Buy or bind

[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
                                  ***