Model.
Using these parameters, the equation (5) and equation (6) above, I am able to calculate d1 and d2. Therefore d1 is 0.34 and d2 is -0.87. After filling in all these parameters in the Black Scholes Formula (4), the result is 5.06. So the value an option to buy the rights for an average a hypothetical sequel is 5.06 millions US-Dollar. Therefore I would recommend continuing with the sequel project, because they were able to buy the rights for about 2 millions US-Dollar, wide under the value.
After all these calculations, I also want to discuss some general issues about this case. First of all it is essential for Arundel Partners to buy the rights of a hypothetical sequel before the first film starts, because after the release, if the movie is a big success, the studio will not sell the rights for a sequel for the same price. If the studio sees the potential of the movie and the asymmetric information is eliminated, it will be impossible for Arundel Partners to buy the rights for about 2 millions US-Dollar. An asymmetric information between producer and Arundel Partner would result of a purchasing the rights of a sequel after the production of the first film – Principal-Agent Theory. The producers have all the information about the first movie and Arundel Partners do not. So it would be impossible for Arundel Partners to buy sequel rights of “good” movies for a fair price.
Arundel Partners should be very particular in choosing movies and sequel to invest in. The one-year returns from the hypothetical sequels show us that not every sequel right is profitable. An example for a not profitable movie is “Bert Rigby, You Are A Fool” from Warner Brothers. This film is maybe the biggest “loser” according to exhibit 7. There are also studios, which do not generate a lot of revenues by contrast with negative costs. For example Twentieth Century Fox. This brings me the idea to calculate separate options values of hypothetical sequels with the Black Scholes Model. The more successful a movie of a studio is, the higher will be the option value.
Conclusion
This innovative business idea is very interesting and really good. But the biggest problem of this business could be gaining revenues. The timeline showed us that it could take 4 years until the first sequel starts gaining revenues. And if Arundel Partners start buying rights for hypothetical sequels for 4 years without any revenues, they could fail because of running out of money. So if they have enough cash in their group, they should go on with this creative idea.
by
memo1903 (student)
