There have been numerous historical claims by First Nations across Canada for damages resulting from the taking of land and the resulting loss of use of such land. Many of these cases have come before the courts. Generally in such cases, there is agreement that either the Federal Government and/or a provincial government has not fulfilled its fiduciary duty. Hence, the disputes before the courts usually pertain to valuing the losses of the First Nation(s) who is (are) the Plaintiff(s) in these cases. Since the original taking of the lands occurred many decades in the past, the court is challenged with difficult valuation issues, which are complicated by a lack of historical data and transaction records. Hence, even if the parties agree on the methodology for valuing the losses and on an annual lease rate, they still need to determine the annual price of the land. A common practice for generating a price trajectory for the land is to use a very small sample of land prices, and interpolate between these prices to estimate the intervening land prices. This practice does not generate the expected trajectory given the known observations. It implicitly assumes a deterministic price process with an annual fixed appreciation of the asset throughout the period. These assumptions are inconsistent both with realistic price movements and the literature modeling asset price processes. Consequently this practice can, and mostly does, generate a very significant bias in the value of the loss. This paper suggests a loss of use valuation method that is based on a land price process consistent with the literature modeling asset price processes.