For those that may not be familiar with the concept, I would like to discuss economies of scale.
This would be where, given a standard unit of measurement (in this case, an acre), there is an inverse relationship between quantity and value per unit. Where 1 acre may be worth $50,000, 5 acres may be worth $40,000 per acre or $200,000, and 10 acres may be worth $25,000 per acre or $250,000.
A common method of expressing value is on a per unit basis.
We could examine the relationship between a subject and a selection of comparable sales in different ways.
We could consider natural break points.
Let's say the subject is an 8-acre lot. There are 3 comps; 1 acre ($50,000), 5 acre ($200,000), and 10 acre ($250,000).
Using natural break points, 1 acre is worth $50,000, 5 acres is worth 1 acre @ $50,000 plus 4 acres @ $37,500 per acre, and 20 acres would be worth 1 acre @ $50,000 plus 4 acres @ $37,500 per acre plus 5 acres @ $10,000 per acre.
In comparison to the subject property of 8 acres:
The 1-acre lot could be adjusted at (4x$37,500)+(3x$10,000) or +$180,000 with an adjusted sale price of $230,000.
The 5-acre lot could be adjusted at (3x$10,000) or +30,000 with an adjusted sale price of $230,000.
The 10-acre lot could be adjusted at (-2x$10,000) or -$20,000 with an adjusted sale price of $230,000.
The range of adjusted sale prices is a point value of $230,000. The subject's indicated value is $230,000.
Conversely, you could perform linear analysis of the properties
We have our three previous sales of 1-, 5-, and 10-acres and their indicated price per acre. Our subject property is 8 acres. Economies of scale would dictate that the value per acre of the 8 acres should be somewhere between price per unit of the 5- and 10- acre parcel. One could do use an HP-12C or equivalent and do a linear regression analysis, but that doesn't translate well to a reader. So, let's use Excel to create table depicting the relationship of the subject and comparable sales and create scattergram to graphically depict the relationships between lot size and price per unit. A copy of the table and the chart is shown below.
After placing a linear trend line on the chart, one could eyeball where the line crosses 8 units and see that the value should be somewhere around $31,000 per acre. Using the 12C, the value per unit is calculated to be $30,900 (rounded). Inserting that value into the table, one can visually see that the estimated value per unit is a near perfect fit. The correlation coefficient (r2) also indicates a near perfect fit. At $30,900 to $31,000 per unit, the indicated value for an 8-unit parcel is $247,200 to $248,000. With appropriate rounding, a value opinion of $248,000 is reasonable and well supported.
So we have two value indications for the subject: $230,000 and $248,000. Which one is right and which one is not? Based on the data available, both are credible. The sale data was insufficient to be truly statistically meaningful. Additional data may reveal additional breakpoints in the comparable sales. Method 2 is essentially a continuous pattern of breakpoints. That may not be completely accurate.
I would say that any final value opinion between $230,000 and $248,000 or $28,750 and $31,000 per acre is reasonable. One could use both approaches and reconcile to $30,000 per acre or $240,000.
So, it would appear there are a number of different ways to kill a bird.