s = rate of rental............ \$1.34 n = ratio of net rentable area to gross building area 60% r = ratio of net income to total income, with allowance for 10% vacancies, or 35% f= (1) 8 stories, (2) 12 stories. i = interest ............. 5%

Then, substituting for the nomenclature in the formula, we obtain for T, or the total investment on which the returns would pay interest:

(1) T=(1.34x60x35x8) / (100x5) =\$45.02 per square foot of building area

(2) T= (1.34x60x35x12) / (100x5) = \$67.50 per square foot of building area

Assuming the proposed structure to be erected upon a plot, say, 75 feet by 100 feet, of which the building occupies 80%, the area of the building will be 6000 square feet.

 (I) Then the 8-story building would justify a total investment of \$45 x 6000 square feet, or.............. \$270,000 (2) The 12-story building would justify a total investment of \$67.50 x 6000 square feet, or \$405,000

These, then, are the total values established by the respective buildings in the land and the structure.

 The cost of an 8-story building may be estimated at 30 cents per cubic foot and its height at 96 feet, so that the total cost would be............... \$172,800 This cost would then establish the value of the land at \$97,200 out of a total investment of......... \$270,000 The cost of a 12-story building taken at 36 cents per cubic foot and a height of 144 feet would be . . . \$311,000 which would establish the value of the land at. . . . \$94,000 with a total investment of.......... \$405,000

There would thus be no advantage in the erection of the 12-story building.

 Let it be assumed, however, that the larger building might be built for 33 cents, or a difference in cost of only 3 cents, per cubic foot, in which case it would cost only .... \$288,000 This would leave for the land value......or an apparent advantage in favor of the 12-story \$117,000 building of \$20,000

"Over-investment involves an additional pledge on the part of the land to maintain its attractiveness as a site, and of the building to continue to fulfil its original purpose"

Appreciation of Value of Land

 It is noticeable, however, that in order to secure this addition to the invested value of the land of....... \$20,000 an increased investment in the building has had to be made of.............................................................. \$105,200 and the depreciation upon this increased cost at thirty years' life at 5% compound interest would be 1.5% on difference in cost, or...................................................... \$1,578 which would use up more of the returns than would pay the interest of \$1000 upon the additional value established for the land.

Therefore, these results show that a 12-story building would not be a really remunerative investment as compared with the more moderate expenditure upon the 8-story building, at even so small a difference in cost as 3 cents per cubic foot.

Example II:

It is proposed to erect (1) a 12-story or (2) a 20-story building for office purposes on a certain plot, the prevailing rate of rentals in the surrounding vicinity being an average of \$1.75 per square foot net rentable area; investment at 4%; building area, say, 5000 square feet.

 s= rate of rental......... . . . \$1.75 n = ratio of net rentable area to gross building area, say............. 65% r = ratio of net income to total income, with allowance for 10% vacancies, or....... 45% f= (1) 12 stories, (2) 20 stories. i= interest 4%

Then

(1) T= (1.75x65x45x12)/(100x4)= \$153.60 per square foot of the building.

Therefore, 5000 square feet x \$153.60 = say, total investment of..............\$768,000 or

(2) T=(1.75x65x45x20) / (100x4) = \$256 per square foot of the building at a difference in construction cost of iy cents per cubic foot. And should the difference be reduced to 14 cents per cubic foot, then the two proposals would stand on an equality as regards net rate of returns; but the larger investment would still load the land unnecessarily.

 Therefore, 5000 square feet x \$256 = total investment of \$1,280,000 12 stories, cost 37 cents x 144 x 5000 = \$266,400, leaving a land value of ............................................................\$501,600 20 stories, cost 54 cents x 240 x 5000 - \$648,000, leaving a land value of........................................................\$632,000 Increased apparent value of land by 20-story building is \$130,400 But increased investment in building is . . . \$381,600 Income on \$130,400 at 4% is.......\$5,216 But loss by depreciation on excess cost of building is, at 4% compound interest on 30 years' life .... ................. \$6,792 Therefore the 12-story building is the better investment by...............................................................\$1,576 per annum

Such unnecessary expenditures, while they may be and are assumed to be remunerative to the extent of a return of annual interest, are speculative risks upon the ability of the building to maintain them. As has been previously remarked, over-investment of any kind involves an additional pledge on the part of the land to maintain its attractiveness as a site, and of the building to continue to fulfil its original purpose for the full term of a period in which its value shall be offset by the land appreciation or by a fund out of net earnings.

Assuming an increase of 60% in the cost of building construction and a rise in the prevailing rate of interest to 7%, it will be found that the rentals assumed in these illustrations are practically doubled. But by such an advance in rental the value of the site has not been affected.

If either pledge should fail, as in the recent instance of a 17-story office building, then the property suffers by the premature removal of the too costly structure, which has really hastened its own demise, while the failure or even the over-success of a more moderately proportioned building, which might bring about its removal in the same time, would do so with a justifiable and reasonable loss.

The erection of steel-framed buildings of one particular height cannot fit in with all values of the sites they occupy, especially on narrow plots in side streets, where great dependence must naturally be placed on the temporary conditions obtaining prior to similar improvements of contiguous properties. Some of the tall, narrow buildings thus located are of the nature of excess investments, or are indications of too great an expenditure in the site. Such buildings, while they temporarily enjoy superior benefits of light and air, derived from their location among smaller neighbors, are bound to lose much of this advantage later, but anticipation of this contingency is very commonly ignored or subordinated to the demand for returns on all the area possibly to be crowded on to the site.

It is an open question whether a large variety of buildings would not gain by a substantial reduction of their floor areas, whereby an increase of the access of light and air to their interiors may be secured.

There is a special value to be attached in certain cases, for mere advertising purposes, to those spaces in a building which front on a street, which advantage is not possessed by rear spaces; but the main asset of street frontage is light and air, for which additional rentals are obtainable.

Direct and abundant light and access to wide unoccupied space increase the rentable value of any part of commercial buildings, over any other part not equally advantaged. Those portions in a building which are more or less deprived of air and light make so low a return as to become unremunerative, constituting a mere burden on the building, reducing its average of rentals. Mr. F. H. Heywood has recently stated, as a result of wide investigation, that the value of court offices decreases 10% per floor from the rental of the floor at the top of the court.

Equal expense is, however, involved in the construction of each part of the structure, and if this feature be carefully considered at the outset, it may be found that some large proportion of the building could be omitted with advantage, reducing the total cost of the building, and raising the rentals of the rear or poorly lighted parts by affording space for light and air, approximating that of the most open or best-lighted space, such as the street frontage. It is better to have a small building all of which produces a high rate of rental than a large building rented at high rates in front and low rates at rear, averaging the same as the smaller building.