DISCLAIMER:–
THIS ARTICLE IS PROVIDED SOLELY FOR EDUCATIONAL PURPOSES TO SUPPORT CANDIDATES PREPARING FOR COMPETITIVE AND PSU EXAMINATIONS. ALL CONCEPTS EXPLAINED HERE ARE BASED ON STANDARD MATHEMATICAL THEORY AND PUBLICLY AVAILABLE ACADEMIC KNOWLEDGE. THE WEBSITE OWNER IS NOT RESPONSIBLE FOR ANY ERRORS, OMISSIONS, OUTDATED INFORMATION OR CHANGES IN EXAM PATTERNS. USERS SHOULD CROSS-VERIFY CRITICAL INFORMATION WITH AUTHENTIC TEXTBOOKS, OFFICIAL NOTIFICATIONS, AND RELIABLE SOURCES. ALL EXAM NAMES AND TRADEMARKS BELONG TO THEIR RESPECTIVE AUTHORITIES. THIS CONTENT IS INTENDED TO GUIDE STUDENTS AND DOES NOT GUARANTEE EXAM SUCCESS.
INTRODUCTION: –
PROFIT AND LOSS IS AN ESSENTIAL CHAPTER IN QUANTITATIVE APTITUDE AND BUSINESS MATHEMATICS. IT FORMS THE BACKBONE OF COMMERCIAL ARITHMETIC AND IS HEAVILY TESTED IN PSU EXAMS, BANK EXAMS, SSC, RAILWAYS, INSURANCE EXAMS AND OTHER CENTRAL/STATE-LEVEL RECRUITMENT TESTS.
THE CHAPTER INVOLVES UNDERSTANDING THE MATHEMATICAL STRUCTURE BEHIND TRANSACTIONS, WHERE GOODS OR SERVICES ARE BOUGHT AT A CERTAIN COST AND SOLD AT ANOTHER PRICE. IT TESTS A STUDENT’S ABILITY TO APPLY PERCENTAGE, RATIO, PROPORTIONAL REASONING AND ALGEBRAIC THINKING TO REAL-WORLD COMMERCIAL SCENARIOS.
THIS ARTICLE AIMS TO PROVIDE A COMPLETE THEORETICAL FOUNDATION FOR PROFIT AND LOSS. IT COVERS EVERY CONCEPT, DEFINITION, DERIVATION, CONDITION AND RELATIONSHIP FOUND IN ALL EXAM PATTERNS.
CHAPTER 1 – BASIC COMMERCIAL TERMINOLOGY
PROFIT AND LOSS PROBLEMS REVOLVE AROUND THREE MAIN QUANTITIES: COST PRICE (CP), SELLING PRICE (SP) AND THE RESULTING PROFIT OR LOSS. A STRONG CONCEPTUAL UNDERSTANDING OF THESE TERMS IS FUNDAMENTAL.
1.1 COST PRICE (CP)
COST PRICE IS THE AMOUNT SPENT TO OBTAIN AN ARTICLE OR SERVICE.
IT INCLUDES:
MANUFACTURING COST
WHOLESALE PURCHASE PRICE
TRANSPORTATION COST
LABOUR CHARGES
PACKAGING COST
STORAGE COST
ANY OVERHEAD EXPENSES DIRECTLY CONTRIBUTING TO ACQUISITION
THUS, COST PRICE IS NOT ALWAYS A SINGLE VALUE, ESPECIALLY IN PRACTICAL SITUATIONS. IN MATHEMATICAL PROBLEMS, CP IS USUALLY GIVEN OR CALCULATED.
1.1.1 TYPES OF COST PRICE
(A) ACTUAL COST PRICE
THE MONEY SPENT ON BUYING THE ITEM IN RAW FORM.
(B) EFFECTIVE COST PRICE
INCLUDES OVERHEAD CHARGES.
IF OVERHEAD CHARGES = OC,
OCEFFECTIVE CP=CP+OC
(C) AVERAGE COST PRICE
WHEN MULTIPLE IDENTICAL ITEMS ARE BOUGHT AT DIFFERENT PRICES, THE COST PRICE PER ITEM BECOMES:
AVERAGE CP=TOTAL COST / NUMBER OF ITEMS
(D) WEIGHTED COST PRICE
USED WHEN ITEMS HAVE DIFFERENT WEIGHTS OR QUANTITIES.
1.2 SELLING PRICE (SP)
SELLING PRICE IS THE PRICE AT WHICH THE ARTICLE IS SOLD.
SP VARIES DUE TO:
MARKET DEMAND
COMPETITION
BARGAINING
DISCOUNTS
PROMOTIONAL SCHEMES
SEASONAL VARIATIONS
SP IS THE FINAL REVENUE RECEIVED BY THE SELLER.
1.3 PROFIT OR GAIN
PROFIT OCCURS WHEN THE SELLER EARNS MORE THAN THE COST INCURRED.
PROFIT=SP−CP
PROFIT IS NOT NECESSARILY RECEIVED IN CASH; IT MAY APPEAR AS:
INCREASE IN STOCK VALUE
INTEREST OR CREDIT VALUE
ADDED FREEBIES THAT DO NOT COST MUCH BUT INCREASE SELLING POWER
PROFIT IS MEANINGFUL ONLY WHEN CP AND SP REFER TO THE SAME ITEM OR SERVICE.
1.4 LOSS
LOSS OCCURS WHEN THE SELLING PRICE IS LOWER THAN THE COST PRICE.
LOSS=CP−SP
LOSS SIGNIFIES FINANCIAL DECAY OR REDUCTION IN ASSET VALUE.
1.5 PROFIT PERCENTAGE (P%)
P%=(PROFIT/CP)×100
PROFIT PERCENTAGE IS ALWAYS CALCULATED ON COST PRICE, UNLESS SPECIFICALLY MENTIONED OTHERWISE.
1.6 LOSS PERCENTAGE (L%)
L%=(LOSS/CP)×100
LOSS PERCENTAGE IS ALSO ALWAYS CALCULATED ON COST PRICE.
CHAPTER 2 – EXTENDED PROFIT AND LOSS RELATIONSHIPS (THEORY)
THIS CHAPTER EXPLAINS DEEPER RELATIONSHIPS BETWEEN CP, SP, PROFIT% AND LOSS% SO THAT STUDENTS CAN DERIVE ANY FORMULA WITHOUT MEMORIZATION.
2.1 SELLING PRICE IN TERMS OF CP AND PROFIT%
IF PROFIT% = P,
SP=CP(1+P/100)
THIS FORMULA INDICATES THAT SP INCREASES PROPORTIONALLY WITH PROFIT PERCENT.
2.2 SELLING PRICE IN TERMS OF CP AND LOSS%
IF LOSS% = L,
SP=CP(1−L/100)
THIS INDICATES A REDUCTION RELATIVE TO CP BASED ON LOSS PERCENT.
2.3 COST PRICE IN TERMS OF SP AND PROFIT%
REWRITING SP FORMULA:
CP=SP/ 1+P/100
2.4 COST PRICE IN TERMS OF SP AND LOSS%
CP=SP/1−L/100
THIS BECOMES EXTREMELY USEFUL WHEN SP IS KNOWN AND CP MUST BE DERIVED BACKWARDS.
2.5 PROFIT% IN TERMS OF CP AND SP
P%=[(SP−CP)/CP]×100
2.6 LOSS% IN TERMS OF CP AND SP
L%=[(CP−SP)/CP]×100L
CHAPTER 3 – MARKED PRICE (MP), DISCOUNT & SELLING PRICE
IN PRACTICAL TRADE, SELLERS MARK THE PRICE HIGHER THAN COST PRICE AND OFFER DISCOUNTS TO ATTRACT BUYERS.
3.1 MARKED PRICE (MP)
MARKED PRICE IS THE LABELLED OR LISTED PRICE ON AN ARTICLE.
IT IS ALWAYS SET HIGHER THAN CP TO GIVE THE SELLER ROOM FOR:
DISCOUNTS
NEGOTIATIONS
SEASONAL OFFERS
MARGIN ADJUSTMENTS
3.2 DISCOUNT (D%)
A REDUCTION OFFERED ON THE MARKED PRICE.
DISCOUNT=(D/100)×MP
3.3 SELLING PRICE AFTER DISCOUNT
SP=MP(1−D/100)
SUCCESSIVE DISCOUNTS, EQUIVALENT DISCOUNTS AND SPECIAL DISCOUNT SCHEMES ARE USED TO ATTRACT CUSTOMERS.
3.4 WHY MARKED PRICE EXISTS – THEORY
MARKED PRICE ALLOWS SELLERS TO:
CREATE PSYCHOLOGICAL IMPACT
OFFER FLEXIBILITY IN PRICING STRATEGY
MAINTAIN PROFIT MARGINS
COMPETE WITH OTHER SELLERS
MAKE ROOM FOR BARGAINING CULTURE IN MARKETS
DISPLAY HIGHER ORIGINAL PRICE TO CREATE ILLUSION OF SAVINGS
CHAPTER 4 – SUCCESSIVE DISCOUNT THEORY (DEEP EXPLANATION)
WHEN MULTIPLE DISCOUNTS ARE APPLIED SEQUENTIALLY, THEY DO NOT SIMPLY ADD.
IF DISCOUNTS ARE d₁ AND d₂, THEN:
NET DISCOUNT=d1+d2−d1d2/100
CHAPTER 5 – MARK-UP AND MARGIN THEORY
5.1 MARK-UP
MARK-UP% IS APPLIED ON CP TO SET MP.
MP=CP(1+MU/100)
5.2 MARGIN (GROSS PROFIT MARGIN)
MARGIN IS THE PROFIT AS PERCENTAGE OF SELLING PRICE OR REVENUE INSTEAD OF COST PRICE.
SOME INDUSTRIES USE:
MARGIN%=(PROFIT/SP)×100
MARGIN AND MARK-UP DIFFER:
MARK-UP IS BASED ON CP
MARGIN IS BASED ON SP
CHAPTER 6 — OVERHEAD EXPENSES (FULL THEORY)
IN REAL COMMERCIAL TRANSACTIONS, THE COST OF AN ITEM IS RARELY LIMITED TO THE AMOUNT PAID TO PURCHASE IT. MOST GOODS INVOLVE ADDITIONAL EXPENSES BEFORE THEY BECOME SALE-READY. THESE ADDITIONAL COSTS ARE COLLECTIVELY KNOWN AS OVERHEAD EXPENSES.
6.1 MEANING OF OVERHEAD EXPENSES
OVERHEAD EXPENSES INCLUDE ALL INCIDENTAL COSTS NECESSARY TO BRING A PRODUCT INTO USABLE OR SALEABLE FORM. THESE EXPENSES MAY BE:
FIXED OVERHEADS – INDEPENDENT OF QUANTITY (WAREHOUSE RENT)
VARIABLE OVERHEADS – PROPORTIONAL TO QUANTITY (TRANSPORT COST PER ITEM)
SEMI-VARIABLE OVERHEADS – PARTLY FIXED, PARTLY VARIABLE
EXAMPLES:
TRANSPORTATION / FREIGHT CHARGES
LOADING OR UNLOADING CHARGES
LABOUR CHARGES
ELECTRICITY, POWER USAGE
PACKAGING
STORAGE CHARGES
INSURANCE ON GOODS
CARRIAGE INWARD
SHOP EXPENSES
THUS, EFFECTIVE COST PRICE (ECP) BECOMES:
ECP=ACTUAL CP+OVERHEAD EXPENSES
6.2 WHY OVERHEAD EXPENSES IMPORTANT IN THEORY
OVERHEADS CHANGE:
TOTAL COST OF PRODUCTION
PROFIT CALCULATION
PRICING STRATEGY
MARK-UP REQUIREMENTS
THEREFORE, THE CP USED IN PROFIT/LOSS CALCULATION MUST BE THE EFFECTIVE CP, NOT THE RAW PURCHASE PRICE.
6.3 OVERHEADS IN BULK PURCHASES
WHEN ITEMS ARE PURCHASED IN BULK:
EFFECTIVE CP PER ARTICLE=TOTAL COST (GOODS + OVERHEADS)/TOTAL NUMBER OF ARTICLES
THIS IS HIGHLY RELEVANT IN:
WHOLESALE TRADE
PSU PROCUREMENT
INVENTORY VALUATION
TRANSPORTED GOODS
AGRICULTURAL PRODUCE
CHAPTER 7 — DISHONEST DEALER THEORY
A DISHONEST DEALER MANIPULATES WEIGHTS, MEASURES OR PRICE STRUCTURE TO CHEAT CUSTOMERS WHILE APPEARING HONEST.
DISHONESTY OCCURS THROUGH:
USING FALSE WEIGHTS
ADDING IMPURITIES (LIKE WATER IN MILK)
SELLING LESS QUANTITY AT THE PRICE OF FULL QUANTITY
MANIPULATING CP OR SP VALUES
DUAL PRICING (LABEL VS. REAL)
UNDERSTANDING THE THEORY HELPS DECODE MANY EXAM PROBLEMS.
7.1 FALSE WEIGHT THEORY
SUPPOSE A DEALER USES A WEIGHT OF 900 G BUT CLAIMS IT IS 1 KG.
HE CHARGES SP BASED ON 1 KG BUT DELIVERS ONLY 900 G.
THUS HIS ACTUAL SELLING PRICE FOR 1 KG BECOMES:
SPACTUAL=SPCLAIMED/0.9
THE GAIN ARISES BECAUSE HIS COST IS FOR 900 G BUT HE CHARGES FOR 1000 G.
7.2 ADULTERATION THEORY
DEALERS MAY MIX CHEAPER MATERIALS:
WATER IN MILK
SAND IN GRAINS
LOW-GRADE OIL WITH HIGH-GRADE OIL
IF PURE MATERIAL HAS CP₁ AND ADULTERANT HAS CP₂ (OFTEN ZERO):
THE EFFECTIVE CP BECOMES:
CPMIXTURE=TOTAL COST OF MIXTURE/TOTAL
THIS IS APPLIED IN MIXTURE PROBLEMS.
7.3 SELLING AT CP BUT STILL GAINING
A DEALER SAYS HE SELLS “AT COST PRICE”, BUT CHEATING THROUGH:
FALSE WEIGHTS
ADULTERATION
CHANGING MEASURES
CLAIMING DIFFERENT PURITY LEVELS
THUS STATED CP ≠ ACTUAL CP.
CHAPTER 8 — SUCCESSIVE PROFIT OR LOSS THEORY
profit or loss applied successively behaves like compounding.
if profit percentages are a% and b%:
net%=a + b+ ab /100
similarly, for successive losses:
net loss%=a + b+ ab /100
FOR ONE PROFIT AND ONE LOSS:
net%=a−b−ab/100
THIS IS EXTREMELY IMPORTANT IN PSU MATHS.
CHAPTER 9 — VALUE CHANGE THEORY: DEPRECIATION & APPRECIATION
9.1 APPRECIATION
APPRECIATION OCCURS WHEN VALUE INCREASES OVER TIME.
COMMON EXAMPLES:
PROPERTY PRICE RISING
SHARE MARKET VALUE RISING
ART PIECE INCREASING IN VALUE
IF VALUE INCREASES AT R% ANNUALLY:
Vn=V0(1+R/100)n
9.2 DEPRECIATION
DEPRECIATION IS REDUCTION IN VALUE DUE TO:
WEAR AND TEAR
USAGE
OBSOLESCENCE
TIME
IF DEPRECIATION RATE = D% YEARLY:
Vn=V0(1−D/100)n
9.3 MIXED APPRECIATION & DEPRECIATION
IN REAL MARKETS, GOODS SOMETIMES:
FIRST APPRECIATE, THEN DEPRECIATE
DEPRECIATE BUT LATER APPRECIATE (ANTIQUES)
NET EFFECT USES SUCCESSIVE % FORMULA.
CHAPTER 10 — BREAK-EVEN POINT THEORY
BREAK-EVEN POINT (BEP) IS WHEN PROFIT = 0.
SP=CP
IN BUSINESS, BEP REFERS TO THE QUANTITY AT WHICH TOTAL REVENUE EQUALS TOTAL COST.
10.1 ROLE OF BEP IN PRICING STRATEGY
BUSINESSES DETERMINE:
MINIMUM UNITS TO BE SOLD
MINIMUM PRICE TO BE CHARGED
MAXIMUM DISCOUNT PERMITTED
THIS IS IMPORTANT IN PSU COMMERCIAL MATHEMATICS.
CHAPTER 11 — CHAIN DISCOUNT THEORY
A CHAIN DISCOUNT IS A SERIES OF SUCCESSIVE DISCOUNTS GIVEN TO WHOLESALERS OR RETAILERS.
if discount chain = d1%, d2%, d3%, then:
net discount=d1+d2+d3−(d1d2)/100−(d2d3)/100−(d1d3)/100+(d1d2d3)/10000
THIS IS A THEORETICAL EXPANSION OF SUCCESSIVE DISCOUNT FORMULA.
CHAPTER 12 — TRADE DISCOUNT VS CASH DISCOUNT
12.1 TRADE DISCOUNT
OFFERED TO WHOLESALERS
DEDUCTED BEFORE CALCULATING TAXES
NEVER SHOWN IN ACCOUNTING BOOKS AS LOSS
12.2 CASH DISCOUNT
OFFERED FOR EARLY PAYMENT
SHOWN AS EXPENSE IN ACCOUNTS
GIVEN ON ALREADY REDUCED PRICE
THEY ARE CONCEPTUALLY DIFFERENT AND APPEAR IN THEORY-HEAVY QUESTIONS.
CHAPTER 13 — TAXATION THEORY IN PROFIT & LOSS
TAXES INFLUENCE SP, CP AND PROFIT CALCULATION.
13.1 SALES TAX / VAT THEORY
OLD SYSTEMS USED:
SP=CP+PROFIT+SALES TAX
SALES TAX APPLIED ON SELLING PRICE.
13.2 GST THEORY
IN GST FRAMEWORK:
CGST + SGST APPLIED ON VALUE-ADDED PORTION
PROFIT = SP (EXCLUDING GST) – CP
GST DOES NOT AFFECT PROFIT DIRECTLY; ONLY THE TAXABLE VALUE CHANGES.
CHAPTER 14 — INVENTORY VALUATION & PROFIT THEORY
THIS IS IMPORTANT FOR PSU FINANCE-ORIENTED EXAMS.
INVENTORY IS VALUED USING:
FIFO (FIRST IN FIRST OUT)
LIFO (LAST IN FIRST OUT)
WAC (WEIGHTED AVERAGE COST)
THESE CHANGE THE EFFECTIVE CP, THUS IMPACTING PROFIT & LOSS COMPUTATION.
CHAPTER 15 — RETAIL PRICING STRATEGY THEORY
RETAILERS USE:
MARK-UP PRICING
PSYCHOLOGICAL PRICING (₹999 INSTEAD OF ₹1000)
ODD-EVEN PRICING
SEASONAL PRICING
DISCOUNT CYCLES
CLEARANCE SALE THEORY
THESE INFLUENCE SP, MP, AND MARGIN.
CHAPTER 16 — UNIFORM PROFIT PRICING THEORY
A SELLER MAY USE:
ONE CP
DIFFERENT SP
UNIFORM PROFIT
UNIFORM PROFIT PERCENTAGE
THE THEORETICAL RELATIONSHIP:
SP1−CP1=SP2−CP2
FOR EQUAL PROFIT SITUATIONS.
CHAPTER 17 — MIXTURE PROFIT THEORY
MIXTURE THEORY BLENDS:
TWO OR MORE COMMODITIES
DIFFERENT CPS
COMBINED SELLING PRICE STRATEGY
EFFECTIVE CP OF MIXTURE:
CPmix=∑(CP×QUANTITY)/TOTAL QUANTITY
CHAPTER 18 — MULTI-TRANSACTION PROFIT THEORY
BUSINESSES OFTEN INVOLVE:
BUYING MULTIPLE TIMES AT DIFFERENT RATES
SELLING MULTIPLE TIMES AT DIFFERENT RATES
THUS:
TOTAL PROFIT=TOTAL SP−TOTAL CP
CHAPTER 19 — WEIGHTED SELLING PRICE & WEIGHTED COST PRICE THEORY
IN COMMERCIAL MATHEMATICS, ESPECIALLY IN WHOLESALE AND RETAIL TRADE, TRANSACTIONS RARELY OCCUR WITH A SINGLE UNIFORM PRICE. SELLERS MAY:
PURCHASE THE SAME PRODUCT AT DIFFERENT RATES
SELL THE SAME PRODUCT AT DIFFERENT RATES
MIX COMMODITIES OF DIFFERENT QUALITIES OR COSTS
ADJUST SELLING PRICE OVER TIME DUE TO DEMAND OR STOCK PRESSURE
TO HANDLE THESE, THE CONCEPT OF WEIGHTED COST PRICE AND WEIGHTED SELLING PRICE IS ESSENTIAL.
19.1 WEIGHTED COST PRICE (WCP)
WHEN THE SAME ARTICLE IS BOUGHT AT DIFFERENT PRICES IN DIFFERENT LOTS, THE OVERALL COST PRICE PER UNIT IS NOT A SIMPLE ARITHMETIC MEAN. IT MUST BE WEIGHTED ACCORDING TO QUANTITY.
IF:
CP1 FOR Q1 UNITS
CP2 FOR Q2 UNITS
CP3 FOR Q3 UNITS
THEN:
WCP=(CP1Q1+CP2Q2+CP3Q3)/Q1+Q2+Q3
THIS THEORY APPLIES HEAVILY IN:
STOCK VALUATION
INVENTORY COSTING
WHOLESALE PRICE AVERAGING
MULTIPLE-BATCH PURCHASES
19.2 WEIGHTED SELLING PRICE (WSP)
SELLERS MAY SELL DIFFERENT QUANTITIES AT DIFFERENT SELLING PRICES.
THUS:
WSP=(SP1Q1+SP2Q2+SP3Q3)/Q1+Q2+Q3
UNDERSTANDING THIS IS CRUCIAL FOR DETERMINING OVERALL PROFIT PERCENTAGE.
19.3 THEORY: WHY WEIGHTED PRICES ARE NEEDED
WEIGHTED PRICES REFLECT:
ACTUAL COMMERCIAL OUTCOME
TRUE PROFITABILITY
PRICE FLUCTUATIONS
MARKET DEMAND VARIATIONS
STOCK CLEARANCE STRATEGIES
SEASONAL SALES
WITHOUT WEIGHTED PRICES, PROFIT ANALYSIS BECOMES INCORRECT OR MISLEADING.
CHAPTER 20 — PRICE REDUCTION THEORY
A SELLER MAY REDUCE PRICE FOR VARIOUS REASONS:
COMPETITION
EXCESS STOCK
FESTIVE OFFERS
CLEARANCE SALES
EXPIRY-INCOMING PRODUCTS
LOW DEMAND
PRICE REDUCTION AFFECTS PROFIT DIRECTLY.
IF PRICE IS REDUCED BY X%:
NEW SP=SP(1−X/100)
IF SP IS REDUCED BUT CP REMAINS SAME:
PROFIT DECREASES
PROFIT MAY CONVERT INTO LOSS
SELLER MAY MAINTAIN VOLUME TO COMPENSATE
20.1 PRICE REDUCTION & REQUIRED QUANTITY INCREASE
IF PRICE IS REDUCED BUT SELLER WANTS TO MAINTAIN TOTAL REVENUE:
INCREASE IN QUANTITY REQUIRED=[X/(100−X)]×100
THIS CONCEPT IS USED IN REVENUE MANAGEMENT THEORY.
CHAPTER 21 — QUANTITY ADJUSTMENT THEORY
A SELLER MAY:
FIX PROFIT PER UNIT
FIX PROFIT PERCENTAGE
SELL DIFFERENT QUANTITIES AT DIFFERENT PRICES
RECEIVE BULK ORDERS
HANDLE DEFECTIVE GOODS
QUANTITY VARIATIONS CHANGE EFFECTIVE PROFIT.
FOR CONSTANT PROFIT PER UNIT:
SP=CP+FIXED PROFIT
FOR CONSTANT PROFIT PERCENTAGE:
SP=CP(1+P/100)
HOWEVER, WHEN QUANTITY CHANGES, TOTAL PROFIT THEORY APPLIES:
TOTAL PROFIT=n(SP−CP)
CHAPTER 22 — WHOLESALER–RETAILER PROFIT CHAIN THEORY
GOODS OFTEN PASS THROUGH MULTIPLE LAYERS:
MANUFACTURER → WHOLESALER → RETAILER → CUSTOMER
EACH LAYER ADDS:
OVERHEADS
PROFIT MARGIN
DISCOUNT STRUCTURE
22.1 MANUFACTURER TO WHOLESALER
MANUFACTURER SETS MP FOR WHOLESALERS.
HE MAY GIVE:
TRADE DISCOUNT
SEASONAL DISCOUNT
VOLUME-BASED DISCOUNT
WHOLESALER’S EFFECTIVE CP BECOMES:
CPw=MP(1−d/100)
22.2 WHOLESALER TO RETAILER
WHOLESALER SETS HIS OWN MARK-UP:
MPw=CPw(1+MU/100)
RETAILER RECEIVES GOODS AT THIS MARK-UP PRICE.
22.3 RETAILER TO CUSTOMER
RETAILER MARKS UP AGAIN:
MPR=CPR(1+MUR/100)
HE MAY OFFER DISCOUNT:
SP=MPR(1−D/100)
22.4 THEORY: WHY MULTI-LEVEL PROFIT EXISTS
EACH LEVEL ADDS VALUE
EACH LEVEL HAS COST OF OPERATIONS
EACH LEVEL NEEDS PROFIT MARGIN
EACH LEVEL FOLLOWS DIFFERENT PRICING ETHICS
THIS IS THE THEORETICAL BASE OF COMPLEX PRICING SYSTEMS.
CHAPTER 23 — COMMISSION THEORY
COMMISSION IS A PERCENTAGE PAYMENT FOR PERFORMING CERTAIN TASKS SUCH AS:
SELLING GOODS
BOOKING ORDERS
COLLECTING PAYMENTS
PROVIDING BROKERAGE SERVICES
FOR MANY PSU PROBLEMS, AGENTS EARN COMMISSION BASED ON SALES.
23.1 COMMISSION PERCENTAGE
IF A SALESPERSON SELLS GOODS WORTH S AND EARNS COMMISSION AT C%:
COMMISSION EARNED=(C/100)×S
23.2 NET EARNINGS THEORY
A PERSON’S ACTUAL INCOME BECOMES:
NET INCOME=COMMISSION EARNED−EXPENSES
REAL COMMERCIAL INCOME IS ALWAYS NET, NOT GROSS.
23.3 BONUS COMMISSION
SOMETIMES EXTRA BONUS IS GIVEN IF SALES EXCEED A TARGET.
THIS IS A FORM OF SUCCESSIVE PERCENTAGE.
CHAPTER 24 — REBATE THEORY
A REBATE IS A PARTIAL REFUND GIVEN AFTER A PRODUCT IS PURCHASED, OFTEN USED TO PROMOTE SALES OF:
ELECTRONICS
APPLIANCES
AUTOMOBILES
INSURANCE PLANS
REBATE DIFFERS FROM DISCOUNT:
DISCOUNT REDUCES SP BEFORE PURCHASE
REBATE IS GIVEN AFTER PURCHASE
THEORETICALLY:
IF REBATE = R% ON SP,
NET COST=SP(1−R/100)
CHAPTER 25 — PROFIT MARGIN VS MARK-UP THEORY
THESE TERMS ARE OFTEN CONFUSED BUT DIFFER CONCEPTUALLY.
25.1 MARK-UP
BASED ON COST PRICE.
MU%=[(SP−CP)/CP]×100
25.2 MARGIN
BASED ON SELLING PRICE.
MARGIN%=[(SP−CP)/SP]×100
25.3 DIFFERENCE BETWEEN MARGIN & MARK-UP (PURE THEORY)
MARK-UP MEASURES HOW MUCH CP IS INCREASED.
MARGIN MEASURES WHAT PORTION OF SP IS PROFIT.
MARK-UP IS USED IN PRICING.
MARGIN IS USED IN PROFIT ANALYSIS.
MARK-UP > MARGIN FOR THE SAME SCENARIO.
UNDERSTANDING THIS CONCEPTUAL DIFFERENCE IS CRUCIAL FOR PSU MATHEMATICS.
CHAPTER 26 — PROFIT TRANSFER THEORY
IF A PERSON GAINS OR LOSES MONEY DUE TO CHANGE IN:
CP
SP
QUANTITY
DISCOUNT
OVERHEADS
THEN PROFIT IS “TRANSFERRED” FROM ONE STAGE TO ANOTHER.
FOR EXAMPLE:
IF SP REMAINS SAME BUT CP RISES → PROFIT DECREASES
IF CP REMAINS SAME BUT SP RISES → PROFIT INCREASES
MATHEMATICALLY, PROFIT TRANSFER IS REPRESENTED AS:
ΔP=ΔSP−ΔCP
THIS IS USED TO ANALYSE FLUCTUATIONS IN BUSINESS.
CHAPTER 27 — CONSTANT PRODUCT PRICE THEORY
SOME GOODS ARE SOLD AS A SET, NOT PER PIECE:
PACKETS
DOZENS
BUNDLES
KITS
PROFIT MAY APPLY TO THE WHOLE BUNDLE.
IF BUNDLE CP = BCP AND PROFIT PERCENT = P:
SPbundle=BCP(1+P/100)
IF ITEMS INSIDE ARE SOLD SEPARATELY AT MIXED SP:
EFFECTIVE PROFIT BECOMES:
OVERALL PROFIT%=[(TOTAL SP OF ITEMS−BCP)/BCP]×100
CHAPTER 28 — QUALITY-BASED SELLING THEORY
DEALERS SOMETIMES SELL GOODS OF MIXED QUALITY:
HIGH-QUALITY AND LOW-QUALITY GOODS
PURE GOODS AND ADULTERATED GOODS
NEW GOODS MIXED WITH OLD STOCK
THIS CHANGES THE EFFECTIVE SP AND CP.
IF GOODS OF DIFFERENT QUALITIES SOLD AT SAME SP:
PROFIT PERCENTAGES DIFFER.
CHAPTER 29 — PROFIT LINKED TO WEIGHT, LENGTH, AREA, VOLUME
IN MANY CASES, GOODS ARE PRICED NOT BY UNITS BUT BY MEASURE:
GOLD → GRAMS
CLOTH → METERS
LAND → AREA
LIQUID → LITRES
GAS → CUBIC METERS
PROFIT IS CALCULATED RELATIVE TO THE MEASUREMENT PARAMETER.
EXAMPLE THEORETICAL FORMULA:
PROFIT=(SP×QUANTITY SOLD)−(CP×QUANTITY BOUGHT)
CHAPTER 30 — PURE ADVANCED NOTES (THEORY)
PROFIT PERCENT IS RELATIVE; PROFIT AMOUNT IS ABSOLUTE.
SMALL PROFIT% ON LARGE CP CAN GIVE HIGH PROFIT AMOUNT.
LARGE PROFIT% ON SMALL CP MAY BE COMMERCIALLY INSIGNIFICANT.
PRICES IN REAL MARKETS VARY UNPREDICTABLY BASED ON DEMAND AND SUPPLY.
MARKED PRICE IS MOSTLY ARTIFICIAL; SP IS REAL.
DISCOUNT INDICATES SELLER WANTS FASTER STOCK TURNOVER, NOT NECESSARILY LOSS.
HIGH DISCOUNT DOES NOT IMPLY LOSS — OFTEN CP IS MUCH LOWER.
“BUY ONE GET ONE FREE” IS PRIMARILY A PRICING PSYCHOLOGY METHOD.
SUCCESSIVE PERCENTAGE CHANGES DO NOT ADD LINEARLY.
LOSS% CANNOT EXCEED 100%, BUT PROFIT% CAN.
A PERSON CAN SELL MORE THAN ONE ITEM TO OFFSET LOSS ON ANOTHER.
IN DEPRECIATION, VALUE NEVER BECOMES ZERO THEORETICALLY; IT ASYMPTOTICALLY APPROACHES ZERO.
APPRECIATION AND DEPRECIATION TOGETHER BEHAVE LIKE COMPOUNDING PERCENTAGES.
A SELLER MAY APPEAR TO SELL AT LOSS BUT STILL GAIN DUE TO HIDDEN CHARGES OR FALSE MEASURES.
IN WHOLESALE TRADE, PROFIT MARGIN IS MORE IMPORTANT THAN PROFIT PERCENTAGE.
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