One way to assess the value of the copyright is look at what booksellers actually paid for it. For example see "The Hoyle Copyright in Hoyle's Lifetime" where we see transactions for shares of the Hoyle copyright implying a value of £187 10s. in 1763 and £261 in 1767.

But how might a bookseller decide how much to pay for a copyright? In this post I am going to present a simplified model for valuing the Hoyle copyright. If the results seem reasonable, I will do the extra work of removing the simplifications.

**Timing of Valuation**

The model will value the copyright only at the book is about to be reprinted, the time time when it is most valuable. Booksellers make money from the copyright by printing new books for the cost of printing, paper, advertising, etc., and selling the books to retail booksellers (and perhaps wholesale booksellers as well; see the discussion below). When a book has just printed, the opportunity to produce new books and thus to make money from copyright ownership must wait until it goes out of print, reducing the value of the copyright. See the discussion in Belanger,

*Booksellers' Sales of Copyright: Aspects of the London Book Trade 1718-1768*. Ph. D. Dissertation. Columbia University. 1970 at pages 105-8. When we compare the model's prediction of copyright value with actual sales, we will have to note the timing of the sales with respect to reprinting.

**Data**

The Longman Archives give us detailed information about print runs and expenses for the Charles Jones edition of

*Hoyle's Games Improved*and the G. H. edition of

*Hoyle's Games Improved and Enlarged*from 1796 to 1868. I am going to use the Longman data from 1796 to 1826 because the data are more consistent year-to-year, letting me work with averages without distorting things greatly.

Printing of the Jones Hoyle. Data from the Longman archives. |

*Hoyle*was reprinted every five years with production expenses averaging £304 and retail sales £1082.

Aside: There are some details I'm overlooking. For example the publishers would often issue sections of the book separately. See for example "Hoyle's Games Improved, Charles Jones (1800)" where I note that the publishers excerpted the treatise on game cocks and issued 500 copies. That would account for a small portion of the expenses (500 of 42,500 sheets) and bring in small additional revenue (although it was a very poor seller, with perhaps half the stock unsold fifteen years later). Similarly, portions of the book were issued separately with each edition from 1803 to 1820. It would be possible to extend the model to account for these separate issues which were governed by the same copyright.

**Assumption**

The model values the copyright at two points in time, five years apart. These are both times when the book is about to be reprinted, so we won't have the timing problem discussed above. The major assumption of my model is this:

*the value of the copyright is the same at the beginning and end of the five-year period.*This assumption would be silly for a typical book where the sales are uncertain. If the book sold well, the value of the copyright would increase; if it sold poorly, the value would decrease, perhaps to zero. Hoyle is an unusual case, a perenniel best-seller, where the booksellers could count on selling an entire print run of 3000 or 4000 books every five years.It seems reasonable that with unchanged prospects for the book, the value of the copyright would be unchanged as well. Perhaps the same model would apply to other best sellers such as bibles, almanacs, and school books.

A lesser assumption is that the bookseller will sell 1/5 of the books at the end of each of the five years. This is unrealistic because the book would likely sell best when it was newly published, with diminishing sales over time. Second it defers each year's sales to the end of the year--a monthly model with decaying sales would be more realistic.

Finally, I am ignoring the generous credit terms that prevailed at the time. Publishers would not pay printers immediately--six months credit was not uncommon. Similarly, publishers extended generous credit to the wholesale and retail booksellers.

**The Model**

The model assumes the following cash flows:

- At the end of year 0, the bookseller purchases the whole copyright.
- At the end of year 0, the bookseller pays for a print run (£304)
- At the end of each year 1 through 5, the bookseller sells 1/5 of the books at some percentage of the retail price of £1082 (see discussion below).
- At the end of year 5 the bookseller sells the copyright for amount originally paid.

Second, it is not appropriate to credit the copyright owner with the full retail price of the book. Some of that profit is attributable to retail bookselling rather than publishing. Indeed there was a third role of wholesale bookselling that existed at the time. There would be separate prices from the publisher to wholesaler, wholesaler to retailer, and retailer to the public. Even where a bookseller played all three roles, we must determine a publisher's price to determine how much revenue is attributable to publishing rather than distribution.

From my reading in the early 19th century book trade, it appears that the wholesale price is about 60-75% of retail. See for example James J. Barnes,

*Free Trade in Books. A Study of the London Book Trade*since 1800. Oxford: Clarendon Press. 1964. p22. I haven't seen discussion of a publisher's price, but there is evidence that for Hoyle, it was 40% of retail. When Hoyle was reprinted in 1803, 72 copies remained unsold from the 1800 edition of 3000 copies. The copyright owners include the value of those unsold books as an expense against printing the 1803 edition at 2s. per copy. The retail price was 5s., providing evidence of a publisher's price of 40% of retail. (from the Longman Archive). For the model, I'll look at the publisher's price varying from 40 to 60%.

**The Model's Output**

Given a discount rate, and a publisher's price, and given that the value of the copyright is the same in the end of year 0 and year 5, you can uniquely solve for the value of the copyright.

Value of Copyright |

I plan to share the model with friends in finance and with book historians. Next essay, I'll share their feedback and compare the modeled value of the copyright with what booksellers actually paid. More soon!

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