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(c) Calculation of correct amount of taxes and commission:

In this case the following should be observed : (1) The commission actually payable will be less than $14,000.00,

whereas the tax will be more than $19,980.00. (2) For every one hundred dollars of taxes payable the commis

sion will be $20 less than $14,000.00. (3) For every $20 less of commissions paid the tax will be $9.20

more, namely:

On account of the excess-profits tax under the second bracket, 40%, or $8.00 On account of the income tax, 10% of the balance of $12.00, or....

1.20

Total

$9.20

(4) It follows from (2) and (3) that for every $100 of taxes

actually payable the commission of $14,000.00 will be reduced by $20 and the tax computed ($19,980) in

creased by $9.20, so that (5) the amount of the tax ($19,980) in the above preliminary calculation is 90.8% of the correct amount, which will

$19,980 therefore be x 100=$22,004.40, and (6) the correct amount of commission will be 20% of $22,004.40

=$4,400.88 less than $14,000.00, or $9,599.12.

90.8

Proof of correctness of solutions:

The following statement will prove the above results:

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Computation of commission
Income before deducting taxes..
Deduct-federal tax payable....

$70,000.00 22,004.40

Profit on which 20% is payable...
Commission @ 20% (as above).

$47,995.60

9,599.12

General rules and formule:

It will be noted that the same percentage (90.8%) is applied to the preliminary results of each method and is computed by (1) applying the rate of commission (20%) to the rate of tax (46%), (the above example illustrating the procedure in cases falling under the second bracket), and (2) thereupon deducting the resulting figure (9.2) from 100, in this case leaving 90.8.

If the rate of commission is c and the tax rate is t, the general formula to ascertain the percentage X to be applied either to the preliminary amount of the commission obtained by the first method or the preliminary amount of the tax obtained by the second method will be

ct

X = 100

100

In case the tax is to be calculated under the second bracket of the excess-profits tax, as in the example given, the above formula works out as follows:

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If the tax is to be calculated under the first bracket,

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If only the normal income tax is payable,

X = 100

20 X 10

= 100 - 2 = 98

100

Inasmuch as there are many cases in which it is difficult to determine whether the tax is to be calculated under the first or the second bracket, it will be well to discuss a method whereby this can be readily determined.

Under the terms of the law, the 1920 excess-profits rate of the second bracket (40%) is applied to all profits over 20% of the invested capital. In other words, 20% of the invested capital is the high limit within which the 1920 rate of the first bracket (20%) will be applied, all income over and above that limit being taxable at 40%. It will also be seen that 20% of the invested capital would in such a case represent the earnings after deducting the unknown amount of the commission at the known rate, or the taxable in

come.

The problem is now reduced to the simple one of finding an amount from which a percentage is deducted when the percentage and the resulting balance are given, as for instance:

What is the amount (x) which leaves $16,580 after deducting 20% of x.

It will at once be seen that $16,580 represents 80% of x, which, therefore, is $20,725.

we now apply this procedure to the adopted hypothetical case we find that 20% of the invested capital, or $20,000, represents the above-discussed taxable income. Upon this amount a federal tax of $3,420 is payable-$1,800 as excess profits and $1,620 as income tax-leaving $16,580 as the balance of profit after first deducting taxes and thereupon 20% commission.

The amount from which the commission is calculated is there

$16,580 fore

$20,725, the commission $4,145, and the amount of .80 income (before deducting either taxes or commission) beyond which the 40% rate will be applicable, $24,145.

In general terms, if the invested capital is C, the amount of the tax T and the rate of commission c, the amount which the earnings

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(after deducting commission) can not exceed without becoming subject to the higher rate of excess-profits tax will be:

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Again applying this test to the hypothetical case discussed in the foregoing pages, where the invested capital is $100,000.00 and the rate of commission 20%, we find :

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This is therefore the amount on which 20% commission, or $4,145, is to be paid, from which it follows that $24,145 is the limit beyond which, with an invested capital of $100,000 and the commission rate of 20%, the earnings before deducting taxes and commission can not rise without becoming taxable under the second bracket. The method or rule to follow in each case will therefore be:

(a) Take 20% of the invested capital.....
(b) Compute the federal tax payable on this amount.
(c) The balance will represent the net profit after deducting

taxes and commission....

$20,000.00

3,420.00

16,580.00

100-C

(d) Divide this balance by

.80

100

(e) The quotient will represent the taxable income, viz.....
(f) Add the above amount of the tax.....
(g) The sum will represent the limit of profit before deducting

either taxes or commission...

20,725.00 3,420.00

24,145.00

PROBLEM II

COMMISSION PAYABLE AFTER DEDUCTING THE ENTIRE AMOUNT OF EXCESS-PROFITS TAX, BUT BEFORE DEDUCTING THE NORMAL

INCOME TAX, OR VICE VERSA

Occasionally the commission is to be computed upon the earnings after deducting excess-profits taxes, but before deducting the normal income tax, or vice versa.

The solution of the first case is very simple and, applied to the standard problem used in this memorandum, will work out as follows:

Income before deducting commission or federal taxes.
Preliminary amount of excess-profits tax..

$70,000.00 21,800.00

Amount on which preliminary commission is to be computed.... $18,200.00 Preliminary commission @ 20%....

9,640.00

Inasmuch as for every $100 of commission actually payable the tax has been $40 overestimated, and for every $40 of taxes overestimated in the above calculation the commission will be $8 higher, it follows that the above preliminary amount of commission ($9,640) represents 92% of the correct amount, which is therefore $9,640

=$10.478.26. This will leave a taxable income of $59,.92 521.74 on which the excess-profits tax will be:

Income

Tax Excess-profits credit

$11,000.00 Portion of income subject to 20% tax...

9,000.00 $ 1,800.00 Portion of income subject to 40% tax..

39,521.74 15,808.69

Total ...

$59,521.74 $17,608.69 Commission will therefore be payable on $70,000.00-$17,608.69 = $52,391.31 and at the rate of 20% will amount to $10,478.26 as above.

It will also be seen that the formula, already given, to ascertain the percentage (X) to be applied to the preliminary amount of commission can be used also in this case, viz:

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100C Likewise the formula ( С T divided by

-) will 5

100 provide the means to find the limit beyond which the taxable income will become subject to the 40% tax. The amount on which the commission would have to be paid would accordingly be

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