The Math Behind Housing Development
Housing development is a complex process that relies heavily on mathematical principles to ensure feasibility and profitability. Key calculations involve understanding costs, financing, and market dynamics.
Key Mathematical Concepts in Housing Development
- Cost Estimation: Developers must accurately estimate construction costs, which include materials, labor, and land acquisition. This involves calculating the total square footage of the project and multiplying it by the cost per square foot. For instance, if a developer plans to build a 2,000 square-foot home at $200 per square foot, the total construction cost would be 2,000×200=400,000.
- Financing: The loan-to-value ratio (LTV) is crucial for securing financing. It compares the mortgage amount to the property value. A lower LTV indicates less risk for lenders. For example, if a property is valued at $500,000 and the loan is $400,000, the LTV is 400,000500,000=0.8 or 80%
- Return on Investment (ROI): Developers assess potential profitability through ROI calculations. The formula is ROI=Final Value−Initial CostInitial Cost. If a property bought for $300,000 sells for $360,000, the ROI would be 360,000−300,000300,000=0.2 or 20%
- Market Analysis: Understanding local market conditions involves calculating metrics like price per square foot and price-to-rent ratios. These calculations help determine competitive pricing strategies and investment viability.
- Project Management: Effective project management relies on precise scheduling and budgeting. Developers use mathematical models to predict timelines and allocate resources efficiently.
Developing new housing is a complicated process that requires years of planning and resources before the first shovel ever hits the ground. These costs and complexities have become even greater in recent years.
Changing macroeconomic conditions, including inflation and rising interest rates, affect the availability and cost of capital, and have pushed up labour and material costs.
Workforce and supply shortages have further exacerbated the already high price of construction in California, and economic uncertainty has made typical financing partners—such as lenders and equity partners—apprehensive about supporting new housing development.
Given these additional layers of uncertainty and the ongoing housing supply shortage, it is more important than ever for policymakers and housing advocates to understand the “math” that developers use to decide whether they can start a project to build more homes.
Without a baseline understanding of these financial concepts, policymakers may create regulations that undermine housing production goals, even if those laws or policies are well-intentioned. However, very few resources exist to explain that math to those outside the real estate industry.
While there are many types of development (e.g., highrises, townhomes, accessory dwelling units), this paper focuses on one specific type: a market-rate, mid-rise, rental apartment building.
Our case study development model is a multistory residential building with a concrete podium first floor (classified under the state’s residential building code as “Type 1”) and wood frame construction above (classified as “Type 5”), hence this construction type is typically called “five-over-one”.
We did not examine for-sale developments because multifamily for-sale projects at this building scale are relatively uncommon. Since different construction types are subject to different costs and code requirements, the results of this prototype analysis should not be extrapolated to other forms of development. For example, high-rise construction above 85 feet (or roughly seven stories) typically requires a shift from wood frame building materials to concrete and steel, which raises the cost of a project considerably.
Conversely, a smaller-scale housing type such as a townhome project would require less intensive construction (e.g., no elevators and wood-frame construction) which might lower the development costs.
Regardless of building type, the financing principles of any new housing development are the same: any project must demonstrate the ability to meet an acceptable financial return to obtain the capital necessary to pay for the construction and operation of the project.