A competitive segment recorded 18 closed sales in the first 3 months of the past year and 63 closed sales in the following 9 months. There are 54 active listings now. Using the average monthly sales pace over the full 12 months, what months of supply is indicated? Round to one decimal place.
Correct Answer
B) 8.0 months
The 12-month pace is total sales divided by total months: (18 + 63) / 12 = 6.75 sales per month, and 54 / 6.75 = 8.0 months. Averaging the two period rates (6 and 7 per month) as if the periods were equal gives 6.5 and 8.3 months; dividing all 81 sales by 9 months gives 9.0 per month and 6.0 months, and using only the 3-month rate gives 9.0.
Why This Is the Correct Answer
Option B is correct because the full 12-month pace is 81 sales / 12 months = 6.75 per month, and 54 listings / 6.75 = 8.0 months of supply.
Why the Other Options Are Wrong
Option A: 6.0 months
Option A, 6.0 months, divides the full year's 81 sales by 9 months instead of 12: 81 / 9 = 9.0 per month, and 54 / 9.0 = 6.0. The sales cover 12 months, so the pace is 81 / 12 = 6.75, giving 8.0 months.
Option C: 8.3 months
Option C, 8.3 months, averages the period rates of 6 and 7 equally to get 6.5, then 54 / 6.5 = 8.3. The 9-month period should carry three times the weight of the 3-month period; the weighted pace is 81 / 12 = 6.75, giving 8.0 months.
Option D: 9.0 months
Option D, 9.0 months, uses only the first-quarter rate of 18 / 3 = 6.0, so 54 / 6.0 = 9.0. The full 12-month pace of 6.75 gives 8.0 months.
Total sales over total months
To average paces across uneven periods, add up all the sales and all the months first, then divide.
How to use: Use this whenever sales counts come from periods of different lengths.
Exam Tip
If the periods differ in length, a simple average of their rates is a trap; compute one overall rate from the totals.
Common Mistakes to Avoid
- -Averaging rates from periods of different lengths equally
- -Using only one sub-period when the full-year pace is asked for
- -Dividing the year's sales by the wrong number of months
Concept Deep Dive
Analysis
The question tests weighting. The two periods are of unequal length, so their monthly rates cannot be averaged equally; the full-year pace is total sales over total months. Once the pace is correct, months of supply is listings divided by monthly sales.
Background Knowledge
Months of supply relates current inventory to the rate at which comparable properties are selling. When sales are reported for periods of different lengths, the average pace over the combined period is total sales divided by total months, which weights each period by its length.
Real-World Application
An appraiser's MLS export splits a year into a slow winter quarter and a busier spring through fall. To report months of supply on a full-year pace, the appraiser totals the year's closed sales and divides by 12 rather than averaging the two period rates.
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