Average Life of Loan Calculation
Definition
The Average Life of a loan is the average number of years that
principal is outstanding.
Here is a simple example:
The average life = 10 blocks / 4 dollars = 2.5 years
The Numerator is the total number of blocks (10), and the Denominator is the number of principal dollars that are borrowed. Each "Block" represents one dollar of principal outstanding for one year.
In the simple case there is only one answer.
Three Possible Methods
Unfortunately, in more complex cases there are at least three possible
answers. This is because, although there is only one way to determine
the numerator, there are three ways to determine the denominator:
Here is a simple, but extreme, case:
There are 20 blocks, so the numerator is 20.
Using Method 1 (initial funding) the Denominator is 1, so the average life equals 20/1 or 20 years, which is clearly a bad answer.
With Method 2, the Denominator would be 1 + 4 + 5 + 5 = 15, so the average life would be 20/15 = 1.33 years.
Since the highest principal balance in the example is 6, Method 3 would produce 20 / 6 = 3.33 years.
Method 3 provides what seems like the most intuitive answer. But the difference between methods 2 and 3 hinge on the interpretation of additional fundings.
Interpretation of Additional Fundings
For example:
The question is, in this example are 'a' and 'b' separate dollars that
each have an average life of one year (method 2), or is 'b' simply 'a'
borrowed again, such that 'a' and 'b' represent the same dollar borrowed
for two years (method 3).
The following example will demonstrate why method 3 is preferable to method 2:
We can see that in the first three examples method 2 leads to an average
life of 2.33 years, and that moving the block forward has no effect
on the calculation until the last step, in which it suddenly changes
and agrees with method 3.
Method 3 (highest principal balance) produced the same answer in every case. Therefore, method 3 seems to provide the most consistent and intuitively obvious answer.
SuperTRUMP uses the highest principal balance for the denominator in its average life calculations.
