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 + Purchases = Merchandise Available For Sale - Ending Merchandise Inventory = Cost of Merchandise Sold $10,000 15,000 25,000 - 4,000 21,000
Example--Continued
Sales - Cost of Merchandise Sold = Gross Profit $30,000 21,000 9,000
Determine Gross Profit
Sales (S) - Cost of Merchandise Sold (C) = Gross Profit (G) $30,000 ? 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 k= 100
30 k= 100
k=.30
Calculate Cost Of Merchandise Sold
Sales (S) $30,000 - Cost of Merchandise Sold (C) ? 9,000 = Gross Profit (G) G = SR C=S-G C=30,000 -9,000 G=30,000 x 30% C= 21,000 G=$9,000
Calculating Merchandise Available and Ending Inventory
Beginning Merchandise Inventory(B) + Purchases (P) = Merchandise Available For Sale(M) - Ending Merchandise Inventory(E) = Cost of Merchandise Sold(C) M=B+P M = 10,000 + 15,000 M= 25,000 E=M-C E = 25,000 - 21,000 E = 4,000 $10,000 15,000 ? ? 21,000
Calculating Merchandise Available Ending Inventory
Beginning Merchandise Inventory(B) + Purchases (P) = Merchandise Available For Sale(M) - Ending Merchandise Inventory(E) = Cost of Merchandise Sold(C) $10,000 15,000 25,000 - 21,000 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) + Purchases (P) = Merchandise Available For Sale(M) - Ending Merchandise Inventory(E) = Cost of Merchandise Sold(C)
$10,000 15,000 25,000 - 21,000 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
We know: B=$10,000 P=$15,000 S=$30,000 R=30%
We must calculate: k G C M E
Step 1 Step 2 Step 3 Step 4 Step 5
G = kS C=S-G M=B+P E=M-C
R k= 100
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
E =
(B
+ P
)
⎡ ⎛ R − ⎢S 1 − 100 ⎣ ⎝
⎞ ⎠
]
]
E = ( 25 , 000 E =
30 ⎞ ⎡ ⎛ E = (10 , 000 + 15 , 000 ) − ⎢ 30 , 000 1 − ⎝ 100 ⎠ ⎣
) − [ 30 , 000 (1 − .3 ) ]
E = ( 25 , 000
( 25
) − [ 30 , 000 ( .7 ) ] , 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
E =
(B
+ P
)
⎡ ⎛ R − ⎢S 1 − 100 ⎣ ⎝
⎞ ⎠
]
]
E = (10 , 000 E = (10
40 ⎞ ⎡ ⎛ E = ( 4 , 000 + 6, 000 ) − ⎢ 5, 000 1 − ⎝ 100 ⎠ ⎣
) − [5 ,000 (1 −
.4 )
]
E = (10 , 000
) − [5 , 000 ( . 6 ) ] , 000 ) − [ 3 , 000 ]
E = 7 , 000