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The computation of commissions and federal taxes is in several instances complicated by the necessity of computing the commission upon profits after deducting the federal tax. Inasmuch as the commission itself is a proper deduction from the gross income, the tax can not be computed without determining the commission, and, vice versa, the commission can not be computed without knowing the amount of the tax.

In the succeeding pages an attempt is made to explain how a procedure can be established and to show the method of dealing with several concrete cases under the 1920 tax, as follows: Problem I—Commission payable after deducting the entire

amount of both excess-profits and income taxes. II—Commission payable after deducting the entire

amount of excess-profits tax but before deducting

the normal income tax, or vice versa. III—Commission payable after deducting a portion of

the federal tax. IV--Commission payable on a sliding scale after deduct

ing the entire amount of both excess-profits and

income taxes. V-Commission payable after deducting taxes but

considering the commission itself as a deductible expense.

In the discussion of the above problems the same hypothetical case has been used throughout, viz.: Invested capital

$100,000.00
Income before deducting taxes and commission... 70,000.00
Rate of commission, to be applied to profits after
deducting federal taxes

20% Wherever necessary the amount of the income and the rate of commission have been modified to cover the particularities of the individual case.

In the treatment of the above problems the principal object has been to present a simple solution by means of ordinary arithmetic, in each case followed by a proof of its correctness. The first problem has been approached from different angles and has been treated somewhat elaborately to show the methods by which certain fundamental rules and formulæ that have been applied throughout can be constructed. Inasmuch as in actual practice it is not always evident under which bracket the excess-profits tax has to be computed, a special effort has been made to establish a procedure whereby this can be definitely ascertained in each case by arithmetical processes.

In problem IV, where the commission is payable on a sliding scale, this procedure becomes rather complicated and recourse has been taken to a very simple algebraic demonstration; also in the treatment of problem V, giving a solution where the commission is considered a deductible expense rather than a distribution of profit, a simple equation of the first degree has been used. The problem has been introduced not so much because it will be frequently met in actual practice as to dispel any notion that such a consideration will materially complicate the solution.

PROBLEM I COMMISSION PAYABLE AFTER DEDUCTING THE ENTIRE AMOUNT OF

BOTH EXCESS-PROFITS AND INCOME TAXES

First method of solution:

The method of calculating followed herein will be (a) first to determine the taxes on the basis of the profits before deducting commission; (b) then to calculate a preliminary amount of commission payable on that basis; and (c) thereupon to ascertain the correct amounts of both taxes and commission.

Tax

(a) Preliminary computation of the tax Excess-profits credit:

Income 8% of invested capital ($100,000)..... $ 8,000.00 Exemption

3,000.00 $11,000.00

Portion of income taxable at 20%:

20% of invested capital ($100,000).... $20,000.00 Less excess profits credit....

11,000.00

9,000.00 $ 1,800.00

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$26,420.00

Preliminary amount of federal tax.....

(b) Preliminary computation of commission Income before deducting commission... Deduct preliminary amount of federal tax.

$70,000.00 26,420.00

Amount on which preliminary commission is to be computed.... $43,580.00 Preliminary commission of 20%......

8,716.00 (c) Calculation of correct amount of taxes and commission (1) It is evident that the commission actually payable will be

higher than $8,716.00; on the other hand, the tax will be

less than $26,420.00. (2) Inasmuch as the commission is payable out of that part of

the profit which is taxable at 46%, the tax will be $46 less than $26,420.00, for every hundred dollars of com

mission payable, namely: On account of excess-profits tax under the second bracket...

$40.00 On account of income tax of 10% on the remainder..

6.00

Total

$46.00 (3) For the same reason the commission will be $9.20 (20% of

$46) higher than $8,716.00 for every $46 of tax thus overprovided.

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

actually payable the tax of $26,420 will be reduced by $46 and the commission determined ($8,716) increased

by $9.20, so that (5) The amount of commission ($8,716) determined in the above preliminary calculation is 90.8% of the correct amount,

$8716 which will therefore be

X 100=$9,599.12 and

90.8

46

(6) the correct amount of the tax will be x $9,599.12=

100 $4,415.60 less than $26,420, or $22,004.40. Second method of solution:

The problem may also be approached by (a) determining as the first step the commissions on the basis of the profits before deducting taxes (instead of first determining the taxes on the basis of the profits before deducting commission as above), (b) calculating the preliminary amount of taxes on the amount of net profit so computed, and (c) thereupon computing the correct amounts of commission and taxes—as follows:

(a) Preliminary computation of commission Income before deducting taxes and commission..

$70,000.00 Commission at 20%.....

14,000.00

Balance

$56,000.00 (b) Computation of the tax on the basis of $50,000.00 taxable

income

Income

Tax Excess profits credit.....

$11,000.00 Portion of income taxable at 20%..

9,000.00 $ 1,800.00 Portion of income taxable at 40%..

36,000.00 14,400.00

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