At the outset, please note that this post focuses on water shares, not water rights. To understand the distinction, visit here and here. Water rights should already have acre-foot quantities associated with them--with the exception of certain circumstances, including undefined sole supply amounts for a water right.
The amount of water associated with a share in a water company (irrigation company, ditch company, canal company, etc.) is not consistent between companies. As an example, there is one water company that I know of where 1 share is equal to 1/10th of an acre-foot of water, and there is another water company that I know of where 1 share is equal to 6 acre-feet of water. The determination of how many acre-feet are associated with each share in a water company is, for the most part, a function of three components: (1) how many total acre-feet the water company is entitled to under its water rights, leases, contracts, etc.; (2) how many shares have been issued in the water company; and (3) how much water the water company's source(s) are able to produce.
As an example, suppose that a water company's water rights, in total, allow for the diversion of 1,000 acre-feet of water from a river for the irrigation of 250 acres (assuming the water company is in an area of the state where the duty is 4 acre-feet per acre). Further suppose that the water company has issued 250 shares of stock. On paper, each share would entitle the owner to irrigate 1 acre with 4 acre-feet of water. Thus, each share represents 4 acre-feet of water. But if it is a drought year and the river is running low, each shareholder may not actually receive 4 acre-feet of water per share.
Some water companies know how many acre-feet are represented by each share, usually because of shareholder change applications or other applications that have previously been filed with the Utah Division of Water Rights. In fact, the Division keeps a list of water companies, and the list includes a spot for information about the number of acre-feet per share. Some companies have this information (see example below), but most do not. The reality is that many water companies will not know how many acre-feet are represented by each share, and a determination of this number could take some investigation, research, and calculation.
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