Formulas Flashcards
Nominal interest rate=
Nominal interest rate= real risk-free rate + expected inflation rate
Required interest rate on security=
Required interest rate on security= nominal risk-free rate + default risk premium+ liquidity
premium + maturity risk premium
Effective Annual Return (EAR)=
Effective Annual Return (EAR)= EAR=(1+periodic rate)m -1
Periodic rate= stated annual rate/m
M= number of compounding periods per year
PV perpetuity =
PV perpetuity = PMT / (I/Y)
NPV =
NPV = ∑( CF / (1+r)^t)
CF= Expected cash flow
r =Discount rate
Holding period return (HPR) =
Holding period return (HPR) = (Ending Value - Beginning Value) / (Beginning Value)
Effective Annual Yield (EAY)=
Effective Annual Yield (EAY)= (1+HPY)^(365/t) -1
HPY= Holding period yield
Geometric Mean=
Geometric Mean= [(1+R1)(1+R2)…. (1+Rn)]^(1/n)-1
Geometric mean return is also known as compound annual rate of return
Harmonic Mean=
Harmonic Mean= N / ∑(1/x)
Position of observation at a given percentile
Ly=(n+1) (y / 100)
Mean Absolute Deviation (MAD)=
(∑Xi - X) / n
X = Arithmetic mean
Population Variance
σ^2 = (∑(Xi-μ)^2) / N
Standard Deviation
σ = square root of variance
Sample Variance
σ^2 = (∑(Xi-μ)^2) / (N - 1)
Chebyshev’s Inequality
Percentage of observations that lie within k standard deviations of the mean is at least= 1-1/k^2
Coefficient of Variation
CV = (standard deviation of x) / (average value of x)
Sharpe Ratio=
(Rp-RFR) / σp
Rp= Portfolio Return
RFR= Risk Free Rate
σp= standard deviation of portfolio return
Sample Skewness (Sk) =
(∑(Xi-x)^3) / (s^3)
s =sample standard deviation
Excess Kurtosis=
Excess Kurtosis= Sample Kurtosis - 3
Multiplication Rule Of Probability
P(AB)=P(A/B)*P(B)
Addition Rule Of Probability
P(A or B)= P(A)+P(B)-P(AB)
Total Probability Rule (Used to determine unconditional probability of an event)
P(A)=P(A/B1)P(B1)+P(A/B2)P(B2)+………+P(A/BN)P(BN)
Expected value of random variable=
weighted average of possible outcomes
Weights = probabilities that the outcome will occur
Bayes Formula
Updated Probability=( Probability of new information for a given event / unconditional
probability of new event )*(prior probability of event)
P/E =
P/E = (Dividend payout ratio) / (k - g)
dividend payout = 1 - retention rate
Weighted Average Cost of Capital =
WACC= (wd)[kd(1-t)]+(wps)(kps)+(wcc)(Kcc)
Wd= percentage of debt in capital structure.
Wps=percentage of preferred stock in the capital structure.
Wcc=percentage of common stock in the capital structure
Factorial
n! = n(n-1)(n-2)*(n-3)…… *1
0!=1
To standardize a normal variable
z=(Observation - Population Mean) / (Standard Deviation)
Roy’s safety first criteria
SFR= ([E(Rp)-Rl]) / (σ p)
**Choose the portfolio with largest SFR
Continuously compounded rate of return
Rcc=ln(1+HPR)
Standard Error of sample Mean
σx= σ / √n
σ= Standard deviation of population
n=Size of the sample
Price Elasticity of Demand =
%∆Quantity Demanded / %∆Price
Cross Price Elasticity =
%∆Quantity Demanded / %∆Price of Related Goods
Income Elasticity =
%∆Quantity Demanded / %∆ in Income
Accounting profit=
Accounting profit=total revenue-total accounting costs
Economic profit=
Economic profit=accounting profit-implicit opportunity costs
Or
Economic profit=total revenue-total economic costs
Normal profit
Normal profit is the accounting profit that makes economic profit equal to zero
Marginal Cost
MC=change in total cost / change in output
Nominal GDP =
∑Pi, tQi, t
Pi,t= Price of good i in year t. Qi,t=Quantity of good I produced in year t
GDP deflator=
GDP deflator= (nominal GDP / value of year t output at year t)*100
Per Capita Real GDP=
Per Capita Real GDP = GDP / population
GDP by expenditure approach
GDP = C + I + G + (X - M)
C = Consumption spending
I = Investments
G = Government purchases
X = Exports
M = Imports
GDP by Income Approach
GDP=national income+ capital consumption allowance+ statistical discrepancy
National Income=
National Income= compensation of employees (wages and benefits)
+ corporate and government enterprise profits before taxes
+Interest Income
+Unincorporated business net income (business owner’s income)
+rent
+indirect business taxes-subsidies
Personal Income=
Personal Income= national Income
+transfer payments to households
-indirect business taxes
-corporate income taxes
-undistributed corporate profits
Personal disposable income=
Personal disposable income = personal income - personal taxes
CPI=
CPI= (Cost of basket at current prices / cost of basket at base period prices)*100
Real Exchange Rate=
Real Exchange Rate= Nominal Exchange Rate(d/f) * ((CPI foreign) / (CPI domestic))
Interest Rate Parity
foward / spot = (1+interest rate (domestic)) / (1+interest rate (foreign))
Income statement equation
Net income = revenues - expenses
Straight line depreciation expense=
(cost - residual value) / (useful life)
Basic EPS=
(net income - preferred dividends) / (weighted average number of common shares outstanding)
Diluted EPS=
(Adjusted income for common shareholders) / (weighted average common and potential common shares outstanding)
Current Ratios=
(Current Assets) / (Current Liabilities)
Quick Ratio=
(current assets – inventories) / current liabilities
Cash Ratio=
(Cash + Marketable Securities) / (Current Liabilities)
P/E =
dividend payout ratio / k - g
Debt to equity ratio=
(Total debt) / (Total Shareholders Equity)
Debt To Capital=
(Total debt) / (Total Debt + Total Shareholders Equity)
Financial Leverage=
(Average Total Assets) / (Average Total Equity)
Interest Coverage Ratio=
(Earnings Before Interest and taxes) / (Interest payments)
Net profit margin=
(Net Income) / Revenue
Net income= earnings after taxes but before dividends
Gross Profit Margin=
(Gross profit) / Revenue
Gross profit= Net Sales- COGS
Operating profit margin=
(Operating Income (EBIT))
Revenue
Return on assets (ROA)=
(Net Income) / (Average Total Assets)
Return on Total Capital=
EBIT / (Average Total Capital)
Return On Equity=
(Net Income) / (Average Total Equity)
or
(Net Income / Revenue) * (Revenue / Equity)
Sustainable growth rate=
RR * ROE
RR= Retention rate
=1-dividend payout
Coefficient of variation sales=
(Standard deviation of operating income) / (Mean sales)
CV Operating Income=
(Standard deviation of operating income) / (mean operating income)
CV Net Income=
(Standard deviation of net income) / (Mean net income)
COGS=
beginning inventory + purchases - ending inventory
Depreciation methods
i) straight line and ii) ddb covered earlier.
ii) units of production depreciation=
(Original cost-salvage value) / (life in output units) * Output units in the period
Effective tax rate=
(Income tax expense) / (Pretax income)
WACC=
(wd) (kd) (1 - t) + (wps) (kps) + (wcc) (Kcc)
Wd= percentage of debt in capital structure.
Wps=percentage of preferred stock in the capital structure.
Wcc=percentage of common stock in the capital structure
t = marginal tax rate
Kd = before tax cost of debt
Kcc = cost of common stock
Kps = cost of preferred stock
After tax cost of debt=
kd (1 - t)
Dividend discount model
D1 / (k-g)
D1= Next year dividend.
k = Required rate of return on common equity.
g = Firm’s expected constant growth rate.
Required Return (RR) =
Rf + (RMarket – Rf) × Beta
RR = required return
Rf = risk-free rate
RMarket = market rate of return
