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Difficulty: MediumWeighted Averages in Applied Contexts

A commercial real estate company manages three office buildings: Building A, Building B, and Building C. Building A contains 20,00020,000 square feet of rentable space leased at an average rate of $45\$45 per square foot per year. Building B contains 30,00030,000 square feet of rentable space leased at an average rate of $50\$50 per square foot per year. Building C contains 50,00050,000 square feet of rentable space. If the overall weighted average rental rate for all three buildings combined is $52\$52 per square foot per year, what is the average annual rental rate per square foot, in dollars, for Building C?

Answer: 56 dollars

Answer

The average annual rental rate for Building C is 5656 dollars per square foot.
To find the average annual rental rate for Building C, determine the total revenue generated by all three buildings combined. With a total square footage of 20,000+30,000+50,000=100,00020,000 + 30,000 + 50,000 = 100,000 sq ft and an overall weighted average rate of $52\$52/sq ft, the total revenue is 100,000×52=5,200,000100,000 \times 52 = 5,200,000 dollars. Subtracting the revenue generated by Building A (20,000×45=900,00020,000 \times 45 = 900,000 dollars) and Building B (30,000×50=1,500,00030,000 \times 50 = 1,500,000 dollars) leaves 5,200,000−2,400,000=2,800,0005,200,000 - 2,400,000 = 2,800,000 dollars that must be contributed by Building C. Dividing this by Building C's 50,00050,000 square feet yields an average rate of 5656 dollars per square foot.

Step-by-Step Solution

1
Determine total combined rentable area and total combined revenue
Total area =20,000+30,000+50,000=100,000= 20,000 + 30,000 + 50,000 = 100,000 sq ft. Total revenue =100,000×52=5,200,000= 100,000 \times 52 = 5,200,000 dollars.
Weighted average rate multiplied by total square footage gives total annual rental revenue across all properties.
2
Calculate known annual revenues from Building A and Building B
Building A revenue =20,000×45=900,000= 20,000 \times 45 = 900,000 dollars. Building B revenue =30,000×50=1,500,000= 30,000 \times 50 = 1,500,000 dollars. Combined A and B revenue =2,400,000= 2,400,000 dollars.
Multiplying individual component weights by their respective rates yields individual group totals.
3
Subtract known revenues from total revenue and divide by Building C's square footage
Building C revenue =5,200,000−2,400,000=2,800,000= 5,200,000 - 2,400,000 = 2,800,000 dollars. Building C rate =2,800,00050,000=56= \frac{2,800,000}{50,000} = 56 dollars.
Isolating the remaining revenue requirement and dividing by Building C's area yields its average rental rate per square foot.

Key Concept

Weighted Average = Total Weighted Sum / Total Weight Sum
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Topics

Weighted Averages in Applied Contexts

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