The Valley Swim Club has 300 stockholders, each holding one share of stock in the club. Ashare of club stock allows the shareholder’s family to use the club’s heated outdoor pool during the summer, upon payment of annual membership dues of $175. The club has not issued any new stock in years, and only a few of the existing shares come up for sale each year. The board of directors administers the sale of all stock. When a shareholder wants to sell, he or she turns the stock in to the board, which sells it to the person at the top of the waiting list. For the past few years, the length of the waiting list has remained relatively steady, at approximately 20 names.

However, during the past winter, two events occurred that have increased the demand for shares in the club. The winter was especially severe, and subzero weather and heavy ice storms caused both the town and the county pools to buckle and crack. The problems were not discovered until maintenance crews began to ready the pools for the summer, and repairs cannot be completed until the fall. Also during the winter, the manager of the local country club had an argument with her board of directors and one night burned down the clubhouse. Although the pool itself was not damaged, the dressing room facilities, showers, and snack bar were destroyed. As a result of these two events, the Valley Swim Club was inundated with applications to purchase shares. The waiting list suddenly grew to 250 people as the summer approached.

The board of directors of the swim club had refrained from issuing new shares in the past because there was never a very great demand, and the demand that did exist was usually absorbed within a year by stock turnover. In addition, the board has a real concern about overcrowding. It seemed like the present membership was about right, and there were very few complaints about overcrowding, except on holidays like Memorial Day and the Fourth of July. However, at a recent board meeting, a number of new applicants had attended and asked the board to issue new shares.

In addition, a number of current shareholders suggested that this might be an opportunity for the club to raise some capital for needed repairs and to improve some of the existing facilities. This was tempting to the board. Although it had set the share price at $500 in the past, the board could set it at a much higher level now. In addition, any new shares sold would result in almost total profit because the manager, lifeguard, and maintenance costs had already been budgeted for the summer and would not increase with additional members.

Before the board of directors could make a decision on whether to sell more shares and, if so, how many, the board members felt they needed more information. Specifically, they would like to know the average number of people (family members, guests, etc.) that might use the pool each day during the summer. They would also like to know the number of days they could expect more than 500 people to use the pool from June through August, given the current number of shares.

The board of directors has the following daily attendance records for June through August from the previous summer; it thinks the figures would provide accurate estimates for the upcoming summer:

139 380 193 399 177 238

273 367 378 197 161 224

172 359 461 273 308 368

275 463 242 213 256 541

337 578 177 303 391 235

402 287 245 262 400 218

487 247 390 447 224 271

198 356 284 399 239 259

310 322 417 275 274 232

347 419 474 241 205 317

393 516 194 190 361 369

421 478 207 243 411 361

595 303 215 277 419

497 223 304 241 258

341 315 331 384 130

291 258 407 246 195


The board has developed the following criteria for making a decision on whether to issue new shares:

1. The expected number of days on which attendance would exceed 500 should be no more than 5 with the current membership.

2. The current average daily attendance should be no more than 320.

3. The average daily weekend (Saturday and Sunday) attendance should be no more than 500. (Weekend attendance is every sixth and seventh entry in each progression of seven entries in the preceding data.)

If these criteria are met, the club will issue one new share, at a price of $1,000, for every two average attendees between the current daily average and an upper limit of 400.

Should the club issue new shares? If so, how many will it issue, and how much additional revenue will it realize?

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