# gross profit calculation by rallym

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```									  Review of Calculation to find
Gross Profit
Sales
- Cost of Merchandise Sold
= Gross Profit
Formula for Cost of
Merchandise Sold
Beginning Merchandise Inventory
+ Purchases
= Merchandise Available For Sale
- Ending Merchandise Inventory
= Cost of Merchandise Sold
Example
Beginning Merchandise Inventory    \$10,000
+ Purchases                          15,000
= Merchandise Available For Sale      25,000
- Ending Merchandise Inventory     - 4,000
= Cost of Merchandise Sold             21,000
Example--Continued
Sales                       \$30,000
- Cost of Merchandise Sold    21,000
= Gross Profit                 9,000
Determine Gross Profit
Sales (S)                       \$30,000
- Cost of Merchandise Sold (C)    -    ?
= Gross Profit (G)                  30% of Sales
[Gross Profit Rate (R)]

G = SR
G=30,000 x 30%
G=\$9,000
Explanation of Gross Profit
Calculation
When multiplying by a percent we convert
the percent to a constant (k) representing
the gross profit rate as a decimal.

R             30
k=            k=            k=.30
100           100
Calculate Cost Of Merchandise
Sold
Sales (S)                          \$30,000
- Cost of Merchandise Sold (C)       -     ?
= Gross Profit (G)                     9,000
G = SR                         C=S-G
G=30,000 x 30%                 C=30,000 -9,000
C= 21,000
G=\$9,000
Calculating Merchandise Available
and Ending Inventory
Beginning Merchandise Inventory(B)    \$10,000
+ Purchases (P)                         15,000
= Merchandise Available For Sale(M)        ?
- Ending Merchandise Inventory(E)     -    ?
= Cost of Merchandise Sold(C)
21,000
M=B+P
M = 10,000 + 15,000
M= 25,000

E=M-C
E = 25,000 - 21,000
E = 4,000
Calculating Merchandise Available
Ending Inventory
Beginning Merchandise Inventory(B)    \$10,000
+ Purchases (P)                         15,000
= Merchandise Available For Sale(M)     25,000
- Ending Merchandise Inventory(E)     - 21,000
= Cost of Merchandise Sold(C)
4,000

M=B+P
M = 10,000 + 15,000
M= 25,000

E=M-C
E = 25,000 - 21,000
E = 4,000
Calculating Merchandise Available
Ending Inventory
Beginning Merchandise Inventory(B)    \$10,000
+ Purchases (P)                         15,000
= Merchandise Available For Sale(M)     25,000
- Ending Merchandise Inventory(E)
- 21,000
= Cost of Merchandise Sold(C)
4,000

M=B+P
M = 10,000 + 15,000
M= 25,000

E=M-C
E = 25,000 - 21,000
E = 4,000
Summary of Calculations
R
We know:                   Step 1   k=
B=\$10,000      S=\$30,000               100
Step 2   G = kS
P=\$15,000      R=30%
Step 3   C=S-G
We must calculate:         Step 4   M=B+P
k                    Step 5   E=M-C
G
C
M
E
Calculating Gross Profit using
Algebra
All the steps previously discussed can be
combined as a mathematical statement.

⎡ ⎛      R ⎞
E = (B + P ) − ⎢ S 1 −              ]
⎣ ⎝     100 ⎠
Calculating Gross Profit Using Algebra
⎡ ⎛      R    ⎞
E   =   (B     + P   )   − ⎢S 1 −             ]
⎣ ⎝    100    ⎠
⎡          ⎛    30 ⎞
E = (10 , 000 + 15 , 000 ) − ⎢ 30 , 000 1 −         ]
⎣          ⎝   100 ⎠
E = ( 25 , 000       ) − [ 30 , 000 (1 − .3 ) ]
E = ( 25 , 000      ) − [ 30 , 000 ( .7 ) ]
E =     ( 25   , 000 ) − [ 21 , 000     ]
E = 4 , 000
Another Problem
Beginning Merchandise Inventory is \$4,000
Purchases amounted to \$6,000 and total sales
equals \$5,000 The Gross Profit Rate is 40%

What is the amount of Ending Merchandise
Inventory?
Solution
⎡ ⎛      R     ⎞
E     =   (B   + P   )   − ⎢S 1 −              ]
⎣ ⎝    100     ⎠
⎡        ⎛    40 ⎞
E = ( 4 , 000 + 6, 000 ) − ⎢ 5, 000 1 −         ]
⎣        ⎝   100 ⎠
E = (10 , 000        ) − [5 ,000 (1 −   .4 )   ]
E = (10 , 000       ) − [5 , 000 ( . 6 ) ]
E = (10        , 000 ) − [ 3 , 000     ]
E = 7 , 000

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