Arundel Partners: The Sequel Project
The maximum per-film price for the sequel rights that Arundel Partners should pay is $5.12M.
If Arundel Partners were to use the traditional DCF methods to find the value of the sequel rights, the NPV would be -$8.42M loss per-film (see Appendix 1).
We assume that Arundel Partners will purchase a portfolio of films similar to one used in the analysis. The average hypothetical net inflow of the sequel ($21.57M) is used to figure out the value of the state variable for the real options model. The state variable is the average hypothetical net inflow of the sequel, discounted using a WACC of 12.36% back to 1989. ...view middle of the document...
|D (down step in binomial tree) |0.705 |
|risk-free rate (based on 10yr US Treasury rate in 1992) |7.03% |
|exp(r∆T) |1.006 |
|q (risk-neutral probability of up move, using Lognormal model) |0.422 |
|Avg Hypothetical Negative Cost of Sequel (discounted to Year 2) |$19.79 |
Table of the parameters and values used to build the binomial trees and find the option price.
Building the Binomial Tree for Asset Values
The binomial model is used to see how the state variable evolves over time, specifically over a time period of 12 months (see Exhibit 1). The maturity or expiration date of the sequel rights option is set for 12 months. Within the first year, Arundel Partners will know whether it will want to exercise the sequel rights. We build the binomial tree for the net inflow values using the Cox-Ingersoll-Ross model. This approach approximates a lognormal distribution for the asset values (net inflow values). We assume that continuously compounded returns on the asset are normally distributed and volatility remains constant. We use the expiration date as one year from the purchase of the sequel rights and the time interval of 1/12 (1 month). We use the standard deviation on the one year return of the portfolio as an estimate for volatility (σ=121%).
Risk-Neutral Probabilities in the Lognormal Model
Once we have the binomial tree, we replace the asset values with the payoff in each state, then value the option using backward induction or dynamic programming. To do the evaluation, we calculate the risk-neutral probabilities. These are weights on the cash flow that allow us to discount by continuously compounded risk-free rate. We use the 10-year US Treasury bond rate in 1991 as the risk-free rate. The 10-year time period is chosen because the ancillary inflows from non-US markets and post-theatre rentals (pay TV, network TV, DVD, etc) can be significant for 10 years. We use the lognormal model to arrive at the risk-neutral probability of an up move of 0.422. The payoff takes is calculated by discounting the average hypothetical negative costs of the sequel to 1992 (year 2) by the risk-free rate (7.03%). The discounted average hypothetical negative costs is $19.79M. We assign the payoffs and work backwards to value the real option using risk-neutral probabilities and discounting by the risk-free rate. We arrive at an option price of $5.12M per film (see Exhibit 2).
Further considerations for Real Options Valuation approach
Real options valuations recognise that the partners at Arundel obtain valuable information after the sequel rights have been purchased and the first films are released in the theatres. This additional information allows the partners to make...