Cost is always related to action. So one must first identify the action a person is taking before assessing its cost.
If the action is continuing to own land that a person already has, then the cost is the current market price because selling the land is the alternative foregone if one holds onto it.
If the action is buying land by an investor with the intention of selling it later for a monetary gain, then the cost is the market price at the time of purchase.
If the action is using land an entrepreneur owns as an asset in production, then the cost is the amortized portion of the current market price of the land. The market price he paid for the land when he acquired it in the past is not relevant for his decision to use the land in production now.
An entrepreneur running a business enterprise continues to own assets and then buys inputs and uses both assets and inputs in production. So today when an entrepreneur decides to use his owned assets and acquire inputs to produce output and sell it in the future with the intention of earning profit, the appropriate costs are the current market prices of inputs and the amortized portion of the current market prices of assets. A year later, When the entrepreneur makes the next production run, the appropriate costs are the current market prices of inputs and the amortized portion of the current market prices of assets. Last year’s market price of assets is no longer relevant for this year’s production decision.