
9 Cal.2d 366 (1937)
E. G. OTIS, as Receiver, etc., Respondent,
v.
LOS ANGELES COUNTY (a Body Corporate and Politic), Appellant.
L. A. No. 15944. 
Supreme Court of California. In Bank.  
July 30, 1937.
 Everett W. Mattoon, County Counsel, and J. H. O'Connor, Assistant County Counsel, for Appellant.
 Meserve, Mumper, Hughes & Robertson for Respondent.
 Allard, Holbrook & Whyte, Cruickshank, Brooke & Evans, Bailie, Turner & Lake, Holbrook & Tarr, Overton, Lyman & Plumb, Loyd Wright, Clock, McWhinney & Clock, Jesse H. Steinhart and B. J. Feigenbaum, as Amici Curiae on Behalf of Respondent.
 SHENK, J.
 The County of Los Angeles appeals from a judgment determining that the county tax levy for the fiscal year 1933-1934 was invalid and excessive in two particulars, and that the plaintiff was entitled to a refund of $250.80 of county taxes paid by him for that year.
 The facts are not in dispute. The plaintiff as receiver of the properties of the Seventh and Grand Avenue Building Company, a corporation, in December, 1933, paid to the tax collector of the County of Los Angeles the sum of $9,166.34. That sum represented the first instalment of taxes for the fiscal year 1933-1934 levied against the properties of the receivership estate on account of taxes for Los Angeles County, the city of Los Angeles, and other taxing entities whose taxes were collected at the same time as the general county tax. The assessed valuation of the plaintiff's properties for the fiscal year in question was $428,000. At the time of payment plaintiff filed a written protest, claiming various items had been illegally levied. Thereafter, pursuant to the provisions of section 3804 of the Political Code, the plaintiff filed a claim for refund with the board of supervisors and upon denial of the claim, filed his complaint, alleging many grounds of alleged invalidity in the levy. The trial court determined that all claims of the plaintiff, except as to two items, were without merit. As to these two items, the court determined that the tax levied to the extent thereof was invalid, and entered its judgment as above indicated.
 The two items involve quite independent considerations but a determination of both hinges upon the proper effect to be given to the county's financial setup for said fiscal year *368 under section 3714 of the Political Code. That setup shows separately the appropriation requirements, including the reserves, also the available funds, including miscellaneous revenues and surplus, all of which are taken into consideration in fixing the tax rate.
 The tax base or assessed valuation, exclusive of securities and solvent credits, was $2,072,316,310. The total amount required for general and special county funds was $35,712,646.59. The amount to be raised by taxation was $35,400,040.65. We are here particularly concerned with the general fund appropriations as bearing upon the ascertainment of the correct amount to be allocated to "unappropriated reserves".
 The budget for general county funds included the sum of $12,352,237.43 for "appropriations"; the sum of $1,744,725 for "unappropriated reserves"; the sum of $3,263,000 for "general reserves", making a total of $17,359,962.43. The budget surplus carried over from the preceding fiscal year was $3,508,174.88.
 The problem first presented involves the construction of section 3714 of the Political Code as amended in 1929, and particularly subdivision 3 thereof, which reads, in its pertinent parts, as follows: "The county board of supervisors may, if it deem advisable, set aside a portion of each fund, other than school funds, to be known as 'unappropriated reserves' which shall not exceed ten per cent of the total amount of said fund exclusive of surplus ... Said budget shall contain an amount or amounts to be known as a general reserve or 'general reserves', if carried in separate funds, in such sum or sums as the county board of supervisors shall deem sufficient ..."
 Assuming to act under the authority of the foregoing provisions of said section 3714 the board of supervisors of the defendant county appears to have included both "unappropriated reserves" and "general reserves" in fixing the amount of "unappropriated reserves". The trial court concluded that in arriving at the amount of "unappropriated reserves" both items of "general reserves" and "unappropriated reserves", as well as surplus should be excluded; that is to say, that the correct computation in arriving at the "unappropriated reserves" was to deduct surplus from the amount of *369 "appropriations" only, and to fix ten per cent of the remainder as the "unappropriated reserves".
 [1] The defendant concedes that the "unappropriated reserves" as fixed by the board is excessive to the extent of $399,495.83, but contends that both the "unappropriated reserves" and the "general reserves" should be added to the "appropriations" in arriving at the percentage for "unappropriated reserves". The contention cannot be sustained as to the inclusion of the "unappropriated reserves". While it is true that the "unappropriated reserves" is a budget item, and therefore properly included in the budget for the purpose of fixing the tax levy it is not an item which enters into the computation of the ten per cent of the several funds in arriving at the amount of the "unappropriated reserves". The weakness of the defendant's position in this respect is that, according to its contention, the fund upon which the statutory ten per cent limitation is to be computed includes the very amount which the computation aims to disclose. Under no construction of the statute would it be permissible to add to the definite amount which forms the basis of the ascertainment of the permissible ten per cent the ten per cent itself. The "unappropriated reserves" should therefore not have been included in the base for the ascertainment of that very fund.
 But it is clear that the "general reserves" should have been included in the base for the ascertainment of the ten per cent for "unappropriated reserves". The "general reserves" constitute a budget item. The fair and we think the only reasonable construction of the statute requires that the fund or funds upon which the ten per cent for "unappropriated reserves" is to be figured include all of the budget items to be raised by taxation for county general fund purposes. Included therein would be the fund of "general reserves", the amount of which is subject to the reasonable discretion of the board of supervisors, and is not dependent upon a limitation otherwise, nor upon a percentage of any other fund or combination of funds. The result of the inclusion of this fund would be that the base for the ascertainment of the percentage should be increased by the amount of the "general reserves", and the refund to the plaintiff decreased accordingly. As already indicated the trial court found that the figure upon which the 10 per cent was to be computed was $8,844,062.55. The trial court should have *370 included the $3,263,000 appropriated for "general reserves". The proper base figure is therefore $12,107,062.55. The proper allowance for unappropriated reserves should have been $1,210,706.25. Inasmuch as the actual allowance for this item was $1,744,725, it is obvious that there was appropriated for this purpose the sum of $534,018.75 in excess of the amount permitted by law.
 [2] The second respect in which the levy was held illegal and excessive in part is based on the following facts: The tax rate for the county for 1933-1934 as fixed by the board of supervisors was $1.20 on each $100 of assessed valuation. This levy was made on real and secured personal property. In addition to this levy the county had other sources of income such as certain estimated miscellaneous receipts. Also under article XIII, section 9a, of the Constitution as added in 1924, a special rate was fixed for unsecured personal property, and pursuant to the 1928 constitutional amendment of article XIII, section 16, of the Constitution, there was a special statutory rate on solvent credits and securities. Political Code section 3627a as it read at the time here involved fixed this rate at one mill per dollar of valuation on solvent credits and two mills per dollar of valuation on stocks and bonds. The proceeds of the taxes levied on solvent credits and securities are divided between the various tax agencies as provided in section 3627a. On the present appeal, as far as the point under discussion is concerned, we are interested only in the proceeds of the tax on solvent credits and securities. It is an admitted fact that the county's estimated share of the revenue from this last named source for the fiscal year in question was known to be $389,581.45, and it is also an admitted fact that in fixing the levy on real and secured personal property the board of supervisors gave no consideration to and did not include the revenue anticipated from the levy on solvent credits and securities. It is obvious that after the amount of all appropriations was fixed by the board of supervisors, so that the amount of money to be raised from all sources was known, a tax levy raising this amount solely on real and secured personal property and completely disregarding such a known material source of revenue, necessarily resulted in an excessive levy on the real and secured personal property. It is admitted by the defendant that had such disregarded revenue been deducted from the amount *371 to be raised on real and secured personal property, the levy on real and secured personal property would have been $.0176 per $100 of assessed valuation less than it was. The defendant contends, however, that the mere fact that the levy on real and secured personal property, when added to the revenue from solvent credits and securities, will produce materially more money than the budget requirements, does not pro tanto invalidate the levy in the absence of fraud or arbitrary or capricious action; that the proper levy and rate, in the absence of fraud, is discretionary with the board; that every tax levy is presumed to be valid; that the failure to include the anticipated revenue on solvent credits and securities can probably be accounted for as a possible allowance for anticipated delinquencies, although there is no evidence that such was the fact. In our opinion these contentions of the defendant cannot be sustained.
 The pertinent statutory provision controlling the fixing of the tax rate is also section 3714 of the Political Code. The first paragraph of that section requires each department head to submit to the county auditor on or before July 10th his itemized estimates of revenues and proposed expenditures for the succeeding fiscal year. Subdivision 2 requires the auditor then to prepare a complete expenditure program for the county and a statement of the "sources of revenue by which it is to be financed. Such tabulation shall set forth the estimated revenue from sources other than taxation for each office ... for the fiscal year to which the budget is intended to apply ... the estimated unencumbered surplus ... and the amount proposed to be raised by taxation ... and the sums necessary to be provided as 'general reserves' ...". By the provisions of subdivision 3 such tabulation is then submitted by the auditor to the board of supervisors. The board is required to "consider the same in detail, and shall ... make, except as otherwise provided in this section, any revisions, reductions or additions therein, that it may deem advisable ... to make said budget conform to the judgment and conclusion of the county board of supervisors as a proper financial program for the county ...". The same subdivision as already pointed out, authorizes the board to include allowances for unappropriated reserves and for general reserves. This subdivision then provides that the auditor's tabulations as revised by the board shall constitute the preliminary *372 budget, which must then be printed and made available to interested taxpayers. Subdivision 4 requires the board to hold hearings on the preliminary budget. At the conclusion of these hearings, and not later than August 30th, the board shall, "by resolution, adopt the budget as so finally determined ... and shall file in their offices a copy of the completed budget. The several amounts specified in the resolution as finally enacted, shall be and become appropriated for the several offices, departments, services, institutions, or districts, for the fiscal year to which the budget is intended to apply ..." Subdivision 5 provides for the levy of the tax. It provides that no later than September 1st the board shall "fix the rates of county and district taxes designating the number of cents levied for each fund upon each one hundred dollars of assessed value of the county for the current fiscal year to raise the amount of the estimated expenditures as finally determined, less the total of the estimated revenues from sources other than taxation, including available surplus ... and must levy the state, county and district taxes. All taxes shall be levied upon the taxable property in the county, as provided by law, in specific sums, and the tax for county and local purposes shall not exceed the amount specified in the budget, after allowing for delinquency as provided in law ..." In Ryan v. Byram, 4 Cal.2d 596 [51 PaCal.2d 872], it was held that all of the above outlined steps "are for the benefit of the taxpayer, are mandatory, and that if any of these steps had been omitted, the tax levy would be invalid".
 It is apparent from the provisions of section 3714 above quoted that the county is required to account for all income and revenue from every known material source and that the amount of the levy is limited to the needs of the county as fixed by the board. The fixing and levying of the tax consists of three main steps: (1) fixing the valuation of the property to be taxed; (2) fixing the amount to be spent, and (3) calculating the rate. The appropriations as fixed by the board constitute the amount of money to be spent by the county during the fiscal year. Within the field of valuation, and within the field of determining the amount to be spent, except as limited by law, the discretion of the board is absolute, and cannot be attacked for anything except fraud. Stated another way, so far as we are here interested, and *373 except as limited by law, the discretion of the board as to the amount to be spent is not subject to review except for fraud. This is all that was held by the many cases cited by appellant on this phase of the appeal. In this case no attack is being made upon the action of the board in fixing the amount to be spent. It seems clear that after the valuations are fixed, and the sources of income and the amounts thereof are known, and after the board determines the amount to be spent, the fixing of the tax rate involves no discretion at all. After all the factors are known, the fixing of the rate is merely mathematical calculation. The board has no "legislative" or other kind of discretion to make this calculation other than the science of mathematics dictates. Nor has it "discretion" to make a mathematical error. Nor has it power to raise by taxation materially more than is required for expenditures except as permitted by law. It is true that any tax rate, made up as it is of various items each assessed separately, and expressed in a rate of four decimal places, will not produce exactly the amount of all the appropriations. There is usually a slight excess--but that is made necessary because of the limitations of the formula applied, and to the extent of that excess the levy is valid.
 The defendant cites three California cases dealing with the alleged discretionary powers of the board. In the case of In re Rogers, 91 Cal.App. 726 [267 P. 729], it was contended that a state levy was invalid because over the entire state an attempt to levy $1,250,000 had resulted in the collection of $1,270,000. The court held that "The record before us shows no error. The tax was levied in all respects as required by law so far as this record shows." The slight excess of $20,000 over the entire state was apparently caused either because of the impossibility of raising exactly the amount desired under a four decimal point rate, or because the estimated and permitted five per cent allowance for delinquencies did not entirely materialize. The court stated: "If the point is good it probably applies to a majority of the funds for which each annual levy is made. This is so because it can be seen at once that the computation of the body making the levy of an ad valorem tax must at all times be an approximation. It may result in collecting a few dollars too much or a few dollars too little. But the error, if any, is not actionable." *374
 In Beck v. Barnes, 129 Cal.App. 187 [18 PaCal.2d 749], there was involved a levy for the same purposes involved in the Rogers case, but for another year. It was claimed that Barnes' tax deed was invalid because the property had been sold for an amount in excess of the amount due, for the reason that there had been collected some $23,000 in excess of the amount required. The court held the excess was due to the fact that the estimated delinquencies had not materialized, and stated: "To give full force to the contention of appellant it would mean that where an estimated delinquency [and one permitted by law] was too large and more money was collected than the exact amount required, the whole tax would be void. ... There is no merit in the contention."
 Ferguson v. Gardner, 86 Cal.App. 421 [260 P. 961], merely holds that the board of supervisors has complete discretion as to the amount of appropriations, which, in the absence of fraud, cannot be questioned. The cases cited from other jurisdictions are of little assistance.
 In the present case the board properly exercised its discretion in fixing the amount of the appropriations. It knew the assessed valuation of real and secured personal property. It knew the amount of surplus and the amount of miscellaneous revenue. It also knew the valuations of the solvent credits and securities in the county, and it knew that the rates in reference to them were fixed by statute on a statewide basis. Obviously, to compute the proper tax rate, all that was required was for the board to take the total of all appropriations, deduct surplus, deduct all anticipated revenue, including the known anticipated revenue on solvent credits and securities, and the balance represented the amount to be raised by taxation on real and secured personal property. It is also obvious that by omitting to deduct from the amount to be raised by the levy on real and secured personal property the known amount to be raised by the levy on solvent credits and securities, the properties on the realty roll, to that extent, were compelled to bear an undue portion of the burden. [3] We find no case in California directly in point, but there are California cases establishing the rule that where the board makes the calculation in such a way as to disregard the taxes to be raised from a portion of the same roll, and thereby increases the burden on the properties on the balance of the roll, the excessive portion of the rate is illegal. In *375 legal effect there can be no difference where the excessive taxes are not raised from the same class of property, but all raised on other rolls, for the same purpose for the same year. In both cases the result is that certain properties are required to bear an excess portion of the tax burden. The following cases appear to be in point on the question under discussion:
 In Madary v. City of Fresno, 20 Cal.App. 91 [128 P. 340], the action was one to recover a refund on taxes alleged to be excessive in the amount of 20 per cent by reason of the following facts: Fresno city taxes were based on county assessments. The city fixed its rate on August 16, 1909, based upon an assessment roll for the city as equalized by the board of equalization. Subsequent to the fixing of the rate the state board of equalization ordered the assessment roll of the county, including the valuations on the city property, increased 20 per cent. This, of course, increased the taxes paid by the taxpayers to the city 20 per cent in excess of the estimated and previously determined needs, just as in the present case the levy on the real and secured personal property produced $389,581.45 in excess of the previously determined needs. The court held that the excess was illegally levied and could be recovered. In discussing the practical effect of the raising or lowering of the valuations and the difference such action has upon city and county taxes, the court, at page 96, stated: "So far as county taxation is concerned, it is a matter of comparative indifference whether the assessed valuation of its taxable property, as determined by the county assessor and board of supervisors, be raised or lowered by the state board of equalization, because the rate of taxation is not fixed by the supervisors until after the action of the state board. The amount of money to be taken from the pockets of the taxpayers of the county for county purposes is not thereby affected. But as to the city, in such case, any change in the assessed valuation by the state board must have one of two effects, equally intolerable; either to deprive the city government of necessary funds or give it what it neither asks nor needs, thereby unjustly adding to the burdens of its citizens. A conclusion so obnoxious and damaging to the taxpayer could be justified only by the plainest provisions of the statute. And not only are there no such plain provisions, but the entire spirit of the law negatives such conclusion." *376 At page 97 the court discussed the power of taxation as follows: "The power of government to exact from the citizen a part of his property in way of taxation is indeed vast, but it is not unlimited. It may be exercised only for the public good and for a public purpose. 'Cooley's definition of taxes as "enforced contribution levied for public need" states concisely both the nature and limitation of taxes. Taxes are the property of the citizens demanded and taken by the government to enable it to discharge its functions. In his work on Tax Titles, Blackwell defines taxes as "burdens imposed by the legislative power upon persons or property to raise money for public purposes". The needs of the government constitute then both the occasion and limitation of the taxing power. To take from the citizen a dollar beyond the needs of government is not taxation; it is extortion.' " And at page 98 it is stated: "It seems eminently just that this money, collected by the city in excess of its needs as determined by the constituted authorities, should be returned to those upon whom the unnecessary burden was imposed, and no merely technical objection should stand in the way of this consummation."
 In Redman v. Warden, 92 Cal.App. 636 [268 P. 686], the action was one to quiet title against a tax deed. The tax deed claimant based his claim to ownership on a tax deed from the tax collector of Los Angeles County issued as a result of unpaid taxes and a sale based thereon for the year 1916. Part of the unpaid taxes included school taxes for the Antelope Union High School District, within which the property was located. The Antelope district included various other districts, one levy being made for the entire district. One of the included districts was the Esperanza School District, and another was the Redman Elementary School District. The property in question was within the last named district. The school district tax was levied on the lands within the Antelope district except that "either inadvertently or designedly" the lands within the Esperanza district were omitted from the levy. The whole district tax was levied upon the remainder of the lands within the district. The effect of the omission of this one source of revenue, i. e., the levy on the lands within the Esperanza district, was "to increase the proportion of such high school tax assessed against plaintiff's property". The trial court held the tax deed valid, *377 but this holding was reversed on appeal on the ground that the tax levied on the property of plaintiff was invalid because of the omissions to include the lands within the Esperanza district. (See, also, Connelly v. San Francisco, 164 Cal. 101 [127 P. 834].)
 In neither the Madary nor Redman cases was fraud an element involved. In the Madary case the excessive levy was largely caused by the acts of third persons, while in the Redman case the court held the tax invalid as to the excess whether such excess was the result of inadvertence or design.
 The reasoning of these cases is controlling here. There can be no legal distinction between a situation where the taxing authorities exclude from the levy a material portion of the property shown on a single tax roll, resulting in an excessive levy on the balance of the property, and the situation here presented where the excessive rate results from the exclusion from consideration of taxes in a material amount raised on separate rolls, for the same year and for the same fund. In both situations the excessive levy results in an increase in taxation on certain property, and to the amount of such excess is invalid.
 [4] The defendant contends that although the board omitted a known material source of income from its calculations, we must assume in support of the levy that the amount excluded was intended by the board as an allowance for anticipated delinquencies. There is no evidence, direct or indirect, that by its omission to include the $389,581.45 in its calculations, it intended that this sum should constitute an allowance for anticipated delinquencies. There can be no doubt that the board can and should make an allowance for anticipated delinquencies, but there can also be no doubt that the proper time to make such allowance is during the preparation of the budget. The allowance for such delinquencies can be made by including such allowance in each appropriation or by making a separate appropriation therefor, or by including it within the reserves. In Ryan v. Bryam, 4 Cal.2d 596, 608, 609 [51 PaCal.2d 872], in speaking of the levy made by the board of supervisors of Los Angeles County for the fiscal year 1935-1936, it was stated: "As to the 10 per cent allowance for anticipated tax delinquencies, it is stipulated that in 1932-1933, the delinquencies amounted to 12.70 per cent; in 1933- 1934, to 11.55 *378 per cent; in 1934-1935, to 9.97 per cent. These facts were explained to the board. The preliminary budget contained no allowance for this item. The auditor explained to the board at length that this was because in fixing the allowance for reserves in the preliminary budget, he had made them large enough to absorb these anticipated delinquencies. When the board determined to pare the reserves, it was obvious that some allowance for this item would have to be made. Although the record is not as clear as might be desired on this point, it fairly appears that prior to August 31st the board determined to make a 10 per cent allowance for this item." Having the power to pass on this question, and to provide for delinquencies at the time the budget is prepared, we must assume that the power was exercised at that time. A reading of section 3714 of the Political Code clearly indicates that the board must fix that allowance at that time and not at the time of fixing the tax rate.
 It may be here noted that since the decision in the Byram case the board has adopted the policy of expressly providing in the budget for expected delinquencies, instead of indirectly providing for them as was the policy prior to that time. It may also be noted that since the trial court's decision in the present case the board in computing the rate has made the proper allowance for the revenue derived from solvent credits and securities.
 It follows that the judgment in so far as it ordered the refund of $75.32 to the plaintiff on the second item is correct. As to the first item computations are necessary in order to arrive at the correct result. These computations should be made by or under the directions of the trial court. Accordingly the judgment is reversed and the cause remanded with directions to the trial court to compute the amount of refund to which the plaintiff is entitled in accordance with the views expressed in this opinion, and render its judgment accordingly, each party to bear its own costs.
 Curtis, J., Seawell, J., Nourse, J., pro tem., and Sturtevant, J., pro tem., concurred.
