But unless a regularly invested and proportionate sinking-fund be maintained, an inevitable dependence must be placed upon the speculative increase in land value to offset the eventual loss of the building. The burden of the entire original cost of the building is then laid upon the land, the increment in value of which is expected to respond to the demand. As buildings of a permanent character usually cost more than the value of the land they occupy, it follows that within the term of their useful existence the land is required to increase at a ratio commensurate not with its own value, but with that of the expenditure on the building.

Fig. 4. Loss on building exactly balanced by gain on land. Neither loss nor gain at any part of term.

Fig. 4. Loss on building exactly balanced by gain on land. Neither loss nor gain at any part of term.

Thus, if on land of a value of $10 per square foot there be erected a building of a value of $20 per square foot of area of its site, the land will be required to advance in value during the term, say, of forty years, at the rate of 5% per annum, in order to bring back its own value and that of the loss on the building at any time. If the building be unduly large, or if the expenditure, especially upon decorative and non-earning features, be extravagant, the whole burden of such additions would have eventually to be borne by the land. It is evident that most careful regard is required to be paid to the avoidance of undue cost of construction.

An examination of the effects of the method of shouldering upon the land the depreciation of the building brings out some curious features which exhibit the undesirability of the practice.

If the rate of increase in land value during the time of useful existence of the building does not exactly follow that of the loss on the building, then there is eventually either a greater loss or a lesser degree of profit, by extending the process until the end of the term.

Fig. 4 shows a term of useful existence of a building of 35.32 years, and a rise in land value exactly equivalent to that of building depreciation, eventuating in neither gain nor loss at any time. Such a combination would seem rare if not wholly unlikely.

In Fig. 5 the loss on the same building is shown, largely overbalanced by gain in land value, but the eventual profit is just as well secured by sale at one half the term and investment of the profit on the land at 4% compound interest.

In Fig. 6 the land fails to respond to the depreciation of the building, and an eventual loss must result. This may, however, be minimized substantially by cutting the loss at half the term and investing the proceeds of the then increase of the land value at compound interest.

Fig. 5. Loss on building exceeded by gain on land. Profit if realized at half of the term produces equal result.

Fig. 5. Loss on building exceeded by gain on land. Profit if realized at half of the term produces equal result.

The effect shown in Fig. 6 is further developed in Fig. 7, in which an assumed life of 35.32 years is again adopted for a building having twice the value of the land. Here the rate of increment is assumed to be 50% greater than even this amount of depreciation, and the total land value at the end of the term to be 400% that of the original. Even with this large ratio of appreciation the eventual profit would be increased by sale of the property about the middle of the term, and the investment of the then profit at 5% compound interest.

The diagonal line P K shows the enhanced values obtained by selling off the property at periods in the existence of the building from fifteen to twenty-one years, and the investment of the profits at 5% compound interest for the rest of the term or any part thereof.

The common practice of dependence upon increment of land values to offset depreciation of buildings is thus found to be erratic and is evidently financially unsound.

It is sometimes the case that the purchaser of an improved property has paid a low price, which is practically a market value of the property, more or less discounted by the depreciation of the building up to that date. This is, in effect, a resettlement of the relation of the land value and the building value, but the process of depreciation is merely started from a new point on the scale, and either the income or the land value must take up the progress of the burden.

There can be little hesitancy, in view of all these features, in pronouncing the common method of dependence upon rising value of land to be unsound.

Figures are often quoted of phenomenal rises in land values. These do not all bear investigation, or, sometimes, show that, with enhanced taxation and long lack of earnings, the property

Fig. 6

Fig. 6

Gain on land less than loss on building. Loss reduced by sale prior to end of term might have represented a better result if realized at some prior date.

The reason for such failure to realize at the opportune time is often not far to seek. After reaching the level at which the average class of buildings erected in the locality return a reasonable income upon book values of the combined properties, the land value of any neighborhood is apt to become steadied, and if the interest of investors, as well as the demand by speculative builders, has for the time ceased, it has no active market.

The growing absorption of all land on the island of Manhattan will naturally set some increase of value on all desirably located land as being a restricted commodity, but the investor in buildings cannot afford entirely to ignore the fact that the isolation of Manhattan is rapidly disappearing by reason of tunnels and bridges to other districts.