Perspective: The Math Behind Unit Mix & Size

By Terrence Llewellyn, Llewellyn Development LLCSuccessful real estate development, given the degree to which it is multidisciplinary, requires a team with complementary skill sets. The teammust be capable of creating a strong vision, engaging architecture, appealing interior design and color selection, and attractive landscaping. The mathematical aspect of product selection is only one small piece of the puzzle; however, it could have a significant impact on the success of your next project.Unit mix and unit sizes are a vital aspect of the successful development of an apartment community. For example, if we build too many three-bedroom apartments, vacancy will be high. If our units are too small or too large, either market reaction or profit margin will be unfavorably impacted.Fortunately, there is a way to formulate both unit mix and unit sizes using household composition demographics, market analysis and mathematics.First, with respect to unit mix, we obtain the age, income and household composition demographics for our submarket. These are aggregate data and as a result pertain to all households in the submarket, regardless of whether they are renters or owners. Next, it is necessary for us to disaggregate this data on the basis of marginal propensity to consume new multifamily for-rent housing.Many central business districts and first-tier suburbs are experiencing substantial renter demand from young, white-collar, unmarried persons. Aggregate demographic data in this example could be disaggregated to exclude households above 29 years of age, households below a certain income level, married households, etc.Once our data points are disaggregated, we can then look at the percentage of single-person households versus two- or three-person households. This gives us an insight into how many one-bedroom, two-bedroom and three-bedroom apartments will be demanded in the submarket.Obviously, the next step is to look at how competitors in this submarket are meeting this demand and where there might be advantages to exploit.Next, with respect to unit size, we must optimize the relationship between revenue per square foot and cost per square foot.Regression analysis is a statistical analysis tool that allows us to understand causality within a complex data set. It is predictive in nature and, if employed properly, can be highly useful to real estate developers. Specifically, regression analysis utilizes the “least squares” method to fit a line through a set of observations. We can analyze how a single dependent variable is affected by the values of one or more independent variables—for example, how an athlete’s performance is affected by such factors as age, height and weight. We can apportion shares in the performance measure to each of these three factors, based on a set of performance data, and then use the results to predict the performance of a new, untested athlete.We took a similar approach for an apartment community currently being developed in the central business district of Charlotte, N.C. We used regression analysis to set the unit size for our one-bedroom units in the following manner.The analysis indicated that a unit size of 692 square feet will optimize the relationship between revenue per square foot and cost per square foot. Please note that the curve is sufficiently steep so as to account for the slightly increased capital cost of constructing a smaller apartment (more kitchens and baths per square foot). Regression analysis also screens out the “noise” associated with atypical transactions. Another important reason to employ these mathematical techniques is to help us avoid product selection decisions that might otherwise be emotionally driven or have a limited appeal to our target market. The most common mistake made by developers is the fallacy of egocentrism. Any thought process that begins with, “If I were the customer, I would want…” is inherently flawed and will eventually result in economic failure and/or unnecessary risk. Math can often help us maintain objectivity and avoid these mistakes.Therefore, product selection should be based upon the following:• Who is the customer? • What is his/her age, income and household composition? • What are his/her wants, needs and desires for housing?• Who are the competitors—not only now, but during our exposure period as well? • What are the competitors building? • What are the strengths and weaknesses of the competitors’ product(s)?A strategic plan can then be formed, based upon a thorough, analytical understanding of the marketplace. It can pinpoint what product choices will result in the highest return on investment at the lowest risk level should be, based upon what is being demanded and what is being supplied, both at the current time and in the future, both quantitatively and qualitatively. Terrence Llewellyn is the principal of Llewellyn Development LLC, a Charlotte, N.C.-based real estate development and services company, focused on developing multifamily assets and on providing analytical, data-driven consulting services.The opinions expressed in this column are those of the author and not necessarily the editors. To comment on this column or to express interest in writing a Perspective, contact Diana Mosher, editor-in-chief, at