3) Assuming a discount rate of 12% (risk free rate of 6% and a risk premium of 6%) calculate the NPV for all the sequels. Use the expected negative costs and the expected revenues given in Table 7.
The above table shows the calculated NPV of each hypothetical sequel by the method described below.
For example:
The most valuable hypothetical sequel is Batman 2. The NPV at t=3 years is calculated by:
NPV(t=3)=$229.11.12-$70.5=$134.05 million
Then, valuing this $134.05 million option at the present t=0 time can be shown by:
NPV(t=0)=$134.051.123=$95.42 million
The same method of calculating NPV was used for each of the movie sequel options listed above and the total static NPV for all sequels added together and discounted to t=0 is a ($238.14) million. From this data alone Arundel would know that making sequels to all production movies would be a losing venture. Therefore, we performed the same calculation for only positive NPV predictions and the results are a $490.87 million gain if we can pick and choose our sequels from the entire group of movie originals. With the knowledge that choice can lead to profit Arundel proposed the time delayed option so they can get a chance to see the probability of success of sequels before they commit to making them.
4) Using the “decision-tree” approach, calculate the per-movie value of the sequel rights to the entire portfolio of 99 movies released in 1989 by the six major studios. Assume that you will only make the sequels that have a positive NPV.
In making this decision tree we know the decision to make the original films was already made and revenue has been realized making it possible to use the decision tree to decide if a sequel to the original should be made. By considering the option to make sequels at t=1 Arundel has given themselves the chance to only spend money on films with a high probability of success while opting not to spend money on films that are likely to fail as sequels. Considering all 99 original films Arundel is able to statistically scrutinize the data in Exhibit 7 for originals with a high probability of producing a successful sequel. Looking back at the table in question three the films have been arranged in descending order according to the highest predicted NPV at t=0. The expected returns on sequels from the 99 original films were then broken up to determine probability of success. Any movie sequel with an expected positive NPV was grouped into the upper probability while any sequel with an expected negative NPV was grouped into the lower probability. The expected returns from the movies in the upper group were then used to estimate probability of sequel success while the lower group made up the remaining difference. Assuming a Risk-Neutral model we can solve for our probability of sequel success as follows:
Expected Return=Rf=Probability of Sequel Success*Upper Group Average Returns+ 1-Probability ofSequel Success*Lower Group Average Returns
There are 26 movies in the upper group and their average expected return is 143%. The lower group included the remaining 73 movies and their average return is (62%). Therefore, with a Risk-Free Rate of 6%, the equation above can be restated as:
Expected Return= Rf=0.06= Probability of Sequel Success*1.43+ 1-Probability of Sequel Success*-.62
Solving for Probability of Sequel Success gives a probability of 33%. Knowing the whole portfolio’s probability of sequel success, we can now put a value on the option. The exercise price for this option is the cost to produce the movies at t=1. From Exhibit 7, the estimated cost to produce the portfolio of 26 sequels at t=3 is about $638 million. Arundel will be exercising the option at t=1 however, so the cost is discounted to t=1 as follows:
Sequel Exercise Pricet=1= Sequel Exercise Pricet=3(1+R)t= $6381.122≈$509 million
With an accurate exercise price, asset value can be used to determine the overall option value of purchasing rights to all 99 movies. Asset value is the estimated revenue Arundel would receive as a result of exercising the option to produce the sequel portfolio. The total expected revenue of the 26 sequels with positive NPV is $1487 million at t=4. Knowing future success can result in $1487 with a $508 investment means there is an upside potential of ($1487-508) = $979. The upside probability however, is only 33%. Therefore, the value of the option can be determined by:
Sequel Option Value= Success Probability*Upside Value+ 1-Success Probability*Downside Value1+Rf
Solving this equation gives a Sequel Option Value of:
Sequel Option Value= .33*979+ .67* 01.06 =$305 million
** Downside value is set to zero because none of the sequels in the lower group produce positive NPV and therefore the option is abandoned. **
If the Sequel Option Value is $305 million for the entire portfolio Arundel would be willing to pay up to $3 million per movie for the option. If the studios are willing to accept $2 million per movie, the option is valuable and should be pursued.
We also thought it would be important to point out that statistical analysis of the expected annual returns revealed two outliers; Look Who’s Talking and Driving Miss Daisy (see Box Plot). The absence of these two movies changes the Sequel Option Value to $315 million. Due to the increased value without the outliers the original calculations were used for added risk mitigation.
5) Assume that a maximum of ten sequels can be made in any given year (choose the sequels that are most likely to be made—for example if the main character in the film dies then a sequel is unlikely to be made) Using the same decision-tree approach, what would you estimate to be the per-movie value of the sequel rights to the entire portfolio of 99 movies released in 1989 by the six major studios?
If only 10 sequels maximum can be made in a year then Arundel should choose the 10 movies predicted to have the highest NPV at t=0. Those would be:
The total expected asset value of the 10 movies is $920 million at a cost of $235 million at t=1. The probability of sequel success is still based on the entire 99 movie portfolio and therefore is still expected to be 33%.
Solving this equation gives a Sequel Option Value of:
Top 10 Sequel Option Value= .33*685+ .67* 01.06 =$213 million
** Downside value is set to zero because none of the sequels in the lower group produce positive NPV and therefore the option is abandoned. **
If the Top 10 Sequel Option Value is $213 million for the entire portfolio, Arundel would be willing to pay up to $2.15 million per movie for the option. If the studios are willing to accept $2 million per movie, the option is valuable and should be pursued however the whole portfolio option will be more profitable.
6) Using the Black-Scholes approach, calculate the per-movie value of the sequel rights to the entire portfolio of 99 movies released in 1989 by the six major studios. (Assume once again that there is no maximum to the number of sequels that can be made in a given year). You must provide details of how you estimated the inputs to the B-S formula.
The per movie value of the sequel rights to the entire portfolio of 99 movies is $5.2 million as shown in the B-S model shown below, with the following inputs:
- Asset value – calculated from the average of cash inflows of all 99 sequels at year zero, since year zero is when the option will be purchased. Therefore, the average PV of net cash inflows at year four ($21.6M) was discounted at the 12% cost of capital rate to obtain $13.73 million. This is the same method used for the Mark II example in the book and lecture.
- Exercise price – is the average net cost of exercising the option to produce all 99 sequels, $22.6M. The B-S formula will discount this price at the risk free rate for three years using the model provided in this course. Again this is the same method used in the Mark II example in the book and lecture.
- Volatility of asset returns – is the standard deviation on what we get from making the sequels which is the one year returns on the 99 hypothetical sequels, 1.21.
- Time to maturity - according to the case the original movie will take a year to film and the popularity of the original can be determined after two months of the film being released, therefore at 14 months (1.1667 years) uncertainty is resolved and the decision on a sequel is made.
- Risk-free rate – 6%, as assumed above in question 2.
HINT: Note that the time to maturity of the options is when uncertainty is resolved not necessarily when the sequel is made. The asset value is what you will get if you exercised the option to make the sequel. Again use average values for all the sequels. Similarly use the average value of the cost to make the sequels for the exercise price. Estimating standard deviation is a little trickier. Note that you do not have past information on returns to each sequel to estimate volatility for a sequel. However, you have information on a portfolio of sequels and you know the returns to these sequels and you could use these to estimate a standard deviation based on a cross-section of returns (DO NOT USE PRICE LEVELS). Also the standard deviation should be based on all 99 sequels – that is it should be based on the entire distribution.
- Carry out a sensitivity analysis of the value of the option to the values of the underlying asset, exercise price, and volatility. Change each variable from –50% to +50% in steps of 10%.
As can be seen in the below tables and graphs, the option value is most sensitive to changes in the asset price. Therefore, the option value is highly dependent on the amount of cash inflows sequels produce.
- What problems or disagreements would you expect Arundel and a major studio to encounter in the course of a relationship like the one described in the case? What contractual terms and provisions should Arundel insist on?
Arundel could encounter a great deal of issues in a relationship like this one, because not only does making a sequel involve the studio it also involves the actors, script writers, producers, directors, and the list goes on. If any of these key players were to back out of the sequel, the sequel could be a flop and a huge waste of money. Also, as pointed out in the case write-up, there is no incentive for the studio to invest a lot of money in making a film that can produce a good sequel. Therefore, the relationship could break down between Arundel and the studios unless there is a way for everyone to share in the sequel’s success and profits. The sequel is a riskier investment than the option calculations above consider. A sufficient amount of protection for Arundel’s investment might be hard to attain unless they can realize a high discount rate. Even if the original is a success and they decide to invest (call) in the movie, it is not a sure thing. In fact, rarely is a real option a sure thing. But, if the original contract includes provisions for actors and other major players to participate in the sequel, and a the economy continues to offer a sufficient risk free rate it can be a viable investment.
by
joosseppi (student)
