Value of Currency Itself What is the value of an individual piece of currency itself based on the efficiencies it allows in trade, in contrast to the value it represents?

For example, people often talk (complain) about the cost of manufacture of a single US cent coin being greater than one cent &mdash; but to me, this seems an irrelevant comparison.  A single coin will be used in many, many transactions over its lifetime, facilitating the efficient transfer of (possibly) thousands &mdash; or tens of thousands &mdash; of dollars.  Surely that is worth far more than one cent.

Without use of that coin, the parties involved may have had to round prices up/down, purchase multiple items at once, or forego certain transactions altogether.  Smaller denominations are useful by the same logic that drives public companies to split their shares, making it possible for people to purchase just a single piece of "penny candy" if they would like, as opposed to being forced to buy "five for a nickel" (or none at all.)

Beyond that, physical currency has a value simply in facilitating efficient trade.  If there weren't enough coins to go around, merchants may have to wait for somebody else to spend them (or the government may have to mint more, which raises its own issues since that also involves introduction of additional inflationary value) before customers have enough to conduct trades.

I realize these are somewhat unrealistic scenarios, since in practice there are typically enough pieces of currency around that trade isn't significantly impacted.  But this shouldn't change the fact that the currency is still increasing the efficiency of trade, in however minor a way, and that in virtue of the large number of trades in which those pieces of currency will (likely) be involved, the aggregated value becomes quite significant.

I want to strongly emphasize here that I am not looking for answers that address things like forex value, etc.  I've found it extremely difficult to even research this topic because of the multiple meanings of all the terms involved (just try searching for "use value of currency" and you'll see what I mean) and a satisfactory answer need only point me in the direction of appropriate articles/books, so long as they directly address the aspect of currency in which I'm interested here.

EDIT: I should also clarify that I'm not primary interested in coins.  That's just an example.  I'm interested in how to estimate the value that a currency provides through facilitating financial transactions, regardless of the physical nature of the currency (e.g. paper, metal, whatever.)
The value of something, in this case money, is based on it's demand; and since you want the value based on it's efficiency, not what it can purchase, you are looking for the value of money based on how efficient money is.
I believe I have just the answer for you. 

Your missing variable is the Velocity of Money. 
The demand for money and the Velocity of Money are inversely related. (your question emphasizes this point, "in contrast to the value it represents?".

The velocity of money (or the velocity of circulation of money") is a measure of how fast money passes from one holder to the next. It is most commonly measured as the income velocity of money, which is the frequency at which the average unit of currency is used to purchase newly domestically-produced goods and services within a given time period. In other words, it is the number of times one unit of money is spent to buy goods and services per unit of time.

Vt = PT/M
where 


Vt is the velocity of money for all transactions in a given time frame;
P is the price level;
T is the aggregate real value of transactions in a given time frame; and
M is the total nominal amount of money in circulation on average in the economy.
Thus PT is the total nominal amount of transactions per period.


Hope this helps.