Investments in real estate consist of various stages, and at each stage, both the risk and the corresponding expected return (Opportunity Cost of Capital) differ. Initially, risks are high, but as more investment is made, future forecasts become clearer and the level of risk decreases.
Source: Commercial Real Estate Analysis and Investments, D. M. Geltner, N. G. Miller, J. Clayton, P. Eichholtz
Let’s begin with the idea that, at a fundamental level, risks depend on two main things: (1) the relationship between operating income and the market, and (2) financial and operating leverage.
In terms of income, both the risk and the discount rate are observable (e.g., in stages 3 and 4 on the graph). Investing in completed real estate is a relatively controllable decision — prices, cap rates, and inflation expectations are already known.
In the development phase, operational leverage risk enters the picture. Even if a project is implemented without financial leverage and all space is pre-leased under long-term contracts, there still exists construction cost risk. Operational leverage in real estate arises from the necessity to complete the building once construction has started. From this perspective, most costs are fixed and the actual cost of construction is unknown in advance.
Therefore, the risk of the development stage exceeds that of the leasing stage — but by how much?
One approach that avoids the need to know the project’s overall OCC is to discount income and expenses using different coefficients:
- Income is discounted as if construction is already completed.
- Expenses are discounted using the risk-free rate.
Let’s look at an example:
Suppose we are building two office blocks, each expected to generate $37,500 per month in rent once completed. One is completed in 6 months, the other in 12 months. Assume the annual nominal discount rate for income is 9%.
Construction requires $6 million, disbursed in tranches according to the contract. If we discount these tranches using the risk-free rate, we get the following picture:
Thus, we obtain the project’s NPV (which includes the value of the land). If we weight the two tables above, we get an OCC of 16.6%, which means that undertaking such a project implies expected returns of 16.6% during the development stage.
It’s also important to understand that timing — when the project is executed and when income begins — has a significant impact on the risk level, and therefore, on this figure.
Now, let’s delve into an important detail: Why did we discount costs at the risk-free rate?
In practice, developers don’t usually do this; they simply include a buffer in the cost estimates to ensure profitability. But in essence, discounting costs at a lower rate reflects the same idea — and there are solid economic and financial arguments for it:
- Most deviations from construction cost forecasts are of a project-engineering nature, meaning they represent non-systematic risks. Since these risks are diversifiable, markets don’t require a premium for them.
- Construction projects are often stabilized via long-term contracts for both materials and subcontractors, significantly narrowing the range of uncertainty.
- Most construction projects are financed with construction loans, which have interest rates higher than the risk-free rate, but this is due to default risk. Because the expected return on such loans is lower (due to yield degradation), and the loans are not long-term enough to carry substantial interest rate risk, removing the default premium brings us close to the risk-free rate.
Canonical formula
A second, more standardized approach that directly leads to the project’s discount rate is the Future Value (FV) method. If we assume the construction project is financed by a loan repaid in full upon completion, then we can treat construction costs as a single transaction that includes the loan interest. In this case, the formula becomes:
Where:
- T is the period
- V is the value of the completed building
- K is the construction cost
- r is the corresponding interest rate.
From this formula, E[rc] = OCC, which is directly calculable. In our example, it equals 20.16%.
In essence, this shifts the analysis from Present Value (PV) to Future Value (FV). There’s also a formula that uses both and reaches the same numerical result.
Finally, if we view operational leverage as analogous to financial leverage, we can apply the WACC formula to derive OCC:
From this, we find that operational leverage is 2.7, which means — assuming an efficient market — the risk premium and the corresponding expected return at the development stage is 2.7 times higher than at the leasing stage.
The diagram shows two companies with similar assets — one at the development stage, the other at the leasing stage:
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P.S.
The land value estimated using this method is consistent with the valuation using the options approach, under the assumption that there exists a condition under which delaying the project is no longer rational. A comparison with the options method is also included in the Excel file. For more details about this method, see: Why the Option Valuation works in Real Estate.
Source: Commercial Real Estate Analysis and Investments, D. M. Geltner, N. G. Miller, J. Clayton, P. Eichholtz