Here's a puzzle. Picture a two specimen trees. Same size, same 100% Species and 100% Condition. For sake of argument say 100% Location, but one is in a back yard and the other in front of the house in a wide, public tree lawn. Do these trees have the same value? Should appraisals find = value?
Here are two twists with opposite conclusions.
Say we take a depreciated replacment cost approach to value. If you feel, as I do, that the cost inputs should reflect the cost to be incurred by the owner to be made whole, then it is quite likely that the municiplality has a lower acquisition, installation & establishment cost (volume discounts, owned equipment, on staff expertise, no inherent profit margin, lower cost of capital). That lower cost would result in lower appraised value than the private tree... unless you changed depreciation to make the two values=, but we've said they are all 100%.
OK, say we take a benefits approach. The tree provides x$ benefits per year over SULE. We do a Discounted Cash Flow (DCF) to get Present Value (PV). If the discount rate = cost of capital, the municipality will typically have a significantly lower cost. A lower discount rate will yield a higher value. Depreciation doe not apply to benefits approaches (or has already been considered in the calculation of benefits). Complicate it a little more. What if the benefits are higher for the public tree because there are multiple beneficiaries? I suppose you could suggest that the existence of multiple beneficiares is the reason for the lower cost of capital (less risk) but at least part of the cost advantage comes from the taxing authority of the public sector.
And what if we take a markets approach? Does the back yard tree influence only the value of one yard? Does the public tree contribute to the value of multiple properties? Does it contribute to them more than the back yard tree does to them?
I think the key issue is that the appraisal MUST define the beneficiareis and the purpose and use of the appraisal. The indications by various approaches must be distinguished. And perhaps most importantly a decision must be made a) IF the indications are to be reconciled to a sing opinion of value and b) WHO makes the rdconciliation... the appraiser or another decision maker (owner, public body or agency, judge, jury, arbitrator, parties in dispute)?