Important formules for ugc net commerce,management (most important) download pdf (quick revision)

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Important Formulas –
Commerce Manangement
For Ugc Net Commerce ,Management Aspirants
Neha Sharma & Diwakar Sir
So Much important Formulas in Exam UGC - NET Commerce,Management , Many question Ask
Directly on the Bases of formulas And also help to solve numerical questions In this Pdf included
formulas Related to Economics, Finance, accounting ,financial Management Etc

Important Formulas – Commerce Manangement
UGC NET PRATICE SET’S = CLICK HERE UGC NET TEST SERIES = CLICK HERE
Important Economics Formulas
AverageTotalCost(ATC)=TotalCostQ
AverageVariableCost(AVC)=TotalVariableCostAverage
Fixed Cost (AFC) = ATC – AVC
TotalCost(TC)=(AVC+AFC)×Output
TotalVariableCost(TVC)=AVC×Output
Total Fixed Cost (TFC) = TC – TVC
MarginalCost(MC)=ChangeinTotalCostsChangeinOutput
MarginalProduct(MP)=ChangeinTotalProductChangeinVariableFactor
MarginalRevenue(MR)=ChangeinTotalRevenueChangeinQ
AverageProduct(AP)=TPVariableFactor
TotalRevenue(TR)=Price×Quantity
AverageRevenue(AR)=TROutput
TotalProduct(TP)=AP×VariableFactor
Economic Profit = TR – TC > 0
A Loss = TR – TC < 0
Break Even Point = AR = ATC
Profit Maximizing Condition = MR = MC
Key Formulas in Macroeconomics
1. GDP = C + I + G + Xn: The expenditure approach to measuring GDP
2. GDP = W + I + R + P: The income approach to measuring GDP
3. Calculating nominal GDP: The quantity of various goods produced in a nation times their current
prices, added together.
4. GDP deflator: A price index used to adjust nominal GDP to arrive at real GDP. Called the ‘deflator’
because nominal GDP will usually over-state the value of a nation’s output if there has been inflation.
5. Real GDP:
6. GDP Growth rate:
7. The inflation rate via the CPI:
8. Real interest rate = nominal interest rate – inflation rate.

9. Unemployment Rate =
10. Money Multiplier =
11. Quantity theory of money: MV = PY – a moneterist’s view which explains how changes in the money
supply will affect the price level assuming the velocity of money and the level of output are fixed.
12. MPC + MPS = 1. Households may consume or save with any change in their income.
13. Spending Multiplier =
14. Tax multiplier = -MPCMPS. It tells you how much total spending will result from an initial change in the
level of taxation. It is negative because when taxes decrease, spending increases, and vis versa. The
tax multiplier will always be smaller than the spending multiplier.
Some other Important Formulas
Average Total Cost (ATC) = Total Cost / Q (Output is quantity produced or ‘Q’)Average
Variable Cost (AVC) = Total Variable Cost / QAverage Fixed Cost (AFC) = ATC – AVC
Total Cost (TC) = (AVC + AFC) X Output (Which is Q)
Total Variable Cost (TVC) = AVC X Output
Total Fixed Cost (TFC) = TC – TVC
Marginal Cost (MC) = Change in Total Costs / Change in Output
Marginal Product (MP) = Change in Total Product / Change in Variable Factor
Marginal Revenue (MR) = Change in Total Revenue / Change in Q
Average Product (AP) = TP / Variable Factor
Total Revenue (TR) = Price X Quantity
Average Revenue (AR) = TR / Output
Total Product (TP) = AP X Variable Factor
Economic Profit = TR – TC > 0
A Loss = TR – TC < 0
Break Even Point = AR = ATC
Profit Maximizing Condition = MR = MC
Explicit Costs = Payments to non-owners of the firm for the resources they supply.

Short Run Average Costs
1. Average Fixed Cost (AFC)
The average fixed cost is the total fixed cost divided by the number of units
produced. Hence, if TFC is the total fixed cost and Q is the number of units
produced, then
AFC=TFCQ
Therefore, AFC is the fixed cost per unit of output.
Example: The TFC of a firm is Rs. 2,000. If the output is 100 units, the average fixed
cost is,
AFC=TFCQ=2000100=Rs.20
If the output is increased to 200 units, then
AFC=TFCQ=2000200=Rs.10
Since TFC is constant, any increase in output decreases the AFC. Note that, while the
AFC can become really small, it is never zero.
2. Average Variable Cost (AVC)
The second aspect of short-run average costs is an average variable cost. Average
variable cost is the total variable cost divided by the number of units produced.
Hence, if TVC is the total fixed cost and Q is the number of units produced, then
$$AVC =frac {TVC}{Q}$$
Therefore, AVC is the variable cost per unit of output.
Usually, the AVC falls as the output increases from zero to normal capacity output.
Beyond the normal capacity, the AVC rises steeply due to the operation of
diminishing returns.
3. Average Total Cost (ATC)

The average total cost is the sum of the average variable cost and the average fixed
costs. That is,
ATC = AFC + AVC
In other words, it is the total cost divided by the number of units produced.
The diagram below shows the AFC, AVC, ATC, and Marginal Costs (MC) curves:
It is important to note that the behaviour of the ATC curve depends upon that of the
AVC and AFC curves. Observe that:
 In the beginning, both AVC and AFC curves fall. Hence, the ATC curve falls as well.
 Next, the AVC curve starts rising, but the AFC curve is still falling. Hence, the ATC
curve continues to fall. This is because, during this phase, the fall in the AFC curve is
greater than the rise in the AVC curve.
 As the output rises further, the AVC curve rises sharply. This offsets the fall in the
AFC curve. Hence, the ATC curve falls initially and then rises.
Marginal Cost (MC)
Another concept to learn in short-run average costs is Marginal Cost. Marginal cost is
the addition made to the cost of production by producing an additional unit of the

output. In simpler words, it is the total cost of producing t units instead of t-1 units.
Let’s look at an example to understand this better:
A firm produces 5 units at a total cost of Rs. 200. For some reasons, it is required to
produce 6 units instead of 5 and the total cost is Rs. 250. Therefore, the marginal cost
is Rs. 250 – Rs. 200 = Rs. 50.
A note about marginal costs: It is independent of fixed costs. This is because fixed
costs do not change with the output. On the other hand, in the short run, the variable
costs change with the output. Hence, marginal costs are due to changes in
variable costs. Therefore,
MC=ΔTCΔQ
Accounting Formulas –
Balance sheet formula
Assets – liabilities = equity (or assets = liabilities + equity)
This basic formula must stay in balance to generate an accurate balance sheet. This means that all
accounting transactions must keep the formula in balance. If not, the accountant has made an error.
Retained earnings formula
Beginning balance + net income – net losses – dividends = ending balance
Income statement formula
Revenue (sales) – expenses = profit (or net income)
Keep in mind that revenue and sales may be used interchangeably. Profit and net income may also
be used interchangeably. The income statement is also referred to as a profit and loss statement.
Gross margin
Sales – cost of sales
Gross margin is not a company’s net income or profit. Other expenses, such as selling, general, and
administrative (SG and A) expenses, are subtracted to arrive at net income.

Operating income (earnings)
Gross profit – selling, general, and administrative (SG and A) expenses
Statement of cash flows formula
Beginning cash balance + cash flow sources (uses) from operations + cash flow sources (uses) from
financing + cash flow sources (uses) from investing = ending cash balance
This formula adds cash sources and subtracts cash uses.
Inventory formula
Beginning inventory + purchases – cost of sales = ending inventory (or beginning inventory +
purchases – ending inventory = cost of sales)
Net sales formula
Gross sales – sales discounts – sales returns and allowances
Book value of fixed (depreciable) assets
Original cost – accumulated depreciation
Straight line depreciation
(Original cost – salvage value) / number of years in useful life
Salvage value is the dollar amount that the owner can receive for selling the asset at the end of its
useful life.
Fundamental Accounting Equation and Double Entry Principle.
• Assets +Expense = Liabilities + Shareholders’ Equity + Revenue
Liabilities = Equity = Net Worth
Revenue – Expense = Income
1. Statement of Retained Earnings or Shareholders’ Equity Statement
Total Equity = Common Par Stock Issued + Paid In Capital + Retained Earnings
1. Current Ratio:

= Current Assets / Current Liabilities
1. Quick/Acid Test ratio:
= (Current Assets – Inventory) / Current Liabilities
1. Average Collection Period:
= Average Accounts Receivable /(Annual Sales/360)
1. PROFITABILITY RATIOS:
Profit Margin (on sales):
= [Net Income / Sales] X 100
Return on Assets:
= [Net Income / Total Assets] X 100
Return on equity:
= [Net Income/Common Equity]
6. ASSET MANAGEMENT RATIOS
Inventory Turnover:
= Sales / inventories
Total Assets Turnover:
= Sales / Total Assets
1. DEBT (OR CAPITAL STRUCTURE) RATIOS:
Debt-Assets:
= Total Debt / Total Assets
Debt-Equity:
= Total Debt / Total Equity
Times-Interest-Earned:
= EBIT / Interest Charges
1. Market Value Ratios:
Price Earning Ratio:
= Market Price per share / *Earnings per share
Market /Book Ratio:
= Market Price per share / Book Value per share
*Earning Per Share (EPS):
= Net Income / Average Number of Common Shares Outstanding

1. M.V.A (Market Value Added):
MVA (Rupees) = Market Value of Equity – Book Value of Equity Capital
1. E.V.A (Economic Value Added):
EVA (Rupees) = EBIT (or Operating Profit) – Cost of Total Capital
1. Interest Theory:
• Economic Theory:
i = iRF + g + DR + MR + LP + SR
– i is the nominal interest rate generally quoted in papers. The “real” interest rate = i – g
Here i = market interest rate
g = rate of inflation
DR = Default risk premium
MR = Maturity risk premium
LP = Liquidity preference
SR = Sovereign Risk
The explanation of these determinants of interest rates is given as under:
1. Market Segmentation:
 Simple Interest (or Straight Line):
F V = PV + (PV x i x n)
 Discrete Compound Interest:
Annual (yearly) compounding:
F V = PV x (1 + i) n
Monthly compounding:
F V = PV x (1 + (i / m) m x n
 Continuous (or Exponential) Compound Interest:
 F V (Continuous compounding) = PV x e i x n

1. Estimated current assets for the next year
= [Current assets for the current year/Current sales] x Estimated sales for the next year
1. Expected Estimated retained earnings
= estimated sales x profit margin x plowback ratio
1. Estimated discretionary financing
= estimated total assets – estimated total liabilities –estimated total equity
1. G (Desired Growth Rate)
= return on equity x (1- pay out ratio)
1. Interest Rates for Discounting Calculations
• Nominal (or APR) Interest Rate = i nom
• Periodic Interest Rate = i per
It is defined as
iper = ( i nominal Interest rate) / m
Where
m = no. of times compounding takes place in 1 year i.e.
If semi-annual compounding then m = 2
• Effective Interest Rate = i eff
i eff = [1 + ( i nom / m )]m – 1
1. Calculating the NPV of the Café Business for 1st Year:
NPV = Net Present Value (taking Investment outflows into account)
NPV = −Initial Investment + Sum of Net Cash Flows from Each Future Year.
NPV = − Io +PV (CF1) + PV (CF2) + PV (CF3) + PV (CF4) + ...+ ∞
1. Annual Compounding (at end of every year):
FV = CCF (1 + i) n – 1
Annual Compounding (at end of every year)
PV =FV / (1 + i ) n . n = life of Annuity in number of years

1. Multiple Compounding:
Future Value of annuity =CCF (constant cash flow)*(1+ (i/m) m*n-1/i/n
Multiple Compounding:
PV =FV / [1 + (i/m)] mxn
1. Future value of perpetuity:
=constant cash flow/interest rate
1. Future value by using annuity formula
FV =CCF [(1+i) n - 1]/ i
1. Return on Investments:
ROI= (ΣCF/n)/ IO
1. Net Present Value (NPV):
NPV= -IO+ΣCFt/ (1+i) t
Detail
NPV = -Io + CFt / (1+i)t = -Io + CF1/(1+i) + CF2/(1+i) ^2 + CF` /(1+i)^3 +..
-IO= Initial cash outflow
i=discount /interest rate
t=year in which the cash flow takes place
1. Probability Index:
PI = [Σ CFt / (1+ i) t ]/ IO
1. Internal Rate Of Return(IRR) Equation:
NPV= -IO +CF1/ (1+IRR) + CF2/ (1+IRR) ^2......
1. Internal Rate of Return or IRR:
The formula is similar to NPV

NPV = 0 = -Io + CFt / (1+IRR)t = -Io + CF1/(1+IRR) + CF2/(1+IRR) ^2 + ..
1. Modified IRR (MIRR):
(1+MIRR) n = Future Value of All Cash Inflows….
Present Value of All Cash Outflows
(1+MIRR) n = CF in * (1+k) n-t
CF out / (1+k) t
1. Equivalent Annual Annuity Approach:
EAA FACTOR = (1+ i)^ n / [(1+i)^ n -1]
Where n = life of project & i=discount rate
BONDS’ VALUATION
The relationship between present value and net present value
1. NPV = -Io + PV
1. Present Value formula for the bond:
n
PV= Σ CFt / (1+rD)t =CF1/(1+rD)+CFn/(1+rD)2 +..+CFn/ (1+rD) n +PAR/ (1+rD) ^n
t =1
In this formula
PV = Intrinsic Value of Bond or Fair Price (in rupees) paid to invest in the bond. It is the
Expected or Theoretical Price and NOT the actual Market Price.
rD = it is very important term which you should understand it care fully. It is
Bondholder’s (or
Investor’s) Required Rate of Return for investing in Bond (Debt).As conservative you
can choose
minimum interest rate. It is derived from Macroeconomic or Market Interest Rate.
Different from the Coupon Rate!
STATISTICS FORMULS –
The important statistics formulas are listed in the chart below:

Mean barx=∑xn
x = Items given
n = Total number of items
Median
If n is odd, then
M = (n+12)th term
If n is even, then
M = (n2)thterm+(n2+1)thterm2
Mode The value which occurs most frequently
Variance σ2 = ∑(x−barx)2n
x = Items given
barx = Mean
Standard Deviation S=σ=∑(x−barx)2n−−−−−−−−√
x = Items given
barx = Mean
Quartile Formula
A quartile divides the set of observation into 4 equal parts. The middle term, between the median
and first term is known as the first or Lower Quartile and is written as Q1.Similarly, the value of
mid term that lies between the last term and the median is known as the third or upper quartile
and is denoted as Q3.Second Quartile is the median and is written as Q2.
When the set of observation is arranged in an ascending order, then the 25th percentile is given
as:
Q1=(n+14)thTerm
The second quartile or the 50th percentile or the Median is given as:
Q2=(n+12)thTerm
The third Quartile of the 75th Percentile (Q3) is given as:
Q3=(3(n+1)4)thTerm
The Upper quartile is given by rounding to the nearest whole integer if the solution is coming in decimal
number. The major use of the lower and upper quartile helps is that it helps us measure the dispersion
in the set of the data given. The dispersion is also called “inter quartile range”, denoted as IQR, inter
quartile range is the difference between lower and upper quartile.
IQR=UpperQuartile−LowerQuartile
Correlation Coefficient Formula
Correlation coefficient formula is given and explained here for all of its types. There are various
formulas to calculate the correlation coefficient and the ones covered here include Pearson’s
Correlation Coefficient Formula, Linear Correlation Coefficient Formula, Sample Correlation
Coefficient Formula, and Population Correlation Coefficient Formula. Before going to the

formulas, it is important to understand what correlation and correlation coefficient is. A brief
introduction is given below and to learn about them in detail, click the linked article.
Formula to Calculate Correlation Coefficient
About Correlation Coefficient
The correlation coefficient is a measure of the association between two variables. It is used to
find the relationship is between data and a measure to check how strong it is. The formulas return
a value between -1 and 1 wherein one shows -1 shows negative correlation and +1 shows a
positive correlation.
The correlation coefficient value is positive when it shows that there is a correlation between the
two values and the negative value shows the amount of diversity among the two values.

Types of Correlation Coefficient Formula
There are several types of correlation coefficient formulas. But, one of the most commonly used
formulas in statistics is Pearson’s Correlation Coefficient Formula. The formulas for all the
correlation coefficient are discussed below.
Pearson’s Correlation Coefficient Formula
Also known as bivariate correlation, the Pearson’s correlation coefficient formula is the most
widely used correlation method among all the sciences. The correlation coefficient is denoted by
“r”.
To find r, let us suppose the two variables as x & y, then the correlation coefficient r is calculated
as:
r=n(∑xy)−(∑x)(∑y)[n∑x2−(∑x)2][n∑y2−(∑y)2]−−−−−−−−−−−−−−−−−−−−−−−−−−−√
Notations:
n Quantity of Information
Σx Total of the First Variable Value
Σy Total of the Second Variable Value
Σxy Sum of the Product of & Second Value
Σx2
Sum of the Squares of the First Value
Σy2
Sum of the Squares of the Second Value
Linear Correlation Coefficient Formula
The linear correlation coefficient formula is given by the following formula
Sample Correlation Coefficient Formula
rxy=SxySxSy
Here, Sx and Sy are the sample standard deviations, and Sxy is the sample covariance.
Population Correlation Coefficient Formula
ρxy=σxyσxσy
The population correlation coefficient uses σx and σy as the population standard deviations and
σxy as the population covariance.

Relation Between Correlation Coefficient and Covariance Formulas
Correlation=Cov(x,y)σx∗σy∗
Here, Cov (x,y) is the covariance between x and y while σx and σy are the standard deviations of x
and y.
 Question 1: Find the linear correlation coefficient for the following data. X = 4, 8 ,12, 16 and Y =
5, 10, 15, 20.
 Question 2: Calculate correlation coefficient for x = 100, 106, 112, 98, 87, 77, 67, 66, 49 and y =
28, 33, 26, 27, 24, 24, 21, 26, 22.
 Question 3: What will be the correlation coefficient for X and Y values for the given values: X=
(1,2,3,4,5) and Y= {11,22,34,43,56}
Central Limit Theorem Formula
The Central Limit Theorem is the sampling distribution of the sampling means approaches a
normal distribution as the sample size gets larger, no matter what the shape of the data
distribution. An essential component of the Central Limit Theorem is the average of sample
means will be the population mean.
Similarly, if you find the average of all of the standard deviations in your sample, you will find
the actual standard deviation for your population.
 Mean of sample is same as mean of the population.
 Standard deviation of the sample is equal to standard deviation of the population divided by
square root of sample size.
Central limit theorem is applicable for a sufficiently large sample sizes (n≥30). The formula for
central limit theorem can be stated as follows:
μx¯¯¯=μ
and
σx¯¯¯=σn−−√
Where,
μ = Population mean
σ = Population standard deviation
μx¯¯¯ = Sample mean
σx¯¯¯ = Sample standard deviation
n = Sample size
Solved Examples
Question 1:The record of weights of male population follows normal distribution. Its mean and standard
deviation are 70 kg and 15 kg respectively. If a researcher considers the records of 50 males, then what
would be the mean and standard deviation of the chosen sample?

Solution:
Mean of the population μ = 70 kg
Standard deviation of the population = 15 kg
sample size n = 50
Mean of the sample is given by:
μx¯¯¯ = 70 kg
Standard deviation of the sample is given by:
σx¯¯¯ = σn√
σx¯¯¯ = 1550√
σx¯¯¯ = 2.121 = 2.1 kg (approx)
Linear Regression Formula
Linear regression is the most basic and commonly used predictive analysis. One variable is
considered to be an explanatory variable, and the other is considered to be a dependent variable.
For example, a modeler might want to relate the weights of individuals to their heights using a
linear regression model.
There are several linear regression analyses available to the researcher.
Simple linear regression
 One dependent variable (interval or ratio)
 One independent variable (interval or ratio or dichotomous)
Multiple linear regression
 One dependent variable (interval or ratio)
 Two or more independent variables (interval or ratio or dichotomous)
Logistic regression
 One dependent variable (binary)
 Two or more independent variable(s) (interval or ratio or dichotomous)
Ordinal regression
 One dependent variable (ordinal)
 One or more independent variable(s) (nominal or dichotomous)
Multinomial regression
 One dependent variable (nominal)
 One or more independent variable(s) (interval or ratio or dichotomous)
Discriminant analysis
 One dependent variable (nominal)

 One or more independent variable(s) (interval or ratio)
Formula for linear regression equation is given by:
y=a+bx
a and b are given by the following formulas:
b(slope)=n∑xy−(∑x)(∑y)n∑x2−(∑x)2
a(intercept)=n∑y−b(∑x)n
Where,
x and y are two variables on regression line.
b = Slope of the line.
a = y-intercept of the line.
x = Values of first data set.
y = Values of second data set.
Solved Examples
Question: Find linear regression equation for the following two sets of data:
x 2 4 6 8
y 3 7 5 10
Solution:
Construct the following table:
x y x2 xy
2 3 4 6
4 7 16 28
6 5 36 30
8 10 64 80
∑x = 20 ∑y= 25 ∑x2 = 120 ∑xy= 144
b = n∑xy−(∑x)(∑y)n∑x2−(∑x)2
b = 4×144–20×254×120–400
b = 0.95
a = ∑y−b(∑x)n

a = 25–0.95×204
a = 1.75
Linear regression is given by:
y = a + bx
y = 1.75 + 0.95 x
Standard Error Formula
Standard error is an important statistical measure and it is concerned with standard
deviation. The accuracy of a sample that represents a population is knows through this formula.
The sample mean deviates from the population and that deviation is called standard error
formula.
SEx¯¯¯=Sn−−√
Where,
s is the standard deviation
n is the number of observation
Solved example
Question: Calculate the standard error of the given data:
x: 10, 12, 16, 21, 25
Solution:
Mean =(10+12+16+21+25)5=16.8
Standard Deviation can be calculated as
14−−√(10−16.8)2+(12−16.8)2+(16−16.8)2+(21−16.8)2+(25−16.8)2
=2167.24−−−−−√=5.418
Standard Error:
SEx¯¯¯=Sn√
=5.4185√=2.42
Degrees of Freedom Formula
It is the number of values that remain during the final calculation of a statistic that is expected to
vary. In simple terms, these are the date used in a calculation. The degrees of freedom can be
calculated to help ensure the statistical validity of chi-square tests, t-tests, and even the more
advanced f-tests. Degrees of freedom is commonly abbreviated as ‘df’. Below mentioned is a list
of degree of freedom formulas. The number of degrees of freedom refers to the number of
independent observations in a sample minus the number of population parameters that must be
estimated from sample data.
Formulas to Calculate Degrees of Freedom
 One Sample T Test Formula
DF=n−1

 Two Sample T Test Formula
DF=n1+n2−2
 Simple Linear Regression Formula
DF=n−2
 Chi Square Goodness of Fit Test Formula
DF=k−1
 Chi Square Test for Homogeneity Formula
DF=(r−1)(c−1)
Solved Examples
Question 1: Find the degree of freedom for given sequence: x = 2, 8, 3, 6, 4, 2, 9, 5
Solution:
Given n= 8
Therefore,
DF = n-1
DF = 8-1
DF = 7
Question 2: Find the degree of freedom for a given sequence:
x = 12, 17, 19, 15, 25, 26 y = 18, 21, 32, 43
Solution:
Given: n1 = 6 n2 = 4
Here, there are 2 sequences, so we need to apply DF = n1 – n2 – 2
DF = 6 -4 -2
DF =0

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