Which of the following formulas is used in direct capitalization to estimate value?

The formula used in direct capitalization to estimate value is the Income, Rate, Value (IRV) formula. This approach is commonly applied in real estate appraisal and investment analysis to determine the value of an income-producing property.

In the IRV formula, the estimated value of a property is calculated by dividing its net operating income (NOI) by the capitalization rate (cap rate). The capitalization rate reflects the investor's desired rate of return based on the risk associated with the investment. Essentially, the formula takes the expected future income from the property and discounts it back to a present value using the cap rate as a key indicator of market conditions and investor sentiment.

The other options do not directly relate to the calculation of property value through direct capitalization. The cash flow method (CFM) focuses on comprehensive cash flows and projections for investment analysis. Return on investment (ROI) measures the efficiency of an investment relative to its cost but does not provide a valuation formula. Present value of revenue (PVR) involves discounting future revenues, which is more associated with investment valuation but does not represent the direct capitalization method specifically. Thus, IRV stands out as the correct choice for estimating value in the context of direct capitalization.