Dividends, Dividends, and Dividends It was September 1, 1995, and Jack Williams, a portfolio manager, was facing a couple of thorny issues related to the valuation of options on dividend-paying stocks. Hoping to balance out the portfolio of one of his more important accounts, Williams was looking with particular interest at the call option on the stock of Amerplex, a high-tech company that had gone public only five years earlier. During the last five years, the stock had done well. (The monthly stock price history is shown in Exhibit 1.) Two years earlier, it had initiated a cash dividend of $.05 per share payable quarterly which was subsequently increased to $.10 (see Exhibit 2 for a complete dividend history of Amerplex). On August 30, 1995, Amerplex announced that it would pay the regular dividend of $.10 plus a special $0.40 cash dividend on November 15, with a holder-ofrecord date of October 20, 1995. Williams was considering purchasing a significant amount of call options on Amerplex with an exercise price of $8 and a maturity date of December 1, 1995. Williams believed that Amerplex was currently underpriced, and although he wanted a position in the stock, he did not have the cash available to buy the stock itself. He was expecting a large cash deposit on December 1, however, and wanted to use the options today to lock in the current price of $8 per share. The options would have to be over-the-counter call options, which Williams would purchase from an investment banking firm. Listed options on Amerplex were not currently available, but Williams was able to collect some interest rate information (see Exhibit 3). The issue for Williams was how to price these options. He wanted to have a reasonable estimate of the potential value of the call options before he entered into negotiations with the investment banking firm. While in graduate school, Williams had studied the Black-Scholes model for pricing European call options, but was not sure that he could use this model in this situation. Of course, as part of the negotiations with the investment bank, he knew that he could specify that he wanted the call options to be European or American. He was not even sure that this choice would make a difference, but he wanted to consider both. This case was prepared by Robert M. Conroy, Professor of Business Administration. This case was written as a basis for class discussion rather than to illustrate effective or ineffective handling of an administrative situation. Copyright 1996 by the University of Virginia Darden School Foundation, Charlottesville, VA. All rights reserved. To order copies, send an e-mail to dardencases@virginia.edu. No part of this publication may be reproduced, stored in a retrieval system, used in a spreadsheet, or transmitted in any form or by any means electronic, mechanical, photocopying, recording, or otherwise without the permission of the Darden School Foundation. Rev. 7/02.
-2- A major question for Williams was what impact the dividend payment would have. Because the holder-of-record date was October 20, 1995, the ex-date 1 for the dividend payment would be October 16, 1995. On this date, the stock price would drop by approximately the amount of the dividend. 2 Since the exercise price of the call option is not adjusted for this price drop, the call option could thus be viewed either as an option on the stock with the dividend before the ex-date or as an option on the stock without the dividend after the ex-date. Williams was concerned about how this situation would affect his valuation of the call option. Would it force him to exercise the option early and, if so, how should he handle this circumstance in valuing the call option? The Average (Asian) Option At the same time, Williams was facing a different situation with regard to another portfolio. He needed to purchase shares in Deal Corporation over the next three months, the result of an agreement with a pension fund. (Deal had not paid a dividend for the last five years and was not expected to resume dividend payments in the near future.) On the first day of the month for the next three months (October 1, November 1, and December 1), the pension fund would supply cash for the purchase. In total, $6,000,000 would be provided, but the exact amount of cash that would be available at the beginning of any month was uncertain. Ideally, the pension fund wanted to fund the purchase in equal installments of $2,000,000, but circumstances might dictate that the amount available in any given month would vary. By the same token, any shortfall or overage in October or November would be made up or subtracted in December to make the total $6,000,000. The key issue for Williams was that he really wanted to lock in the price of the stock. Deal was trading at $20 per share, and Williams was concerned that the price could change substantially over the next three months. Williams knew that he could purchase call options with a strike price of $20 per share and maturity dates of October 1, November 1, and December 1. (Exhibit 4 shows the price quotes from an investment bank for options with these maturities and a strike price of $20.) He wondered, however, if there might be a more effective method of purchasing the options. One alternative that Williams had read about involved using an average option, a new type of option which would pay in cash the difference between an average value and the strike price of the option. In this particular situation, Williams would be interested in an option that would pay the difference between the simple average of the stock prices on October 1, November 1, and 1 The ex-date for a dividend is the day on which the stock is sold without the dividend payment. On this date, buyers of the stock do not receive the dividend payment. The ex-date is four working days before the holderof-record date. Because settlement of the sale of shares of stock takes five days (i.e., the purchaser does not officially own the stock until five days after the date of sale), purchasers on the ex-date will not officially own the stock until the day after the holder-of-record date. Thus, they do not receive the dividend. 2 The empirical evidence is somewhat mixed on the exact percentage of the dividend by which the stock price will drop. Generally, however, it is assumed that the stock price will drop by the full amount of the dividend on the ex-date.
-3- December 1 and a strike price of $20. For example, if Williams bought one share of Deal on October 1 at $22, one share on November 1 at $19, and one share on December 1 at $23, and at the same time had purchased three average options with a strike price of $20, his net cost on December 1 for the shares would be $64 less the $4 gain on the average option position 3 for a total cost of $60, or $20 per share. Williams had two questions: (1) What would be the advantages and disadvantages of purchasing individual options that mature on October 1, November 1, and December 1 compared with the average option? (2) How should he price an average option? He needed a good estimate of the value before he began to deal with the investment bankers. Without such an estimate, he would have to take the investment bank s estimate at face value. In addition, he would not be comfortable negotiating terms. If he could understand how to value this type of option, he could then understand how different terms could affect the value of the option. 3 The average stock price was ($22 + $19 + $23) / 3 = $21.33333. The gain on each option would be $1.3333 and if three were purchased the total gain would be 3 x $1.33333 = $4.
-4- Exhibit 1 Amerplex Monthly Stock Price Date Stock Price Date Stock Price Aug-01 90 $ 4.25 Mar-01 93 $ 6.21 Sep-01 90 4.92 Apr-01 93 6.00 Oct-01 90 4.65 May-01 93 6.40 Nov-01 90 5.20 Jun-01 93 6.20 Dec-01 90 5.59 Jul-01 93 6.35 Jan-01 91 5.67 Aug-01 93 6.49 Feb-01 91 5.22 Sep-01 93 6.87 Mar-01 91 5.78 Oct-01 93 7.40 Apr-01 91 5.42 Nov-01 93 7.03 May-01 91 5.38 Dec-01 93 6.79 Jun-01 91 4.93 Jan-01 94 6.27 Jul-01 91 4.80 Feb-01 94 5.56 Aug-01 91 4.97 Mar-01 94 6.15 Sep-01 91 5.01 Apr-01 94 6.33 Oct-01 91 5.16 May-01 94 5.81 Nov-01 91 4.87 Jun-01 94 6.21 Dec-01 91 5.23 Jul-01 94 6.85 Jan-01 92 5.31 Aug-01 94 5.92 Feb-01 92 5.37 Sep-01 94 6.46 Mar-01 92 5.17 Oct-01 94 6.79 Apr-01 92 4.96 Nov-01 94 5.95 May 01 92 4.90 Dec-01 94 6.50 Jun-01 92 5.27 Jan-01 95 6.88 Jul-01 92 5.23 Feb-01 95 6.07 Aug-01 92 5.54 Mar-01 95 6.85 Sep-01 92 5.72 Apr-01 95 7.21 Oct-01 92 5.25 May-01 95 6.75 Nov-01 92 5.50 Jun-01 95 7.15 Dec-01 92 5.30 Jul-01 95 7.45 Jan-01 93 5.76 Aug-01 95 7.61 Feb-01 93 5.99 Sep-01 95 7.98
-5- Exhibit 2 Type Div. Rate Ex-date Holder of Record Date Pay Date Qtr. $ 0.10 Jul-10-95 Jul-14-95 Sep-01-95 Qtr. 0.10 Apr-10-95 Apr-14-95 Jun-01-95 Qtr. 0.10 Jan-10-95 Jan-14-95 Mar-01-95 Qtr. 0.10 Oct-12-94 Oct-17-94 Dec-01-94 Qtr. 0.10 Jul-11-94 Jul-15-94 Sep-01-94 Qtr. 0.05 Apr-11-94 Apr-15-94 Jun-01-94 Qtr. 0.05 Jan-07-94 Jan-13-94 Mar-01-94
-6- Exhibit 3 Treasury Bills Maturity Days to Maturity Bid Ask Chg. Ask Yld. Sep-07-95 6 5.41 5.31-5.39 Sep-14-95 13 5.45 5.35 +0.04 5.43 Sep-21-95 20 5.37 5.27 +0.01 5.36 Sep-28-95 27 5.37 5.27-5.36 Oct-05-95 34 5.37 5.33-0.01 5.43 Oct-12-95 41 5.41 5.37-5.48 Oct-19-95 48 5.35 5.31-5.42 Oct-26-95 55 5.39 5.35 +0.01 5.47 Nov-02-95 62 5.4 5.38-5.51 Nov-09-95 69 5.41 5.39-5.52 Nov-16-95 76 5.39 5.37-5.51 Nov-23-95 83 5.4 5.38 +0.01 5.52 Nov-30-95 90 5.39 5.37 +0.01 5.52 Dec-07-95 97 5.39 5.37-5.52 Dec-14-95 104 5.39 5.37-5.53 Dec-21-95 111 5.36 5.34-0.01 5.50 Dec-28-95 118 5.37 5.35-5.52 Jan-04-96 125 5.38 5.36 0.02 5.54 Jan-11-96 132 5.36 5.34-5.52 Jan-18-96 139 5.3 5.28 +0.01 5.46 Note: The Ask Quote is determined as follows: 100 Ask Pr ice 360 = Ask Quote. 100 #of days Ask Yield is determined as: 100 Ask Pr ice Ask Price 365 # of days = Ask Yield.
-7- Exhibit 4 Investment Bank Custom Options Quotations Current Stock Price Strike Price Expiration Date Call Price $ 20.00 $ 20.00 Oct-01-95 $ 0.64 20.00 20.00 Nov-01-95 0.91 20.00 20.00 Dec-01-95 1.21 20.00 20.00 Jan-01-96 1.42 20.00 20.00 Feb-01-96 1.52 20.00 20.00 Mar-01-96 1.67 20.00 25.00 Oct-01-95 0.00 20.00 25.00 Nov-01-95 0.01 20.00 25.00 Dec-01-95 0.05 20.00 25.00 Jan-01-96 0.11 20.00 25.00 Feb-01-96 0.19 20.00 25.00 Mar-01-96 0.26