Expert: Josh - 1/23/2010

Question
QUESTION: Hello:


I read the following in a textbook and was somewhat confused by what was written:

"A mill is $0.001. A tax rate of 80 mills is a tax rate of $80 per $1000 of assessed value."


When I converted the 80 mills, the amount became $0.08. If one mill is $0.001, then 80 mills will be 80 times $0.001, which is $0.08. I assume that this is equivalent to $80 per $1000.


If a house and property is assessed at $100,000, the tax will be $8000, $100,000/$1000 X $80.00. The same amount is obtained if the $100,000 is divided by $1.00 and them multiplied by $0.08.

Why do you think the author appeared to go from $0.08 per $1.00 to $80.00 per $1000 of assessed value?



ANSWER: Hi Kenneth,

All of these are equivalent. I see no distinction between any of these.
After all, 0.08/1 is the same ratio as 80/1000.

---------- FOLLOW-UP ----------

QUESTION: Hello:

I want to thank you for your reply and comments.

From the above quotation: "a mill is $0.001."

Does this quote represent that 1 mill equals $0.001 per $1.00 of assessed value?

ANSWER: Yes, absolutely. We should not think of the "mill" as a dollar figure per se. It actually represents a ratio. So, what is the ratio relative to? The ratio is 0.001:1 (i.e., 0.1 cent per dollar OR 0.1%).

---------- FOLLOW-UP ----------

QUESTION: I want to thank you for your reply.

What calculation would you use to convert mills to dollars?

For example, 5.753 mills equals how many dollars?

Answer
As I mentioned in my previous reply, we should not think of "mill" as a denomination. It simply represents a ratio, so it has no units. It makes no sense to convert it in terms of "dollar".

Think of 1 "mill" as specifying a ratio of 1/1000, OR 0.1%.
Then, whatever amount you are interested in, for instance, 5.753 "mills" is strictly equivalent to 5.753*1/1000 or 0.5753%. Altogether, "5.753 mills" still represents nothing but a ratio.

It just turns out that in finance, people are dealing with things measured in dollars. So, for example if you sell something for $2000.00 via an agent who charges a commission of 5 mills, then $2000 * 0.5% = $10 will be deducted. As you can see, "5 mills" acts like a multiplier. It is a proportion relative to something yet to be specified. The amount to be charged only becomes apparent when one specifies a monetary value "viz., $2000" and this is what the 0.5% (or 5 mills) is relative to.

When we deal with other problems, e.g., chlorination of water, or finding the amount of salt in a tank of sea water, we can still use the same idea. for example, suppose the salt content is 0.5% (5 milli-Liter per Liter). Here the 2000 might be measured in Gallon (instead of dollar), but the amount (of salt) is still calculated in the same way: e.g., as 2000 [Gallon] * 0.5% = 10 [Gallon].

So, you can think of 5.753 mill as ($0.005753/$1 or 0.5753 cent per dollar). This is a ratio without units. Until you multiply this by some dollar amount, it makes no sense to convert it into a dollar figure. Now, some may say that "5.753 mill is equivalent to 0.5753 cent". This is not technically correct, although people can sort of understand what it is saying. The implicit assumption is that this represents a ratio of 0.5753 cent per unit of dollar. Again, ratios, fractions, percentages etc. have no unit.