Mr. Justice McReynolds
delivered the opinion of the Court.
The respondent owns a one-sixth interest in several leases executed 1901, 1902, 1903, and 1905, which authorize the lessee to take iron ore from certain Minnesota lands for twenty-five, forty-five and fifty years from their respective dates. These leases require payments quarterly of 25 cents royalty per ton upon all ore extracted; provide for minimum annual production and termination under specified circumstances.
During the year 1917 she received out of such royalties $260,072.30; during 1918, $219,940.43. For 1917 she was allowed $99,561.20 as depletion; for 1918, $84,979.55. Income tax was assessed against her upon the balances and payment exacted. Thereafter she unsuccessfully claimed refunds because the sums allowed for depletion were insufficient. The present suit followed.
The Revenue Act of 1918, c. 18, 40 Stat. 1057, 1066, 1067, (approved February 24, 1919) provides—
"Sec. 214. (a) That in computing net income there shall be allowed as deductions:

"(10) In the case of mines, oil and gas wells, other natural deposits, and timber, a reasonable allowance for depletion and for depreciation of improvements, according to the peculiar conditions in each case, based upon cost including cost of development not otherwise deducted: Provided, That in the case of such properties acquired prior to March 1, 1913, the fair market value of the property (or the taxpayer's interest therein) on that date shall be taken in lieu of cost up to that date: Provided further, That in the case of mines, oil and gas wells, discovered by the taxpayer, on or after March 1, 1913, and not acquired as the result of purchase of a proven tract or lease, where the fair market value of the property is materially disproportionate to the cost, the depletion allowance shall be based upon the fair market value of the property at the date of the discovery, or within thirty days thereafter; such reasonable allowance in all the above cases to be made under rules and regulations to be prescribed by the Commissioner with the approval of the Secretary. In the case of leases the deductions, allowed by this paragraph shall be equitably apportioned between the lessor and lessee."
Section 5, Revenue Act of 1916, c. 463, 39 Stat. 756, 759, is in the margin. Neither party suggests that this dif fers from the corresponding provision in the act of 1918, supra, in any way here material.
In her claim presented to the tax officer for refund of overpayment for 1917 respondent said—
"Tax as assessed is based upon income received from royalties from iron ore mines. Depletion amounting to $99,561.20 was allowed to taxpayer, whereas depletion amounting to $203,510.86 should be allowed. The latter amount is the present worth of the ore mined in 1917, as of March 1, 1913, and is arrived at by discounting the amount received in 1917 at 5% to March 1, 1913."
A like statement appears in her claim concerning overpayment for 1918.
The declaration has two counts. The first, relating to payments for 1917, alleges—
" That the value or market price of said ore in the ground untouched and unextracted on March 1, 1913, and on all dates subsequent thereto, exceeded the sum of twenty-five cents per ton, so that every ton of ore paid for under said leases in the year 1917 was disposed of at a price actually less than the market price of the ore, and if then sold free of said lease, would have realized more than twenty-five cents per ton. The actual deple tion of the mines by each ton of ore extracted was more than twenty-five cents when extracted.
" That under the terms of the law the depletion for ore extracted or considered to be extracted was fixed at the market value of the ore in place in the mine at the time and place of extraction, but if such depletion allowance per ton exceeded the amount fixed as the royalty per ton in the lease, the depletion allowance to the plaintiff could not exceed such royalty, but since the royalty when paid included an amount of interest on' the payment considered as deferred from March 1, 1913 to the date of actual payment of royalty and (sic) the allowance of such depletion .in successive years could never exceed the market value of the ore in the mine on March 1, 1913.
" That each payment for ore extracted consisted of two parts, one of which was interest on the deferred payment and the other of which was the actual present worth of the payment deferred from March 1, 1913'. Said actual present worth is accurately represented for each ton by that sum which put at interest on March 1, 1913, would produce at the date of payment for ore the royalty paid per ton; to put it in another way, the actual present worth of the ore extracted is accurately ascertained by taking from the royalty per ton paid, the part of the royalty, when and as paid, which represented interest on the deferred payment from March 1, 1913.
" That such an allowance of depletion in successive years and in the year 1917 did not and could not exceed the market value of such ore on March 1, 1913.
' *
" That if of each payment for each ton of ore extracted, the amount of such payment which represents interest on the payment as deferred and actually paid, be figured, the income of the owner will be accurately determined as that part of the twenty-five cents, which represents interest.
" That for the year 1917 a correct calculation under the rule above shows that upon the tons of ore extracted and paid for on January 14,1917, of the payment of 25‡ per ton $0.2095 was for selling price or principal and $0.0405 was interest on the deferred payments and that on the 330,507 tons extracted the plaintiff was entitled to depletion of $69,251.05; that upon the ore paid for on April 10, 1917, $0.2074 was for selling price or principal and $0.0426 was interest , on the deferred payments and that on the 48,958 tons extracted the plaintiff was entitled to depletion of $10,153.29; that on the ore paid for on July 10, 1917, $0.2053 was for selling price or principal and $0.0447 was interest on the deferred payments and that on the 231,090 tons extracted plaintiff was entitled to depletion of $47,434.55; that upon the ore paid for on October 10, 1917, $0.2032 was for selling price or principal and $0.0468 was interest on the deferred payments and that on the 432,120 tons extracted the plaintiff was entitled to depletion of $87,791.42; that plaintiff is entitled to depletion amounting for the year 1917 to $214,630.31."
Count two contains similar allegations concerning the payment for 1918.
In the trial court, after. requests, by both sides for directed verdict, the respondent had judgment and this was affirmed by the'Circuit Court of Appeals.
The latter court said—
"The sole controversy is over the correctness of the Government's method of arriving at the value of the iron ore in the ground on March 1, 1913, a matter not covered by thé revenue acts in question, nor by any regulation of the Treasury Department."
This does not accurately state our understanding of the issue. It was necessary for the taxpayer to show the illegality of the exactions. " The burden of establishing that fact rested upon it, in order to show that it was entitled to the deduction which the Commissioner had disallowed, and that the additional tax was to that extent illegally assessed." Botany Mills v. United States, 278 U. S. 282, 289, 290; United States v. Anderson, 269 U. S. 422, 443. The real point is whether respondent established her claim for refund by adequate evidence. And we think she did not.
On March 1, 1913, she was the lessor of mines from which the lessee had the right to extract ore during many years, paying therefor when taken out 25 cents per ton. Her rights were merely to receive the royalties stipulated and to regain possession when the leases terminated. Manifestly, the fair market value of this interest in 1913 was much less than 25 cents per ton of the estimated contents of the mines, but respondent introduced no evidence which tended to show such value. The suggestion that market value per ton on March 1, 1913, was equivalent to the sum which if then put at simple interest would have amounted to 25 cents when the ore was actually taken out and the stipulated royalty became payable can not be accepted. This method of estimation would decrease the 1913 market value with the passing of every year. Moreover it disregards the fact that respondent's interest was in the mines considered as entireties and not in particular parts of ore beds which the lessee had agreed to remove during designated future years.
Under the statute it became necessary for respondent to establish the fair market value of her interest in the mines on March 1, 1913, or at least that such value was not below what she claimed it was. Otherwise, she could not recover. She introduced three witnesses who testified as to ore values. No one of them gave an estimate of the value of her interest at that time. Replying to the question, "You do not mean to testify that Mrs. Spalding's interest in that ton of ore as of March 1, 1913, or at any other time, was worth 25 cents or any other sum," one of them said: " That question is based upon Mrs. Spalding's one-sixth ownership of a lease at 25 cents per ton. That question is an entirely different one from the one asked me by Mr. Zane. It would require a good deal of calculation and certain assumptions as to how fast that ore would be shipped. Then it would require discounting against those assumptions to present value. That calculation would take time, and I can not answer that without working it out." The other two gave no estimate of such value.
The judgment of the court below must be reversed. The cause will be remanded to the District Court for further proceedings in conformity with this opinion.
Reversed.
Me. Justice Butler took no part in the consideration or decision of this cause.
" Sec. 5. That in computing net income in the case of a citizen or resident of the United States—
(a) For the purpose of the tax there shall be allowed as deductions—
*
"Eighth, (a) In the case of oil and gas wells a reasonable allowance for actual reduction in flow and production to be ascertained not by the flush flow, but by the settled production or regular flow; (b) in the case of mines a reasonable allowance for depletion thereof not to exceed the market value in the mine of the product thereof, which has been mined and sold during the year for which the return and computation are made, such reasonable allowance to be made in the case of both (a) and (b) under rules and regulations to be prescribed by the Secretary of the Treasury: Provided, That when the allowances authorized in (a) and (b) shall equal the capital originally invested, or in case of purchase made prior to March first, nineteen hundred and thirteen, the fair market value as of that date, no further allowance shall be made. No deduction shall be allowed for any amount paid out for new buildings, permanent improvements, or betterments, made to increase the value of any property or estate, and no deduction shall be made for any amount of expense of restoring property or making good the exhaustion thereof for which an allowance is or has been made,"