Chapter X: Financing Highways and Highway Transportation Lines (1)

Highway financing may be divided for consideration into two parts, namely: financing the road and financing the operation of the road. Both are necessary if goods are to be transported from where they are plentiful, grown, manufactured, or stored, to where they are needed for sale, consumption or transshipment. Money is required for both parts and it must be obtained in some legal manner.

As has been shown roads developed from mere trails that originally were paths along which by common consent, force, or otherwise the privilege of passing was gained. This, when ownership in land was recognized, became an easement. After the development of civil governments the right to traverse and transport goods over such roadways, that is, the easement, was vouchsafed to the inhabitants and protected by laws. In England the right of way over another’s land became known as the king’s highway, as all public property was held and measures taken in the name of the king. In the United States it is known simply as a public highway. The highway is in reality the right of passage, not the beaten track, for in both England and the United States the laws recognize the privilege the traveler has when for any reason the road becomes blocked or obstructed of taking to the fields and making another track. Equity courts may grant damages for such usage of private land by the public but no court will attempt to prevent it; if necessary they will, however, by writ of mandamus command road officers to repair the established roads so as to make them passable. In England the law allowed the traveler to turn into the adjacent field, whether cultivated or not, whenever the track became worn or rutted. In order to keep the used way within due bounds and at the same time maintain it in a passable condition the freeholders, perhaps at first voluntarily then by force of laws, worked the roads once or twice a year. By doing this they saved their lands and crops from being trampled down. It has also been shown how Edward I took up the question of improving the highways as a police measure in order that it might be safe for man and goods to pass along the road without being attacked from ambush by robbers.

Such robberies have taken place in the development of every land, and those who have made a profession of it are variously styled highwaymen, bandits, brigands, and so on. Even to the present day, as has been shown in a preceding chapter, highway robbery still exists, although the profession of highwayman no longer commands the respect of reputable society as was the case during the time of Robin Hood, and Claude Duval of England, and of the Robber Barons of Germany.

Thus the public good demanded that the time of the freeholders and the money of the government be expended upon the highways. Of late years in the United States the “working out” of road or poll taxes has been practically abolished and the taxes are collected in money which is expended in road construction and maintenance by persons regularly delegated for that purpose. With the increased use and the building of better types of roadways more and more money is demanded so that the financing of highway improvements has become a matter of vast importance. The money must come from either private sources or from the public. If from the public it results directly from taxation or is borrowed and the obligations paid off by taxation.

=Private Financing.=--A few persons of wealth have built roads as a benefaction to the public. Perhaps one of the most ambitious projects of this sort is the DuPont Road, which is located through the state of Delaware from north to south. The intention of the DuPont family is to make this road eventually one of the finest in the world. It has been very carefully laid out and constructed. Later it is to be widened and beautified. Some $3,000,000 have already been expended, and it is contemplated to spend $1,500,000 more. It might be well if more men of wealth would commemorate their names by constructing and endowing roads.

In spaces about wharfs and depots, although on privately owned ground and privately constructed, the pavement is often used generally as a highway. Such places are of course primarily for the convenience of the steamship or railway companies and they are maintained at their own expense. However, all such expense forms a part of the cost of operation and no doubt is charged to the patrons in the overhead, or it is intended to be a means of advertising in the hope that it will increase business.

In timbered and rough mountainous countries, roads have frequently been built and maintained by the companies interested in lumbering, mining, or other enterprises therein, and thrown open to the general use of the public. Here the companies figure that the benefit to be derived by them more than balances the expense. Furthermore, the use of them by the public, while a minor consideration as far as the road itself is concerned, is a means of maintaining a friendly feeling with the inhabitants.

Turnpike or toll roads, as has already been pointed out, were very extensively built in the days preceding the advent of the steam railway. These were built with money raised by the ordinary methods for financing industrial enterprises. A good many thousands of miles of such roads were chartered and constructed by private capital amounting to millions of dollars before the steel tracks put them out of business. Only a few now remain in Pennsylvania and Virginia with now and then scattered short stretches of roadway, and bridges over larger streams elsewhere, and ere long they, too, will be taken over by the states and become a part of the great public highway. As late as 1915 a private toll road in Tuolumne County, California, operated by a mining company was purchased by the state and nation, a portion of it being within the Yosemite National Park, and made a part of the California state system. The people will never be content to go back to the inconvenience of being stopped by a turnpike every 4 or 5 miles to pay a toll amounting in many cases from 1 to 2 cents per ton-mile, when the same amount of money in the form of licenses and taxes will keep up magnificent systems of public “free” highways.

=Public Financing.=--Every civic government has its methods for the collection of revenue to pay its necessary expenses. One of the easiest things theoretically to do, then, is to collect by a tax on the property of the district--state, county, township--sufficient money to meet expenses, including the building and maintenance of roads, from the property holders in proportion to their wealth and turn it over to the proper officers for expenditure. When roads were yet simple things, before they had become elaborate and complicated structures, that might have been done. Practically, however, even then the working of the roads was a farce; men sat around, told stories, retailed the neighborhood gossip and smoked their pipes or whittled sticks, while the horses hitched to the scraper or plow stood limp with one hip lower than the other, eyes half shut lazily swishing at the flies with their long tails. Soon the necessary hours were passed, their poll or road tax had been “worked out.” The roadway was left in an almost impassable condition to be gradually worn smooth during the intervening six months until it came time again to work the roads. To most of those old timers the working of the road was a necessary evil and done only because the law required it. When occasionally a road supervisor insisted on a full day’s work for a day’s credit he was a skinflint and at the next election lost his job.

The tremendous amount of money necessary to construct present types of roads must, in the long run, be obtained from the citizens through some medium of taxation. A tax is a compulsory contribution levied upon persons, property, business, occupations, privileges, or enjoyment of the people for the support of government or governmental functions. When levied upon persons it is usually called a poll or head tax; when upon property, a property tax; when upon business it may be a capital tax, sales tax or an income tax; when upon occupations, an occupation tax; when upon privileges, a license; and when upon enjoyment, a pleasure tax. A good many of them may be lumped together under the name of revenue taxes. Some are collected personally by a specified officer of the government, while others are collected indirectly by the sale of stamps which are attached to the article or transaction taxed.

Taxes may also be classified as direct, indirect and special, all of which are of great importance to the highway.

=Direct Taxes.=--Direct taxes are levied directly upon property or persons. State laws usually prescribe that general property taxes shall be levied uniformly over the assessed values of the district concerned. A poll tax is levied on all persons of a particular age or class, as all able-bodied males between the ages of twenty-one and fifty years. An income tax is levied according to some prescribed rule on the annual incomes of persons and corporations. An income tax is really a tax on business, either present or past.

In either case, whether the levy is on his poll, upon the assessed valuation of his property, or upon his declared income, the taxpayer contributes, theoretically at least, in direct proportion to his ability to pay. The amount of the tax is definitely ascertained some little time in advance of payment and is collected directly by an officer of government.

The levying of labor or poll taxes on persons living within a particular road district easily expanded to the levying of property taxes to care for the local roads. However, as the cost of road building and maintenance increased the fronting or contiguous property could not stand the entire burden, the zone of taxation was widened to include larger areas, the township, the county or the state, depending on the importance of the highway.

=Indirect Taxes.=--Indirect taxes are those not levied upon the various persons or the property of the district, but are placed upon some article of consumption or some article of manufacture, upon imports and exports, or some privilege or pleasure. The government does not look to each individual for its money, but to the seller or manufacturer or importer of the article taxed, or the licensee, or the operator of the theater or other pleasure resort. The amount of the tax is added to the price at which the article is sold or to the fee charged so that it is at last borne by the ultimate consumer, in proportion to his consumption of the article taxed, or the privilege enjoyed.

Federal aid moneys all come from indirect taxes, for the Constitution forbids the national government to levy direct taxes.

In Alaska 65 per cent. of the “Alaska Fund,” a fund derived from all returns from liquor, occupation or trade licenses obtained outside incorporated towns, must by Congressional law of 1905-1906; be spent in Alaska for roads, trails, and bridges.

License fees on motor cars and sales taxes on gasoline belong to the class of indirect taxes, and are attempts to charge the user of the road in proportion to the wear and tear produced by him or his consumption of it. If the motor car is an express truck, a bus, or a taxicab the tax is passed on to the patron, and this patron charges it to the cost of living and attempts to pass it on to his employer through increased wages or those who do business with him. It is finally paid for by that visionary personage the ultimate consumer--everybody.

=Special Taxes.=--Special taxes are those levied upon property for a particular improvement that is demanded by public interest. They are not uniform but must be levied in proportion to the benefits accruing to the property from the improvement. This class of taxes is very popular for financing the building of roads and the paving of streets as well as other public construction. The area adjacent to the road or pavement for a certain specified distance back, or possibly, halfway to the next thoroughfare, is assessed for the improvement and in road work is technically known as “fronting property.” Each piece of fronting property is required to pay toward the whole cost of improvement an amount proportional to the benefits derived from the improvement.

These benefits evidently decrease as the distance from the improvement increases. They may not always vary in the same ratio, but appraisers will usually follow some definite rule and deviate from it only in extreme cases and as local conditions demand. That they should not decrease directly as the distance but in some geometrical ratio, most engineers agree. Law courts have frequently upheld assessments made upon some such basis.

For the purpose of initiating an improvement by petition it is customary to adopt a fixed scale for the measure of the benefits, based upon distance, that will probably be derived from the improvement. Some legislative bodies have enacted definite rules for evaluating “influence” in petitioning. Generally the rule is based upon some mathematical variation. For example that the assessed value or influence of property of uniform width extending back from the roadway shall vary as the square root of the maximum distance back. In the figure on page 313, a lot of one-unit area fronting the street is given a value of 31.62. This is from the mathematical formula

_y_² = 1000_x_

where _y_ represents the assessed value or influence in petitioning, and _x_, the distance back, considering the value of _y_ = 100 for _x_ = 10.

To draw the curve mark off on a straight line ten equal distances; at the mid-point of these distances or units erect perpendiculars. From the formula calculate values for _y_ as shown in the table; lay these off on the verticals and plot the curve through their extremities. To clarify this some, suppose that upon the center of the first space, there being one unit area or lot here, there is stacked up the value of the assessed benefits 32 (31.62) silver dollars. On the next space, since there are two lots extending back from the street, the stack would contain 45 (44.72) silver dollars--continue this for each space and for the number of lots extending back. A curved line passing through the tops of the stacks representing the assessed values will be the influence curve plotted.

+---+------+------+
|_x_| _y_² | _y_ |
+---+------+------+
| 1 | 1,000| 31.62|
| 2 | 2,000| 44.72|
| 3 | 3,000| 54.77|
| 4 | 4,000| 63.25|
| 5 | 5,000| 70.71|
| 6 | 6,000| 77.46|
| 7 | 7,000| 83.67|
| 8 | 8,000| 89.44|
| 9 | 9,000| 94.87|
|10 |10,000|100.00|
+---+------+------+

Assessment curve.]

For the purpose of initiating an improvement the unit in which the prospective benefits are to be measured is usually adopted by the governing or assessing authorities. Dollars will not do because the cost will not be known until after the improvement has been finished. In the case of roads and streets the unit quite generally used is the “front-foot.” The number of front-feet in any paving district will be the same as the number of abutting feet along the street to be improved. A different definition for “front-foot” is given on page 318. The petitioning power or influence of the several properties constituting the whole frontage is proportional to the number of front-feet assigned to each property, and these are assigned according to the adopted rule which is supposed more or less closely to measure the benefits to be derived from the improvement.

When it comes to paying for the improvement the total cost up to the time of payment, including all charges against the district of whatsoever character, is divided by the number of front-feet giving the cost per front-foot, from which may readily be determined the cost to be assessed to each property according to the number of front-feet assigned to it.

To illustrate this more concretely, consider a road one mile long. Its abutting length is 2 miles, one on each side, or 10,560 feet. The total number of units of influence in the whole assessed area, and the number of units of assessed benefits, is 10,560 front-feet. The number of these units assigned or assessed to a particular plot of land is technically called its “frontage.” Since all land for a specified distance from the roadway must share in the benefits and in the cost, therefore, a piece of property may have frontage even though it does not touch the street or roadway to be improved.

In order to facilitate computation, more or less arbitrary variations are made from the theoretical curve of assessment thought to be ideal. Each infinitesimal portion of land bears a different assessment value according to its position in relation to the improvement. It would be impracticable to divide the land into an infinite number of strips of infinitesimal width and calculate the assessment for each. This could be done by mathematical analysis if all the boundary lines were straight lines and mathematical curves, but the work would be even then too laborious to pay. It is customary to divide the assessed territory along each side of the roadway into zones with edges parallel to the road, and to each zone is given a weight or proportional part of all the assessed value. The weights are obtained from the mathematical curve and are given values corresponding approximately with theoretical calculations.

=Zone Weights.=--To determine the proper zone weights the influence curve is plotted as in figure on page 319. The base line, AB, is divided into as many parts as it is desired to have zones; from the mid-point of each part a perpendicular to the base line is erected to meet the curve, shown in the table, as mid-ordinates. These are each multiplied by 100 and divided by the longest, in the case of five zones, 94.85, to get them into percentages of the whole. These are now adjusted to near numbers for easy multiplication. For example, to multiply by 33¹⁄₃ add two ciphers and divide by 3; to multiply by 25 add two ciphers and divide by 4; and so on.

FIVE-ZONE TABLE

----+------------+----------+------+---------------+-------
Zone|Mid-ordinate|Percentage|Weight|Adjusted Weight| Sum
----+------------+----------+------+---------------+-------
1 | 31.62 | 33.3 | 33.3 | 33¹⁄₃ | 33¹⁄₃
2 | 54.77 | 57.7 | 24.4 | 25 | 58¹⁄₃
3 | 70.71 | 74.6 | 18.9 | 16²⁄₃ | 75
4 | 83.67 | 88.5 | 13.9 | 15 | 90
5 | 94.87 | 100.0 | 11.5 | 10 | 100
----+------------+----------+------+---------------+-------

To get weights for six zones take the mid-ordinates at 8¹⁄₃, 25, 41²⁄₃, 58¹⁄₃, 75, and 91²⁄₃, as follows:

----+------------+----------+------+--------+-------+--------+-------
| | | | | |Another |
| | | |Adjusted| |Adjusted|
Zone|Mid-ordinate|Percentage|Weight| Weight | Sum | Weight | Sum
----+------------+----------+------+--------+-------+--------+-------
1 | 28.86 | 31 | 31 | 30 | 30 | 33¹⁄₃ | 33¹⁄₂
2 | 50.00 | 52 | 21 | 20 | 50 | 20 | 53¹⁄₃
3 | 64.45 | 67 | 15 | 15 | 65 | 16²⁄₃ | 70
4 | 76.70 | 80 | 13 | 12¹⁄₂ | 77¹⁄₂ | 10 | 80
5 | 87.02 | 91 | 11 | 12¹⁄₂ | 90 | 10 | 90
6 | 95.73 | 100 | 9 | 10 |100 | 10 |100
----+------------+----------+------+--------+-------+--------+-------

=To Calculate the Frontage.=--As has already been stated, in some states in order to initiate a road improvement to be paid for by special assessment a petition for the same signed by the owners of a majority of the frontage is necessary. To determine the frontage for this petition general rules are laid down by proper authority or laws enacted, stating the necessary procedure and the weights allowed for calculating frontage based upon distance from the roadway to be improved. In one state the land up to a distance of 2 miles back on each side of the roadway may be formed into an improvement district which constitutes the fronting territory or frontage. The frontage on each side of the roadway is divided into four zones equal in width. The first zone, the one nearest the road, has a weight of 50, or it may be said to contain 50 per cent. of the total frontage; the second zone has a weight of 25, or contains 25 per cent. of the frontage; the third, 15 per cent.; and the fourth, 10 per cent. Along a mile of the road there are, of course, two miles or 10,560 front-feet frontage. This 10,560 front-feet is not considered to be uniformly distributed over the entire 4 square miles (assuming the district 2 miles each side the road) of assessed territory abutting the mile of roadway. Nor to be decreased according to the mathematical laws stated above. But the distribution is by arbitrary rule laid down by legislative authority. In this particular case, assuming a straight roadway and equal zones, the first one will contain 50 per cent. of 10,560 = 5280 front feet. Since the actual area of the zone is 1 square mile = 640 acres, there are 5280 ÷ 640 = 8¹⁄₄ front-feet per acre in this zone. The table will show similar results for each of the four zones:

----+------+--------+-----------------------------------
| | | Front-feet for varying acreages
| | Front +-----+-----+-----+-----+-----+-----
| | feet | 1 | 10 | 20 | 40 | 80 | 160
Zone|Weight|per mile| acre|acres|acres|acres|acres|acres
----+------+--------+-----+-----+-----+-----+-----+-----
1 | 50 | 5280 |8.250|82.50|165.0| 330 | 660 |1320
2 | 25 | 2640 |4.125|41.25| 82.5| 165 | 330 | 660
3 | 15 | 1584 |2.475|24.75| 49.5| 99 | 198 | 396
4 | 10 | 1056 |1.650|16.50| 33.0| 66 | 132 | 264
----+------+--------+-----+-----+-----+-----+-----+-----

As an illustration, suppose two taxpayers have farms of exactly the same size, 800 acres each, but placed differently in regard to the road, see figure below. Their influences or petitioning power may be calculated in front-feet from the preceding table thus:

Two farms of the same shape but situated differently with regard to the improved highway have different “petitioning influences” and are assessed differently for improvements. Farm _A_ is in contact with the road for 5280 ft., and has an influence or assessment value of 4158 front-feet. Farm _B_ is in contact 1320 ft. and has an assessment value of 2442 front-feet.]

----+------+----------------+----------------
| | Farm A | Farm B
| +-----+----------+-----+----------
| | |Influence | |Influence
Zone|Weight|Acres|Front-Feet|Acres|Front-Feet
----+------+-----+----------+-----+----------
1 | 50 | 320 | 2640 | 80 | 660
2 | 25 | 240 | 990 | 160 | 660
3 | 15 | 160 | 396 | 240 | 594
4 | 10 | 80 | 132 | 320 | 528
| +-----+----------+-----+----------
Total | 800 | 4158 | 800 | 2442
| +----------+-----+----------
Contact Feet | 5280 | | 1320
-----------------+----------+-----+----------

=Procedure with Unequal Zones or Irregular Lots.=--Where the zones are not equal in area or the property lines do not intersect the roadway at right angles or the lots are irregular in shape, the method of procedure is not quite so simple, although the principle is the same. While it is customary to make the zones of uniform width this is not absolutely necessary. Likewise the ratio of weights vary with different states and cities. One city uses 33¹⁄₃, 20, 16²⁄₃, 10, 10, 10 for the weights in its six zones; another uses 33¹⁄₃, 25, 16²⁄₃, 15 and 10. Neither of these, as shown in the tables on pages 315 and 316 varies materially from the theoretical ratio.

Using the latter of these ratios a small district has been worked out as shown in the figure and table on page 320. Incidentally this also shows a good method of recording lot assessments during the process of computations. The work is readily checked. The sum of the lot areas must equal the sum of the zone areas and that of the whole district. The sums of the weighted areas for the same divisions must balance. The sums of front-feet likewise. Also cross and vertical summations may be made to check.

=Second Method of Apportioning Assessments.=--A second method based upon a different definition has something in its favor. If the front-foot is defined as a lot 1 foot wide measured in the direction of the street extending directly back through all the zones to the limit of the assessed area it will have a weighed area of _W__{1}_z__{1} + _W__{2}_z__{2} + _W__{3}_z__{3} ... and so on, where _W__{1} represents the weight of the zone, whose width is _z__{1}, and _W__{2} the weight of the zone, width _z__{2}, etc. If _z__{1} = _z__{2} = _z__{3} ... etc., as is usually the case the weighted area of 1 front-foot is (_W__{1} + _W__{2} + _W__{3} ... ) _z_ = _Wz_ = 100_z_, since _W_ is always = 100. The total number of front-feet in the district, or in any lot, will be the number of weighted feet in the district or in the lot, divided by 100_z_. In the district represented on p. 320, the number of front-feet is the total frontage, 1,936,000 divided by 4000 = 484; and for each lot the amount shown in the table. The results obtained by the two methods are directly proportional, so that either may be used for making assessments. In fact they are proportional to the weighted areas, so that the weighted areas may be used instead of the front-feet if desired.

=Rule for Assessment.=--To get the assessment for any particular lot divide the total cost of the improvement by the total number of front-feet in the district and multiply the quotient by the number of front-feet in the lot.

+----+-----+-----------------+--------------+---------------+
|ZONE| WT. | ZONES | LOT 1 | LOT 2 |
| | +------+----------+----+---------+-----+---------+
| | | AREA | WTD. AREA|AREA|WTD. AREA| AREA|WTD. AREA|
+----+-----+------+----------+----+---------+-----+---------+
| 1 |39¹⁄₃|22,800| 760,000 |4800| 160,000 | 3600| 120,000 |
| 2 |25 |20,400| 510,000 |2400| 60,000 | 3600| 90,000 |
| 3 |16²⁄₃|18,000| 300,000 | 300| 5,000 | 3300| 55,000 |
| 4 |15 |15,600| 234,000 | | | 1200| 18,000 |
| 5 |10 |13,200| 132,000 | | | | |
+----+-----+------+----------+----+---------+-----+---------+
|Total |90,000|1,936,000 |7500| 225,000 |11700| 283,000 |
+----------+------+----------+----+---------+-----+---------+
|Front Feet 1^{st} Method 600| | 69.73 | | 87.71 |
+----------------------------+----+---------+-----+---------+
| „ „ 2^{nd} „ 484| | 56.25 | | 70.75 |
+----------------------------+----+---------+-----+---------+

+----+-----+-----------------+---------------+---------------+
|ZONE| WT. | ZONES | LOT 3 | LOT 4 |
| | +------+----------+-----+---------+-----+---------+
| | | AREA | WTD. AREA| AREA|WTD. AREA| AREA|WTD. AREA|
+----+-----+------+----------+-----+---------+-----+---------+
| 1 |39¹⁄₃|22,800| 760,000 | 2400| 80,000 | 3000| 100,000 |
| 2 |25 |20,400| 510,000 | 2400| 60,000 | 3000| 75,000 |
| 3 |16²⁄₃|18,000| 300,000 | 2400| 40,000 | 3000| 50,000 |
| 4 |15 |15,600| 234,000 | 2400| 36,000 | 3000| 45,000 |
| 5 |10 |13,200| 132,000 | 1200| 12,000 | 3000| 30,000 |
+----+-----+------+----------+-----+---------+-----+---------+
|Total |90,000|1,936,000 |10800| 228,000 |15000| 300,000 |
+----------+------+----------+-----+---------+-----+---------+
|Front Feet 1^{st} Method 600| | 70.66 | | 92.97 |
+----------------------------+-----+---------+-----+---------+
| „ „ 2^{nd} „ 484| | 57.00 | | 75.00 |
+----------------------------+-----+---------+-----+---------+

+----+-----+-----------------+---------------+---------------+
|ZONE| WT. | ZONES | LOT 5 | LOT 6 |
| | +------+----------+-----+---------+-----+---------+
| | | AREA | WTD. AREA| AREA|WTD. AREA| AREA|WTD. AREA|
+----+-----+------+----------+-----+---------+-----+---------+
| 1 |39¹⁄₃|22,800| 760,000 | 3000| 100,000 | 6000| 200,000 |
| 2 |25 |20,400| 510,000 | 3000| 75,000 | 6000| 150,000 |
| 3 |16²⁄₃|18,000| 300,000 | 3000| 50,000 | 3000| 50,000 |
| 4 |15 |15,600| 234,000 | 3000| 45,000 | | |
| 5 |10 |13,200| 132,000 | 3000| 30,000 | | |
+----+-----+------+----------+-----+---------+-----+---------+
|Total |90,000|1,936,000 |15000| 300,000 |15000| 400,000 |
+----------+------+----------+-----+---------+-----+---------+
|Front Feet 1^{st} Method 600| | 92.97 | | 123.97 |
+----------------------------+-----+---------+-----+---------+
| „ „ 2^{nd} „ 484| | 75.00 | | 100.00 |
+----------------------------+-----+---------+-----+---------+

+----+-----+-----------------+---------------+
|ZONE| WT. | ZONES | LOT 7 |
| | +------+----------+-----+---------+
| | | AREA | WTD. AREA| AREA|WTD. AREA|
+----+-----+------+----------+-----+---------+
| 1 |39¹⁄₃|22,800| 760,000 | | |
| 2 |25 |20,400| 510,000 | | |
| 3 |16²⁄₃|18,000| 300,000 | 3000| 50,000 |
| 4 |15 |15,600| 234,000 | 6000| 90,000 |
| 5 |10 |13,200| 132,000 | 6000| 60,000 |
+----+-----+------+----------+-----+---------+
|Total |90,000|1,936,000 |15000| 200,000 |
+----------+------+----------+-----+---------+
|Front Feet 1^{st} Method 600| | 61.99 |
+----------------------------+-----+---------+
| „ „ 2^{nd} „ 484| | 50.00 |
+----------------------------+-----+---------+

First Method

Front-Feet = 600
Weighted Area
per front Foot
1,936,000
= --------- = 3226²⁄₃
600

Lot frontage
= Weighted area
of Lot ÷ 3226²⁄₃

Second Method

1,936,000
Front Feet = ---------
4000

= 484

Frontage of each lot
= weighted area of
lot ÷ 4000]

It should be remembered that the assessment of cost must be in proportion to the benefits to be derived from the improvement. The assessors will therefore have to use sound judgment and modify the mathematical results if deemed wise. As a rule it is best never to deviate, though, unless there are extraordinary good reasons.

=Miscellaneous Sources of Revenue.=--A few years ago much was said relative to the right of a city to take a portion of the earnings of public service corporations as compensation to the public for the use of its streets. Many cities granted franchises under such agreements and until the automobile depleted the earnings of street railways and the general costs of manufacturing gas and electricity went up received considerable revenue from these public utility organizations. While in most cities this went into the general fund money was usually appropriated from that fund for street maintenance and improvement, so indirectly, at least, the roadways profited. In the large cities franchises for the use of the public streets at, above, or beneath the surface are sufficiently valuable to warrant good returns to the public. It seems logical that such money be used for street improvements. Bus and truck lines fall directly under this head, and since they are very largely conducive to the distruction of pavements, it would seem as though they ought to pay for at least a part of this damage. The tax might be graduated according to weight as is now in most states the automobile license tax.

A number of cities are entering the commercial and industrial enterprises such as the sale of water, gas, electricity, ice and coal. While usually these are operated on a low margin so as not to make money there is nevertheless, here, an opportunity to secure necessary funds for public improvements. And if the operation of these enterprises is such that private competitors can make reasonable profits the people will be the gainer by having more available funds for worthy objects. It may not be the proper province of the government to go into gainful enterprises in competition with its own citizens. In fact, public opinion in America has been so one-sided on such questions that wherever private enterprises have been taken over by the states or the nation they have thereafter been conducted free or at the bare cost of operation. The turnpike roads were bought by the states and made part of the free public road system. Cities like Cleveland and San Francisco have handled their street railways at the bare cost of operation. Efforts are being made to make the Panama Canal free to certain classes of commercial shipping. Government land reclamation by irrigation and drainage has been made so that it could be paid for by the settlers in small amounts, running through long periods of time. But notwithstanding all this there is an awakening to the possibilities that may come from the development and operation by government of resources that were formerly considered fair game for private exploitation.

Such disputes as the two nation-wide industrial strikes of 1922, the coal miners and the railway craftsmen, are rapidly forcing those not directly connected with the “operators” or the “strikers” to the opinion that government ownership is the remedy for industrial ailments of this character. They point to the Post Office Department as an argument in favor. While it is a fact there has been no trouble so far with postoffice employees, it does not follow that the same would be true with the railway, coal mining, and cotton industries. And if the Government should begin taking over industrial and commercial enterprises, where would be the end of such paternalism, and would it lead to sovietism? It is barely possible that governmental regulation has already gone too far.

But, nevertheless, from some such sources as have been mentioned or from a sales tax on gasoline may eventually come a relief to the burden of taxation which now and increasingly so in the future must otherwise be borne by the land.

=Bonds.=--It is not always possible to raise by taxes sufficient money to make public improvements on a pay-as-you-go basis. It would not be economical to attempt to pave one-tenth the width of a street each year. One patch would be worn out before the next is put down. The whole must be done at the same time in order not to be vastly wasteful. And, in order to enjoy the improvement while money is being collected for its payment, the municipality must resort to borrowing. It is also argued that since future generations will enjoy the improvement they should be required to help pay for the same. The indebtedness represented by the bonds become a lien against the assessed property in the state, county, township, or district over which they have been laid. The taxes to pay off the bonds will be levied uniformly over all property or specially in proportion to accruing benefits according to conditions prescribed at the time the improvements were made.

=Kinds of Bonds.=--Bonds are certificates of indebtedness by means of which the repayment of borrowed money may be spread over a series of years. They are classified as Sinking Fund, Annuity and Serial, depending on their manner of payment.

_Sinking fund_ bonds are paid as a whole at the end of their term, interest being paid annually, or at some other fixed regular period, upon their face value. The name arises because of the custom of establishing a sinking-fund into which a certain proportion of the debt is to be paid annually, and this loaned out so that at the end of the period it will amount to the face of the bonds. Since there is always time lost between the collection and loaning of the sinking fund money the interest derived therefrom will not usually be the same as that of the bonds. For this reason and from the further fact that sinking funds are frequently drawn upon for other purposes than that for which they were created this type of bonds is less economical than either of the other two types.

The sinking fund which must be raised annually to discharge a debt of _P_ dollars in _n_ payments, if it can be loaned at _i_ per cent, is given by the formula:[197]

_i_
Sinking fund = ------------------- . _P_
(1 + _i_)^{_n_} - 1

To illustrate the use of the formula let the debt be $10,000, the average rate that can be expected from the sinking fund 4 per cent, and the time five years. Substituting in the formula,

.04
_S_ = ------------- . $10,000
(1 + .04)⁵ - 1

To solve, the denominator is first evaluated:

Log (1 + .04)⁵ = 5 log 1.04
= 5 × 0.017033
= 0.085165

Taking the antilog,

(1 + .04)⁵ = 1.21665

and

(1 + .04)⁵ - 1 = 0.21665

Then

0.4 × $10,000
_S_ = ------------- = $1846.27.
0.21665

Annuity tables, which may be seen at nearly any bank or brokers’ office, or in Bulletin 136, U. S. Department of Agriculture, give the annuity which will amount to 1 in five years at 4 per cent as 0.1846271; this multiplied by $10,000 gives $1846.27.

To the nearest cent the following tabular statement shows the growth of the sinking funds:

----+------------+---------------+---------------+------------------
|Sinking-fund| |Annual Payments|Total Sinking-fund
|at Beginning|Interest during| into | at End
Year| of Year | Year | Sinking-Fund | of Year
----+------------+---------------+---------------+------------------
1 | 0. | 0. | $1,846.27 | $ 1,846.27
2 | $1846.27 | $ 73.85 | 1,846.27 | 3,766.39
3 | 3766.39 | 150.66 | 1,846.27 | 5,763.32
4 | 5763.32 | 230.53 | 1,846.27 | 7,840.12
5 | 7840.12 | 313.61 | 1,846.27 | 10,000.00
----+------------+---------------+---------------+------------------

If this loan, the bonds, bore 5 per cent interest the cost to the borrower would have been the principal plus the interest on principal less the interest on the sinking fund:

$10,000 + $2500 - $768.65 = $11,731.35;

or the interest on the loan plus the sinking-fund payments:

$2500 + $9231.25 = $11,731.35

_Serial Bonds_ are such that a fixed amount of the principal is retired at definite periods of time. Usually the amount retired is an aliquot part of the whole. The payments to be made at any particular time is the fixed portion of the principal plus the interest on the unpaid portion up to that date. The periods of retirement are usually annual or semi-annual.

Assuming the principal to be _P_ and that one nth part of it is paid each year, the formulas are:

( 1 ( 1 - _k_))
Annual payment for the _k_th year = _P_(--- + _i_(1 + -------)).
(_n_ ( _n_ ))

( 1 - _k_)
Interest for the _k_th year = _Pi_(1 + -------).
( _n_ )

Total amount of interest to the end of ( 1 - _k_)
the _k_th year = _Pik_(1 + -------).
( 2_n_ )

Total amount of interest and principal ( 1 ( 1 - _k_))
paid up to the end of the _k_th year = _Pk_(--- + _i_(1 + -------)).
(_n_ ( 2_n_ ))

The following table shows how a debt of $10,000 bearing 5 per cent interest would be discharged by equal annual payments in five years:

----+------------+------------+----------------+------------
|Principal at| |Principal Repaid|
|Beginning of|Interest for| at end of |Total Annual
Year| Year | Year | Year | Payment
----+------------+------------+----------------+------------
1 | $10,000 | $ 500 | $ 2,000 | $ 2,500
2 | 8,000 | 400 | 2,000 | 2,400
3 | 6,000 | 300 | 2,000 | 2,300
4 | 4,000 | 200 | 2,000 | 2,200
5 | 2,000 | 100 | 2,000 | 2,100
| +------------+----------------+------------
|Totals | $1,500 | $10,000 | $11,500
----+------------+------------+----------------+------------

_Annuity Bonds_ are those wherein a uniform periodic payment is made to discharge the debt in a given time. The formula for the necessary payment to discharge a debt of _P_, with interest rate _i_ in _n_ years is,

_i_
Annual payment = -------------------- . _P_.
1 - (1 - _i_)^{_-n_}

Results may be taken from books of tables already referred to or by means of logarithms the formula may be solved. For example let it be required to discharge a debt of $10,000 in five equal payments, the rate of interest being 5 per cent.

Solution:

(1 + _i_)^{_-n_} = 1.05⁻⁵.

Log 1.05 = -0.021189
-5 Log 1.05 = -0.105945
= 9.894055-10
Log⁻¹(9.894055-10) = 0.783529
1 - 0.783529 = 0.216471
Log Annual Payment = Log _i_ - Log 0.216471 + Log _P_
= Log 0.05 - Log 0.216471 + Log 10,000
= (8.698970 - 10) - (9.335398 - 10) + 4.000,000
= 3.363572
Annual Payment = Log⁻¹ 3.363571 = $2309.748.

The following table shows the repayment of the loan by annual payments of $2309.75:

----+------------+------------+----------------+-------------
| Principal | | |
| Owing at | |Principal Repaid|
|Beginning of|Interest for| at End |Total Payment
Year| Year | Year | of Year | for Year
----+------------+------------+----------------+-------------
1 | $10,000.00 | $500.00 | $1,809.75 | $2,309.75
2 | 8,190.25 | 409.51 | 1,900.24 | 2,309.75
3 | 6,290.01 | 314.50 | 1,995.25 | 2,309.75
4 | 4,294.76 | 214.74 | 2,095.01 | 2,309.75
5 | 2,199.85 | 109.99 | 2,199.75 | 2,309.74
| +------------+----------------+-------------
|Totals | $1548.74 | $10,000.00 | $11,548.74
----+------------+------------+----------------+-------------

Since it is more convenient to have the bonds in even hundreds of dollars and the interest in dollars some adjustment from the theoretical amounts are usually made but such that the annual payments will be near the theoretical. Sometimes, too, the bonds are made smaller for the first few years then gradually increase so that the natural growth in population and wealth may bear its proportional burden. One adjustment for the example just given is shown:

----+------------+------------+----------------+-------------
| Principal | | |
Year| Owing at | |Principal Repaid|
|Beginning of|Interest for| at End |Total Payment
| Year | Year | of Year | for Year
----+------------+------------+----------------+-------------
1 | $10,000 | 500 | $1,800 | $2,300
2 | 8,200 | 410 | 1,900 | 2,310
3 | 6,300 | 315 | 2,000 | 2,315
4 | 4,300 | 215 | 2,100 | 2,315
5 | 2,200 | 110 | 2,200 | 2,310
| +------------+----------------+-------------
| Totals | $1,500 | $10,000 | $11,550
----+------------+------------+----------------+-------------

=Total Cost by the Three Kinds of Bonds.=--The total cost of a loan, as shown by the following table taken from Bulletin 136, U. S. Department of Agriculture, is generally greatest under the sinking fund plan and least under the serial. The serial, too, is the simplest to compute.

TOTAL COST OF A $100,000 LOAN FOR 20 YEARS

Interest Compounded Annually[198]

--------+--------------------------+--------+--------
Annual | Sinking-fund Bond Com- | |
Interest| pounded Annually at | |
on +--------+--------+--------+Annuity | Serial
Bonds | 3% | 3¹⁄₂% | 4% | Bond | Bond
--------+--------+--------+--------+--------+--------
4 |$154,431|$150,722|$147,163|$147,163|$142,000
4¹⁄₂ | 164,431| 160,722| 157,163| 153,752| 147,250
5 | 174,431| 170,722| 167,163| 160,485| 152,500
5¹⁄₂ | 184,431| 180,722| 177,163| 167,359| 157,750
6 | 194,431| 190,722| 187,163| 174,369| 163,000
--------+--------+--------+--------+--------+--------

The sinking-fund bonds are made out to run the full period and are paid for from the proceeds of the sinking-fund at the end of the term. Serial and annuity bonds are made to mature in proportion to the amounts paid each year. In the example used the serial system would retire $2000 worth of bonds each year, while with the annuity system $1800 would be retired at the end of the first year; $1900, the next; $2000, the third; $2100 the fourth, and $2200 the fifth.

Interest coupons, that is, notes for the payment of interest at stated intervals and providing for interest upon the interest if not paid at maturity, are usually attached to the bonds for the entire period that they run, one to be clipped at each interest pay day.

=The Term of Bonds.=--Several states and some of the large cities have issued bonds for road improvements for long series of years. This has met considerable opposition on the ground that the bonds should not run longer than the life of the improvement, otherwise there may be another series of bonds lapping upon the first, and perhaps a second and third upon these. The arguments in favor of the long terms are that some parts, at least, of the improvement will be permanent, that reconstruction will cost less than original construction so that lapping will do little harm, and that money may be obtained at a lower rate on long-term than on short-term bonds.

It is a quite general practice for the abutting property-holders to pay for the first pavement by special assessment. Resurfacing is frequently and general repairs almost universally paid for by the city as a whole. It would seem, especially where property-holders pay on the installment plan, that a term of bond well within the life of the pavement ought to be adopted. Ten years seems a reasonable time, fifteen years at the longest. If borrowing is continued and one loan lapped upon another there comes a time when the charges for paying off the debt and the interest will more than equal the amount that can be borrowed. For instance suppose a man can continue to borrow $1000 per year on five years’ time, $200 to be paid each year. During the first year he would owe $1000, and at the end of the year he pays $200 on the principal and the interest. He borrows another $1000, so during the second year he is in debt $1800 and must pay at the end of the year $400 principal and $108 interest. The third year he is in debt $2400 and pays on principal $600 and interest $144. The fourth year his debt is $2800, and payment on principal $800 and the interest, $168. The fifth year and every year following the debt is $3000 and the payment necessary on principal $1000 and the interest $180. The payments on the principal amount is equal to exactly the sum he can borrow. While the amounts used in the illustration are small the principle is the same for loans upon long-term bonds.

It would be better for cities and states to progress more slowly than to have saddled upon them a debt in perpetuity. There are times, however, when municipalities or other districts will find it the best policy to borrow money and issue bonds. Serial and annuity bonds have this advantage that as the improvement depreciates in value with time the burden of indebtedness for the improvement becomes less. But it can scarcely be considered the part of wisdom to have the bonds run longer than the life of the pavement for which they were issued. The pay-as-you-go plan is by far the most economical method of procedure, but it cannot always be followed. There are times when budgetary appropriations are insufficient and the people will not stand for heavy taxation. In one city it had been the custom for the city by general taxation to pay for paving intersections. As the intersections amounted to about 30 per cent. of the total area paved that was thought to be an equitable division, because the entire city receives some benefit from each pavement put in. But the applications for paving were much more each year than the city could pay for from its ordinary budget. The amount of paving done each year was limited by the area of intersections that the city was able to lay. Some districts said, “We will pay for the whole pavement, intersections and all, rather than go without or wait over one or two years.” The city council allowed this to be done, and, soon, even went further and passed an ordinance taxing the whole cost including the intersections to the fronting property. This method has been in use for several years and the city of less than 70,000 inhabitants has more than 200 miles of pavement, and no citizen was ever known to protest the scheme. Of course the public as a whole could have paid for all these intersections by general taxation just as easily as the private property-holders could, but if taxes had been raised for that purpose there would have been many complaints that the poor were being taxed to pave the streets in front of the residences of the rich.

In fact, the last idea mentioned is one of the arguments in favor of large bond issues such as are found in several of the states like New York, Maryland, Illinois, California, Missouri and other states, to say nothing of cities and counties. The argument is that the entire state, county or city system should be constructed about the same time that all may have equal benefit of it and that there shall be no intentional partiality. Nelson P. Lewis states in the American Highway Engineers’ Handbook in effect that on a 4 per cent basis the $100,000,000 bonds of the state of New York will mean an annual tax of $4,890,000 for interest and sinking-fund charges, to say nothing of the annual maintenance and renewal expenses, running through two generations. He claims the same system of roads could have been built, at no greater annual appropriations, in twenty years’ time and the people would not have been saddled with debt, and it will require at least half that time to complete the system with the bonds and the debt.

In Illinois, on the other hand, the debt, some $60,000,000 is to be paid from the automobile licenses, which will be used for its amortization. In Maine automobile licenses are also being used to pay bonds, but only $500,000 will be issued in any one year and the total outstanding cannot by law exceed $2,000,000.

Maryland uses a short-term-bond--fifteen years--and provides that any road renewals required before that time shall be paid for out of general appropriations.

New York city had issued bonds until more than two-thirds of the total taxation for streets had to go to interest and amortization so some years ago a change was made to what they called the pay-as-you-go plan. It took four years to make the change, so, now, non-revenue-producing improvements are made without issuing bonds. Revenue-producing enterprises, such as water supply, transit lines, and water-front improvements, are still financed by long term, 50-year bonds.

=Stocks and Bonds.=--Railways, interurban trolley lines, street-car lines, and toll roads have been financed largely by stock subscriptions. Public roads, being without a revenue-producing power, cannot be financed in this manner, except perhaps in exceptional cases where a few persons are willing to donate their money or are building for private use but are willing to share the same with the public. Large bridges may occasionally be built in this manner, the stockholders exacting toll for passage in order to get a return on their investment. However, such cases are negligible in the great national scheme of public highways.

=National and State Aid.=--The history of National and State Aid in the United States has been treated quite fully in Chapter V. It will not be necessary to repeat that here. Suffice to say that with possibly a few exceptions all the states in the Union now have some form of state aid--money, engineering advice, testing materials, convict labor, etc.; also the territories of Alaska, Hawaii, the Philippine Islands, and Porto Rico, or else the governments of these divisions directly take charge of the construction of a part or a whole of the roads. The acceptance of Federal Aid practically made it necessary for the states to have highway departments to distribute the Federal Aid money and the equal amount the state had to put up to match it. Several of the states like New York and California had raised by bond issues large sums of money before federal aid was available and distributed it to counties that would coöperate in the building of roads to be united into a comprehensive state system. New Jersey, the first State Aid state, and Massachusetts, a close follower, had already “paved the way” as an example for other states to follow.

=Federal Aid.=--The Federal Aid road act, approved July 11, 1916, appropriated “out of any money in the Treasury not otherwise appropriated, for the fiscal years ending June 30, 1917, the sum of $5,000,000; for the fiscal year ending June 30, 1918, the sum of $10,000,000; for the fiscal year ending June 30, 1919, the sum of $15,000,000; for the fiscal year ending June 30, 1920, the sum of $20,000,000; and for the fiscal year ending June 30, 1921, the sum of $25,000,000.” In addition there was appropriated $10,000,000--$1,000,000 per year until 1926--for the survey, construction and maintenance of roads within or partly within the national forests in coöperation with the states in which these forests are located.

The Secretary of Agriculture was by the Act, after making a deduction of 3 per cent, to cover expenses of administration, authorized to apportion the remainder “among the several states in the following manner: One-third in the ratio which the area of the State bears to the total area of all the States; one-third in the ratio which the population of each State bears to the total population of all States...; one-third in the ratio which the mileage of rural delivery routes and star routes in each State bears to the total mileage of rural delivery routes and star routes in all the States....”

States desiring to avail themselves of the benefits of the act were required to “submit to the Secretary of Agriculture project statements setting forth proposed construction of any rural post road or roads therein.” If approved the states were further to “furnish to him surveys, plans, specifications and estimates therefor as he may require.” Only such projects as were “substantial in character” might be approved. “Items included for engineering, inspection, and unforeseen contingencies” may not be greater than 10 per cent of the total cost of the work. Upon the final approval by the Secretary of Agriculture of the plans, specifications and estimates and its certification to the Secretary of the Treasury the Act provides that there should be “set aside the share of the United States payable under this Act on account of such project,” not to “exceed fifty per centum of the total estimated cost thereof.”

© _Underwood and Underwood_

A NATIONAL HIGHWAY IN THE MOUNTAINS OF MARYLAND]