AP Answer Final

Topics: Net present value, Mathematical finance, Time Pages: 6 (1477 words) Published: April 5, 2015


Arundel Partners: The Sequel Project


Ngai Chiu Wing Edward / 51042814
Ng Cheuk Yiu Hugo / 50649257
Lau Chau Nan, Evelyn / 9700 4330
Kuo, Constantino / 5106 4265
Pang Hhong Yu, Francesca / 50191000
Ng Ka to, Irin / 9747 5858
Suen Hung Kit, Philip / 5114 4321
Kuok, Kenneth / 5101 2428

Estimate the per-film value of a portfolio of sequel rights such as Arundel proposes to buy. You will try two different methods to solve this problem: some appropriate DCF approach, and the Black-Scholes approach. You may find it helpful to consult the Appendix, which explains how these figures were prepared. (Suppose the appropriate discount rate for risky cash flows is 12%. Risk-free rate, for discounting safer cash flows, is at 6%.)

The central stone of Arundel partners’ project is to establish a correct price for the whole rights portfolio. To do this two methods are presented: a) calculating the hypothetical sequel performances and obtaining a total value of investment using an appropriate rate for discounting to present time b) using a simple Black-Scholes options pricing model to calculate the price of the rights call. The data which we will use to compute our calculations was provided by David Davis and the Paul Kagan Associates which are presented in exhibits 6 to 9.

Calculating the NPV of all the profitable sequels of a studio.

The data used assumes that the sequel’s estimated negative cost and US theater rentals are 120% and 70% respectively, of the corresponding items for the first film. On exhibit 7 we find the present value at year 4 and the PV of the negative cost at year 3 from the hypothetical sequels. Since the right of a film give us the opportunity to decide weather investing into the sequel is profitable, the decision is made on Year 3. If at that time the first film had no big success, the sequel would be immediately discarded, thus no investment would be made and the chances of loss would be null. The following drawing presents the option on the sequel of a film:

Since the positive branch of the tree would be the only path really followed, we will only take into account those films which have a positive NPV. From the hypothetical sequel data we discount the net inflows at year 4 and negative costs at year 3 to the present time at year 0. The table below shows the 26 sequel films that have a positive NPV. The total sum of the 26 sequels account for 490.1 M$ which divided by all the 99 portfolio sequels gives us a price of 4.95M$ per film.

Calculating the value of a right with the B-S-M model.

This approach consists of using the B-S option pricing formula to model the portfolio right of the sequels. The variables of the BS model for a set of stochastic variables are So, K, r, T, and sigma. And we apply it on the portfolio in the following way:

the PV of the portfolio value
the average negative cost of the set of films
the risk free rate at 6%
the time in which the decision of making the sequel is made (Y 3) 3
the standard deviation of the sequels return

Using the data on Exihibit 7, we can obtain the mean values of the Portfolio value at Y4 which we will discount to Y0 using a rate of return of 12% for risky businesses. The strike price K will be the mean value of the negative cost of films. The time T for the maturity of the right will be set on Y3, time in which the production of the sequel must be decided. Finally sigma, will be the standard deviation of the one-year returns of all the films of the portfolio. The results are summarized in the above table. If we were to use the Call option table the inputs for moneyness and Cumulative volatility would be: Moneyness: 0.72483

Cumulative Volatility: sigma*sqrt(T) = 1.21
The nearest value on the table would be 35.5% to equate C/S, but we will use a Call option...
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