Maximum Return from a Collection of Standard and Special Appreciating Assets

In a variety of circumstances, a portion of the items in a collection of appreciating assets (such as a collection of forest stands or fine wines) are “special” in that their value growth with age follows a different pattern than the “standard” assets. Of interest is the order of selling, harvesting, or otherwise converting the assets that maximizes the total discounted return accrued. For a zero interest rate and no special assets, the situation is analogous to an inventory depletion model for which FIFO (“first in, first out”) is known to be optimal. However, we show by example that FIFO is not optimal when special assets are present. We introduce SAFO (“smallest appreciation, first out”) and prove it is the optimal ordering under all interest rates and for any number of special assets.