Which of these methods replaces a structure with modern construction techniques?

Functional Replacement is the correct choice in this context because it specifically refers to the method of replacing a structure using modern construction techniques and materials that may not be the same as those originally used. This approach focuses on restoring the utility of the building, ensuring it serves the same function as before while possibly utilizing newer, more efficient, or more durable materials.

In contrast, stated amount typically refers to a policy provision where the insured states the value of the property, but it doesn't necessarily involve any construction methods. Replacement cost involves restoring the property to its original state with similar materials and construction methods without consideration for depreciation. Agreed value is a feature where the insurer and insured agree on the value of the property upfront for policy purposes, but again, it does not entail modern construction techniques and methods. Therefore, functional replacement stands out as the most directly related to modernizing the construction techniques used to replace the structure.