**Subject:** Buy or bind

From: Walter Henry <*whenry*>

Date: Saturday, May 12, 1990

Date: Saturday, May 12, 1990

[As most of you know, I am usually bored blind by messages that don't pass through at least one networked computer, but the other day Hilary Kaplan phoned with a subject so interesting that I overlooked the dullness of the medium. She asked for comments on the matter of whether a library would be better off paying a premium for new hardcover books or, instead, buying paperbacks and immediately having the books rebound by their library binder. The hypothesis, obviously, is that trade bindings are so miserable that you almost certainly need to rebind them eventually, so why not save the premium and do it all at once. Here is a response, sent to Hilary Sat 05-26-1990]: hilary, I've given your question a bit of thought and have at least a suggestion of an answer. In order to work it through we need to accept a few working assumptions: (A1) When a book is rebound it has a functionally infinite life (obviously not true, but for the purposes of this model it is close enough) (A2) The cost of Rebinding Later is the same as the cost of Rebinding Sooner. That is, except for inflation, there will be no change in the rebinding costs (no change resulting from economies of scale, introduction of new technologies, changing labour environment, etc.). We will do all calculations in current dollars, ignoring the effects of inflation. Now, the gist of the question is this: we can either invest money at some point in the future, retaining use of our money until then [Deferred Rebinding (DR)] or we can invest the money now and lose the use of it [Immediate Rebinding (IR)] As any stinking running dog capitalist capitalist will tell you, investing money (ie using the use of it) carries a measurable cost, usually expressed as an interest rate, and in our case, we are concerned with the interest rate adjusted for inflation. In other words, we are interested in how much money the investment would throw off, in current dollars, if it were left in the endowment instead of being invested in IR. To by a new book hardbound, we incur a premium. The new hardbound book has some expected Time to Failure (TTF). We may not know what this time is, but in order to make our decision we will have to find some way to estimate it. We could, for example, do a survey and estimate the mean TTF (or better yet the median, which is resistant to outliers) Clearly, there is some value of the TTF of the trade binding at which the cost (ie investment value) of IR exceeds the premium. If the expected TTF of any item is greater than this value, then it is profitable to Defer Rebinding. Otherwise IR will be more profitable. The calculation is fairly straightforward. We are looking for the number of compounding periods that it takes for our investment (the Rebinding Cost (RC)) to grow to (Rebinding Cost + Premium), which is given as ln( (RC+Premium) / RC) ---------------------- ln(1+PeriodicInterestRate) Note that RC should be the total real cost of rebinding, including staff time, overhead, etc., because the value we need is the amount of money that is being removed from the endowment. The Hardcover Premium is simply the difference between the real cost of a new hardcover and a new softcover. For the sake of this exercise, let us add the following assumptions (A3) Money is worth 5% after inflation. This is a realistic figure that is sustainable over the long-term. (A4) Interest compounds Monthly (arbitrary). Thus the Periodic Interest Rate is .05/12. (Different compounding rates don't make a huge difference in the results). The table below gives time in months (expected TTF) at which it becomes more profitable to do buy the hardcover. An example: If a given Hardcover book costs $9 more than a softcover, and your total cost of rebinding (including overhead) is $25, then you should buy the hardcover if you expect that (particular) copy to last more than 74 months (6 years). Otherwise, do IR. In other words, unless the book is to be placed on Physics Reserves or given some other Seal of Doom, the chances are that you will save money by buying the hardcover and deferring rebinding until the little guy actually needs it. Hard- Investment (Cost of Rebinding) Cover $5 $15 $25 $35 $45 $55 $65 Premium ----------------------------------------------------------- $1 | 44 16 9 7 5 4 4 $2 | 81 30 19 13 10 9 7 $3 | 113 44 27 20 16 13 11 $4 | 141 57 36 26 20 17 14 $5 | 167 69 44 32 25 21 18 $6 | 190 81 52 38 30 25 21 $7 | 211 92 59 44 35 29 25 $8 | 230 103 67 50 39 33 28 $9 | 248 113 74 55 44 36 31 $10 | 264 123 81 60 48 40 34 $11 | 280 132 88 66 53 44 38 $12 | 294 141 94 71 57 47 41 $13 | 308 150 101 76 61 51 44 $14 | 321 159 107 81 65 55 47 $15 | 333 167 113 86 69 58 50 $16 | 345 175 119 91 73 61 53 $17 | 356 182 125 95 77 65 56 I don't know what real values of RB should be (Ella Harsin might be able to provide these), but the model is simple, and it will be trivial to plug in better values if desired. Estimating the TTF for a given volume (or the maximum likelihood estimator of central tendency for a given class of volumes (eg the mean or median TTF for smythe-sewn art books with rigid spines) is, of course, not a trivial matter. If you are really serious about this stuff, it wouldn't be too terribly hard to set up a Time Series study to measure Time To Failure. The techniques would come from Life Testing, a somewhat specialized branch of statistics, but it shouldn't be too difficult to find a consultant. You could probably knock off a reasonable survey for a few grand and get a nice publication to boot. Hope this helps, w *** Conservation DistList Instance 4:1 Distributed: Tuesday, May 12, 1990 Message Id: cdl-4-1-005 ***Received on Saturday, 12 May, 1990

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