No. At a point in time, the value doesn't change. It is the buyers expectations that are changing. If the cap rate is going lower, say under 10% (your provided reference point) , the buyer is expecting less return on his investment. This is likely in a less risky investment, such as a newer building or a strong leasing market. If it is going higher than 10%, the buyer is expecting a higher rate of return on his investment. In the real world, this is usually caused by a perceived increase in risk, such as an area with higher vacancy rates/collections. That being said, on paper, your answer is yes, because it is a simple math equation. If the income stays the same(leases in place), the cap is inversely proportional to the value.
Dec 2, 2008