100 Essential Financial Formulas with Practical Examples
100 Essential Financial Formulas with Practical Examples
Whether you’re a finance student or a professional, mastering these formulas is key to making sound decisions. In this article, each formula is explained and paired with a practical example to show you how it’s applied in real-world scenarios.
Table of Contents
I. Banking & Loan Formulas
1. Loan EMI Formula
EMI = [P × r × (1+r)^n] / [(1+r)^n – 1]
Explanation: P = principal, r = monthly interest rate (annual rate/12), n = total number of months.
Example: For a ₹1,00,000 loan at 12% p.a. over 5 years (60 months), r = 0.01; EMI ≈ ₹2,220 per month.
2. Compound Interest
FV = PV × (1 + r)^n
Explanation: PV = present value, r = interest rate per period, n = number of periods.
Example: ₹10,000 at 8% compounded annually for 5 years gives FV = 10,000 × (1.08)^5 ≈ ₹14,693.
3. Simple Interest
SI = P × r × t
Explanation: P = principal; r = annual rate; t = time in years.
Example: ₹10,000 at 6% for 3 years: SI = 10,000 × 0.06 × 3 = ₹1,800.
4. Present Value (PV)
PV = FV / (1 + r)^n
Explanation: Discounts a future sum (FV) to its value today.
Example: To have ₹15,000 in 4 years at 5% annual discount rate: PV = 15,000 / (1.05)^4 ≈ ₹12,313.
5. Future Value (Single Sum)
FV = PV × (1 + r)^n
Explanation: Finds the future value of a current sum.
Example: ₹8,000 at 7% for 3 years: FV = 8,000 × (1.07)^3 ≈ ₹9,793.
6. Annual Percentage Rate (APR)
Explanation: The yearly interest rate charged on a loan, not accounting for compounding.
Example: A monthly rate of 1% yields an APR of approximately 12%.
7. Effective Annual Rate (EAR)
EAR = (1 + r/n)^n – 1
Explanation: Converts a nominal rate to an annualized rate accounting for compounding.
Example: For a 12% nominal rate compounded monthly: EAR = (1 + 0.12/12)^12 – 1 ≈ 12.68%.
8. Discount Factor
DF = 1 / (1 + r)^n
Explanation: Factor used to discount future cash flows.
Example: With r = 5% and n = 3, DF = 1 / (1.05)^3 ≈ 0.8638.
9. Sinking Fund Payment
PMT = (FV × r) / [(1 + r)^n – 1]
Explanation: Calculates periodic deposits needed to accumulate a desired future value.
Example: To accumulate ₹50,000 in 5 years at 6% annual rate: PMT ≈ ₹743 per year.
10. Rule of 72
Years to Double ≈ 72 / (annual growth rate in %)
Explanation: Estimates the number of years required to double an investment.
Example: At a 9% growth rate: 72 / 9 = 8 years.
II. Investment & Valuation Formulas
11. Net Present Value (NPV)
NPV = Σ [CFₜ / (1 + r)ᵗ] – Initial Investment
Explanation: Sums the present values of future cash flows then subtracts the initial cost.
Example: For cash flows of ₹3,000, ₹4,000, and ₹5,000 over 3 years at 10%, with an investment of ₹10,000, NPV ≈ (3000/1.1 + 4000/1.21 + 5000/1.331) – 10,000 ≈ -₹644.
12. Internal Rate of Return (IRR)
Explanation: The discount rate that makes the NPV equal to zero.
Example: For cash flows of -₹10,000, ₹3,000, ₹4,000, ₹5,000, and ₹6,000, the IRR is approximately 12% (calculated using iterative methods).
13. Modified IRR (MIRR)
MIRR = [(FV of positive CF / PV of negative CF)^(1/n)] – 1
Explanation: Adjusts for different reinvestment and finance rates.
Example: If positive CF’s FV is ₹15,000, negative CF’s PV is ₹10,000 over 3 years, MIRR ≈ [(15000/10000)^(1/3)] – 1 ≈ 14.47%.
14. Return on Investment (ROI)
ROI = [(Gain – Cost) / Cost] × 100%
Explanation: Measures profit relative to investment cost.
Example: If an investment costs ₹10,000 and returns ₹15,000, ROI = [(15,000–10,000)/10,000]×100% = 50%.
15. Compound Annual Growth Rate (CAGR)
CAGR = (Ending Value / Beginning Value)^(1/n) – 1
Explanation: The mean annual growth rate over n years.
Example: From ₹100,000 to ₹144,000 over 2 years: CAGR = (144,000/100,000)^(1/2) – 1 ≈ 20%.
16. Discounted Cash Flow (DCF)
Explanation: Uses forecasted cash flows discounted at a chosen rate to determine value.
Example: Forecasted cash flows of ₹10,000 per year for 5 years at 8% discount rate yield DCF ≈ ₹40,000.
17. Dividend Discount Model (DDM)
Price = D₁ / (r – g)
Explanation: Values a stock based on expected future dividends.
Example: With next year’s dividend of ₹5, required return 10%, and growth 3%, Price = 5/(0.10–0.03) ≈ ₹71.43.
18. Price-to-Earnings (P/E) Ratio
P/E = Market Price per Share / EPS
Explanation: Indicates how much investors pay per rupee of earnings.
Example: Stock at ₹50 and EPS ₹2 gives a P/E of 25.
19. Price-to-Book (P/B) Ratio
P/B = Market Price per Share / Book Value per Share
Explanation: Compares market value to accounting value.
Example: If market price is ₹80 and book value is ₹40, P/B = 2.
20. Dividend Yield
Dividend Yield = Annual Dividend per Share / Market Price per Share
Explanation: Shows the return from dividends relative to share price.
Example: Annual dividend ₹4 and price ₹100 gives 4% yield.
III. Corporate Finance & Business Analysis Formulas
31. Net Income
Net Income = Revenue – Expenses
Example: Revenue ₹500,000 minus expenses ₹350,000 gives net income of ₹150,000.
32. Gross Profit Margin
Gross Margin = [(Revenue – COGS) / Revenue] × 100%
Example: Revenue ₹400,000 and COGS ₹250,000 yields margin = ((400,000–250,000)/400,000)*100 = 37.5%.
33. Operating Profit Margin
Operating Margin = (Operating Profit / Revenue) × 100%
Example: Operating profit ₹80,000 on revenue of ₹400,000 gives 20% margin.
34. EBITDA
EBITDA = Operating Profit + Depreciation + Amortization
Example: Operating profit ₹70,000, Depreciation ₹20,000, Amortization ₹10,000 yield EBITDA = ₹100,000.
35. Contribution Margin
Contribution Margin = Price per Unit – Variable Cost per Unit
Example: Selling price ₹100 and variable cost ₹60 gives a margin of ₹40 per unit.
36. Breakeven Point (Units)
Breakeven Units = Fixed Costs / (Price per Unit – Variable Cost per Unit)
Example: Fixed costs ₹50,000, margin per unit ₹25 yields 50,000/25 = 2,000 units.
37. Breakeven Point (Revenue)
Breakeven Revenue = Fixed Costs / Contribution Margin Ratio
Example: Fixed costs ₹75,000 and margin ratio 0.5 yields 75,000/0.5 = ₹150,000.
38. Margin of Safety
Margin of Safety = [(Actual Sales – Breakeven Sales) / Actual Sales] × 100%
Example: Actual sales ₹200,000, breakeven ₹150,000 gives (50,000/200,000)*100 = 25%.
39. Operating Leverage
Explanation: Reflects how a change in sales volume affects operating income.
Example: If a 10% sales increase leads to a 20% increase in operating profit, operating leverage is high.
40. Financial Leverage
Financial Leverage = Total Assets / Equity
Example: Assets ₹1,000,000 and equity ₹500,000 yield leverage of 2.
41. Combined Leverage
Explanation: The combined effect of operating and financial leverage.
Example: If operating leverage is 1.5 and financial leverage is 2, combined leverage = 1.5×2 = 3.
42. DuPont Analysis
ROE = (Net Profit Margin) × (Asset Turnover) × (Equity Multiplier)
Example: Margin 10%, turnover 1.8, equity multiplier 1.5 yield ROE = 0.10×1.8×1.5 = 27%.
43. Economic Value Added (EVA)
EVA = NOPAT – (Capital Employed × WACC)
Example: NOPAT ₹120,000, capital ₹800,000, WACC 10% yield EVA = 120,000 – (800,000×0.10) = ₹40,000.
44. Market Value Added (MVA)
Explanation: The difference between the market value and invested capital.
Example: If market value is ₹1,200,000 and invested capital is ₹1,000,000, then MVA = ₹200,000.
45. Cash Flow Return on Investment (CFROI)
Explanation: A cash-based performance measure comparing operating cash flow to invested capital.
Example: Operating cash flow ₹150,000, invested capital ₹1,000,000 yield CFROI = 15%.
46. Price-to-Cash Flow Ratio
P/CF = Market Cap / Operating Cash Flow
Example: Market cap ₹2,000,000 and operating cash flow ₹250,000 yield P/CF = 8.
47. EBITDA Margin
EBITDA Margin = (EBITDA / Revenue) × 100%
Example: EBITDA ₹100,000 on revenue ₹500,000 gives margin = 20%.
48. Straight-Line Depreciation
Depreciation = (Cost – Salvage Value) / Useful Life
Example: Cost ₹50,000, salvage ₹5,000, life 10 years: Depreciation = (50,000-5,000)/10 = ₹4,500 per year.
49. Accumulated Depreciation
Explanation: The total depreciation charged on an asset since acquisition.
Example: After 3 years at ₹4,500 per year, accumulated depreciation = 3 × 4,500 = ₹13,500.
50. Amortization
Amortization = Cost of Intangible Asset / Useful Life
Example: A patent costing ₹10,000 over 20 years: Amortization = 10,000/20 = ₹500 per year.
IV. Excel & Data Analysis Formulas
51. SUM
=SUM(range)
Example: =SUM(A1:A5) adds all numbers in cells A1 through A5.
52. AVERAGE
=AVERAGE(range)
Example: =AVERAGE(B1:B10) calculates the mean of cells B1 to B10.
53. COUNT
=COUNT(range)
Example: =COUNT(C1:C8) counts numerical cells in the range C1 to C8.
54. VLOOKUP
=VLOOKUP(lookup_value, table_array, col_index, [range_lookup])
Example: =VLOOKUP(D1, A1:B10, 2, FALSE) finds D1 in column A and returns corresponding value from column B.
55. HLOOKUP
=HLOOKUP(lookup_value, table_array, row_index, [range_lookup])
Example: =HLOOKUP("Total", A1:Z3, 2, FALSE) finds "Total" in first row and returns value from second row.
56. IF
=IF(logical_test, value_if_true, value_if_false)
Example: =IF(E1>50, "High", "Low") returns "High" if E1 > 50.
57. COUNTIF
=COUNTIF(range, criteria)
Example: =COUNTIF(F1:F10, ">100") counts cells in F1:F10 greater than 100.
58. SUMIF
=SUMIF(range, criteria, [sum_range])
Example: =SUMIF(G1:G10, "Apples", H1:H10) sums H1:H10 where G1:G10 equals "Apples".
59. INDEX-MATCH
Explanation: A powerful alternative to VLOOKUP. MATCH finds the position, INDEX returns the value.
Example: =INDEX(J1:J10, MATCH("Oranges", I1:I10, 0)) finds "Oranges" in I1:I10 and returns corresponding value from J1:J10.
60. TEXTJOIN
=TEXTJOIN(delimiter, ignore_empty, text1, [text2], ...)
Example: =TEXTJOIN(", ", TRUE, K1:K5) concatenates text in K1:K5 separated by commas.
V. Risk & Portfolio Management Formulas
61. Beta
Explanation: Measures a stock’s volatility relative to the market.
Example: A beta of 1.2 means the stock is 20% more volatile than the market.
62. Standard Deviation
σ = √[Σ (xᵢ – μ)² / (n – 1)]
Example: Calculated standard deviation of portfolio returns might be 8%.
63. Variance
Variance = σ²
Example: If σ = 8%, then variance = 0.08² = 0.0064 or 0.64%².
64. Covariance
Cov(X, Y) = Σ [(Xᵢ – μₓ)(Yᵢ – μᵧ)] / (n – 1)
Example: A positive covariance indicates that two assets tend to move together.
65. Correlation Coefficient
ρ = Cov(X, Y) / (σₓ × σᵧ)
Example: ρ = 0.8 indicates a strong positive relationship between two assets.
66. Value at Risk (VaR)
Explanation: Estimates the maximum loss over a specified period at a given confidence level.
Example: A 95% VaR of 10% on a ₹1,000,000 portfolio suggests a maximum loss of ₹100,000 on 5% of days.
67. Expected Shortfall (ES)
Explanation: The average loss given that losses exceed the VaR threshold.
Example: If losses beyond VaR average 12%, then ES is 12% of portfolio value.
68. Sharpe Ratio
Sharpe Ratio = (Rₚ – Rf) / σₚ
Example: Portfolio return 12%, risk-free 3%, σₚ 9% yields (12–3)/9 = 1.
69. Treynor Ratio
Treynor Ratio = (Rₚ – Rf) / βₚ
Example: If Rₚ = 12%, Rf = 3%, βₚ = 1.2, then Treynor Ratio = (9%)/1.2 = 7.5%.
70. Jensen's Alpha
Alpha = Rₚ – [Rf + βₚ (Rₘ – Rf)]
Example: With Rₚ=15%, Rf=3%, βₚ=1.1, and Rₘ=12%, Alpha = 15% – [3% + 1.1*(9%)] = 15% – 12.9% = 2.1%.
71. Information Ratio
Information Ratio = Active Return / Tracking Error
Example: If active return is 4% and tracking error is 2%, ratio = 4/2 = 2.
72. Sortino Ratio
Sortino Ratio = (Rₚ – Rf) / Downside Deviation
Example: With Rₚ=14%, Rf=3%, and downside deviation 5%, ratio = (11%)/5 = 2.2.
73. R-Squared
Explanation: Indicates the proportion of a portfolio’s variance explained by the benchmark.
Example: An R² of 0.85 means 85% of portfolio variability is explained by market movements.
74. Downside Deviation
Explanation: The standard deviation of only the negative returns.
Example: If only losses have a standard deviation of 4%, then downside deviation = 4%.
75. Real Rate of Return
Real Return = (1 + Nominal Return) / (1 + Inflation Rate) – 1
Example: Nominal return 10%, inflation 3% yields (1.10/1.03)-1 ≈ 6.8% real return.
76. Nominal Rate of Return
Explanation: The stated return without adjusting for inflation.
Example: If an investment grows from ₹100,000 to ₹110,000, nominal return = 10%.
77. Fisher Equation
Explanation: Relates nominal rate, real rate, and inflation: (1 + Nominal Rate) = (1 + Real Rate) × (1 + Inflation Rate).
Example: If real rate = 5% and inflation = 2%, nominal rate ≈ (1.05×1.02) – 1 = 7.1%.
78. Effective Interest Rate
EIR = (1 + r/n)^(n) – 1
Example: A 12% rate compounded quarterly gives EIR = (1+0.12/4)^4 – 1 ≈ 12.55%.
79. Discount Rate
Explanation: The rate used to discount future cash flows; reflects risk and opportunity cost.
Example: A discount rate of 8% means future cash flows are worth 8% less per year.
80. Terminal Value
Terminal Value = Final CF × (1+g) / (r – g)
Example: Final cash flow ₹20,000, growth 3%, discount rate 8% gives Terminal Value = 20,000×1.03/(0.08–0.03) ≈ ₹412,000.
81. Perpetuity
PV = Cash Flow / r
Example: A perpetuity paying ₹5,000 annually at a discount rate of 5% has PV = 5,000/0.05 = ₹100,000.
82. Dividend Payout Ratio
Dividend Payout Ratio = (Dividends per Share / EPS) × 100%
Example: If EPS is ₹8 and dividend is ₹2, ratio = (2/8)*100 = 25%.
83. Retention Ratio
Retention Ratio = 1 – Dividend Payout Ratio
Example: If dividend payout is 25%, retention ratio = 75%.
84. Sustainable Growth Rate
SGR = ROE × Retention Ratio
Example: ROE 15% and retention ratio 60% yield SGR = 0.15×0.60 = 9%.
85. Beta Calculation (Statistical)
Explanation: Beta is typically computed via regression of asset returns on market returns.
Example: A regression might yield a beta of 1.2, meaning 20% more volatility than the market.
86. Tracking Error
Tracking Error = Standard Deviation of (Portfolio Return – Benchmark Return)
Example: A tracking error of 2% indicates small deviations from the benchmark.
87. Active Return
Explanation: The difference between portfolio return and benchmark return.
Example: If portfolio return is 14% and benchmark is 11%, active return = 3%.
88. Information Ratio (Reiterated)
Information Ratio = Active Return / Tracking Error
Example: With active return 4% and tracking error 2%, ratio = 2.
89. R-Squared
Explanation: The percentage of return variability explained by the market.
Example: An R² of 0.85 means 85% of the variation is market-driven.
90. Downside Deviation
Explanation: Standard deviation computed using only negative returns.
Example: Calculated downside deviation might be 3.5%.
92. Maximum Drawdown
Explanation: The largest percentage drop from a peak to a trough in portfolio value.
Example: A portfolio peak of ₹1,000,000 dropping to ₹800,000 gives a drawdown of 20%.
93. Calmar Ratio
Calmar Ratio = Annualized Return / Maximum Drawdown
Example: Annual return 12% and drawdown 20% yield 0.6.
94. Downside Beta
Explanation: Measures sensitivity of asset returns during market downturns.
Example: A downside beta of 0.8 suggests lower volatility in downturns.
95. Upside Beta
Explanation: Measures sensitivity during market upswings.
Example: An upside beta of 1.3 indicates higher gains when the market rises.
96. Active Risk (Tracking Error)
Active Risk = √[Σ (Portfolio Return – Benchmark Return)² / (n – 1)]
Example: If computed active risk is 2.5%, that is the volatility of active returns.
97. Portfolio Variance
Portfolio Variance = wᵀΣw
Example: With a given weights vector and covariance matrix, variance might compute to 0.004 (or 0.4%²).
98. Portfolio Standard Deviation
Portfolio Std. Dev. = √(Portfolio Variance)
Example: If variance is 0.004, then standard deviation ≈ 6.32%.
99. CAPM – Security Market Line (SML)
Expected Return = Rf + β (Rₘ – Rf)
Example: With Rf 3%, market premium 7%, and β of 1.2, expected return = 3 + 1.2×7 = 11.4%.
100. Custom Portfolio Metric
Explanation: Combine various metrics to gauge overall portfolio performance.
Example: An analyst might use a weighted combination of Sharpe Ratio and active return to decide on portfolio adjustments.
Conclusion
This comprehensive guide has presented 100 essential financial formulas across banking, investment valuation, corporate finance, Excel data analysis, and risk/portfolio management. Each formula is accompanied by a practical example to illustrate its real-world application.
Mastering these formulas will help you analyze financial performance, evaluate investments, manage risks, and make informed decisions. Bookmark this guide and refer back to it as you enhance your financial acumen.
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