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Borrowing increases cash and debt by the same amount. Equity is the residual claim after liabilities.
A café has ₹80,000 in assets and ₹50,000 of liabilities. Equity is ₹30,000.
Common mistake. Cash from a loan is a financing inflow. It does not enter revenue or profit.
Open the lessonElasticity compares the percentage change in demand with the percentage change in price.
At ₹100 you sell 100 tickets. At ₹110 you sell 80. The midpoint elasticity is about −2.33.
Common mistake. A steep line on a chart is not an elasticity estimate without knowing its units and the baseline.
Open the lessonExpected value weights every possible outcome by its probability.
A 60% chance of ₹100 and a 40% chance of losing ₹50 yields an expected ₹40.
Common mistake. Expected profit does not tell you whether you can survive the loss scenario.
Open the lessonDiscount future cash flows into today’s money, then subtract the investment.
At 10%, ₹120,000 next year is worth ₹109,090.91 today. Subtract ₹100,000 to get ₹9,090.91.
Common mistake. Subtract sunk costs only if they are still avoidable. A payment already made is outside the incremental decision.
Open the lessonEvery sale contributes its price minus variable cost toward fixed costs.
₹60,000 fixed cost, ₹500 price and ₹300 variable cost give 300 units.
Common mistake. Using revenue per unit as the denominator ignores the cost of making each additional unit.
Open the lessonA sale can count as revenue before the customer pays. Inventory can use cash before it becomes an expense.
₹100 profit plus ₹20 depreciation minus ₹60 more receivables yields ₹60 cash flow, holding other items constant.
Common mistake. Comparing profit to cash flow without checking working capital can misdiagnose the business.
Open the lessonIn a simple graduated system, each rate applies to the slice of taxable income in that bracket.
In a fictional schedule, the first ₹100,000 is exempt and the next slice taxed at 10%. At ₹150,000, liability is ₹5,000, or 3.33%.
Common mistake. Applying the top bracket to all income overstates liability in a simple slice-based schedule.
Open the lessonPortfolio risk depends on how assets move together as well as their individual volatility.
Two equally weighted 20%-volatility assets with zero correlation give about 14.14% portfolio volatility.
Common mistake. Diversification may weaken when correlations rise under stress.
Open the lessonHigher yields discount fixed future payments more heavily.
A one-year $1,000 bond with a 5% coupon is worth $1,050 ÷ 1.10 = $954.55 at a 10% yield.
Common mistake. Coupon rate sets the contractual payment. Market yield changes the price.
Open the lessonA call gives its buyer the right to buy at the strike. Profit at expiry subtracts the premium.
With strike $100 and premium $6, a spot of $104 yields a $4 payoff and a $2 loss.
Common mistake. Confusing the strike with the buyer’s break-even price overlooks the premium.
Open the lessonReal return measures purchasing power. Nominal return measures currency growth.
An 8% return with 5% inflation produces about 2.86% real growth.
Common mistake. Subtracting inflation is an approximation that gets less accurate at larger rates.
Open the lessonAnchoring gives an initial number more influence than the evidence warrants.
A stock fell from ₹100 to ₹60. Revised cash flows imply ₹45 under your assumptions.
Common mistake. Calling a stock cheap because it fell ignores the change in fundamentals.
Open the lessonAn importer who owes dollars loses purchasing power when USD costs more INR. A forward can fix the INR cost.
A $10,000 payable at a forward rate of ₹84/USD costs ₹840,000 under the contract.
Common mistake. A hedge should match the exposure direction. Selling dollars forward would add risk to this payable.
Open the lessonValue at risk estimates a loss threshold at a specified horizon and confidence level.
A model with 95% VaR of ₹100,000 gives a threshold, not a bound on possible loss.
Common mistake. Treating VaR as maximum possible loss hides extreme outcomes.
Open the lessonForecast free cash flow, discount it, then estimate what remains beyond the explicit forecast.
With $10m cash flow in year one, WACC 10% and zero growth forever, EV is $100m.
Common mistake. Putting interest expense in FCFF mixes equity financing with a firm-level discount rate.
Open the lessonEnterprise value approximates the value of operating assets. Equity value belongs to shareholders.
At $60m equity, $18m debt and $8m cash, EV is $70m.
Common mistake. Subtracting operating cash that the business needs can understate the acquisition cost.
Open the lessonBorrowing reduces entry equity. Remaining debt reduces what shareholders receive at exit.
Buy for $100m with $60m debt. Exit at $120m EV with $40m debt remaining. $80m proceeds on $40m equity gives 2×.
Common mistake. Lower entry equity amplifies losses as well as gains. Fees and interim distributions are excluded here.
Open the lessonSynergy creates value only if the incremental benefit exceeds the premium and integration costs.
$20m of gross synergy PV less $8m of integration costs and a $15m premium implies −$3m for the acquirer.
Common mistake. A recurring savings run rate is not the same as its risk-adjusted present value.
Open the lessonComparable companies offer valuation anchors when their economics and metrics are aligned.
At 8× and $9m normalized EBITDA, implied EV is $72m.
Common mistake. A median is only as informative as its peer group. Negative EBITDA makes the multiple hard to interpret.
Open the lessonCoverage tests cash available for debt service against scheduled interest and principal.
₹120 crore available against ₹100 crore of principal and interest gives 1.20×.
Common mistake. EBITDA can ignore tax, maintenance capital and working capital required to produce available cash.
Open the lessonLoss depends on whether a borrower defaults, how much is exposed, and how much can be recovered.
2% default probability × 40% loss severity × ₹1 crore exposure gives ₹80,000.
Common mistake. Expected loss is a portfolio planning estimate. It is distinct from a single borrower’s realized loss.
Open the lessonAuthorization, clearing and settlement answer different questions. Reconciliation matches internal records to external movements.
₹10,000 in settled sales minus ₹150 fees and a ₹350 refund yields ₹9,500.
Common mistake. Retrying an uncertain payment without idempotency can create a duplicate charge.
Open the lessonIf two portfolios produce the same payoff in every modeled state, no-arbitrage gives them the same price under the model assumptions.
Stock moves to $120 or $80. A $100-strike call pays $20 or $0. Replication uses 0.5 shares and debt with $40 due at expiry.
Common mistake. Delta depends on the modeled states and changes as time and spot move.
Open the lessonCarbon intensity divides emissions by a measure such as output or revenue. Absolute emissions measure total volume.
Emissions increase from 100 to 110 tonnes while production rises from 100 to 125 units. Intensity falls from 1.00 to 0.88 tonnes per unit.
Common mistake. Presenting an intensity decline as an absolute emissions reduction can mislead investors.
Open the lessonUnder accrual accounting, revenue follows the work performed. Cash collection settles the claim and can happen later.
Record ₹24,000 of March revenue. Collect ₹15,000 and leave ₹9,000 in receivables. April collection of the balance raises cash by ₹9,000 and lowers receivables by the same amount.
Common mistake. Adding April collections to April revenue would count the same service twice. Receiving cash before performing a service would be a different case, generally involving a liability.
Open the lessonEquilibrium is where quantity demanded matches quantity supplied. A shift in the whole demand curve changes that crossing.
With a = 100 and b = 20, price is ₹16. Both curves give 68 units. At ₹10, buyers want 80 units and sellers offer 50, leaving a shortage of 30.
Common mistake. Higher demand means more buying at the same price. Moving along an unchanged demand curve is a response to price, a different event.
Open the lessonCompare true and false alerts in the population. When defaults are uncommon, false alerts can outnumber true ones.
Of 1,000 similar borrowers, expect 50 defaults at a 5% base rate. At 80% sensitivity, expect 40 true flags. At a 10% false-positive rate, expect 95 false flags. The share of flagged borrowers expected to default is 40 ÷ 135 ≈ 29.63%.
Common mistake. Reading sensitivity as the probability of default after a flag reverses the conditioning.
Open the lessonA project funded by a mix of debt and equity must earn enough to compensate both groups. WACC combines their required returns.
60% equity at 12%, 40% debt at 8% and a hypothetical 25% tax rate give 7.2% + 2.4% = 9.6%.
Common mistake. Using book weights or applying one corporate discount rate to unrelated project risks can distort a valuation.
Open the lessonDuPont analysis decomposes return on equity into profit margin, asset turnover and the equity multiplier.
Sales ₹200 lakh, net income ₹16 lakh, average assets ₹160 lakh and average equity ₹80 lakh. 8% margin × 1.25 asset turnover × 2 equity multiplier = 20% ROE.
Common mistake. Calling a higher ROE an operating improvement without checking margin, turnover and leverage separately.
Open the lessonModified duration estimates the percentage price change for a small yield change. A five-year duration gives roughly a 5% move for a one-point yield change.
A five-year zero at 5% yield has modified duration 5 ÷ 1.05 ≈ 4.76 years. A 0.50-point yield rise gives an approximate 2.38% price decline.
Common mistake. Enter a 50 basis point move as 0.005 in the formula, not 0.50.
Open the lessonCAPM adds compensation for exposure to broad market movements to the risk-free rate.
At a 4% risk-free rate, beta 1.2 and a 5% market risk premium, cost of equity is 4% + 1.2 × 5% = 10%.
Common mistake. Substituting the full market return for the market risk premium double-counts the risk-free component.
Open the lessonA cash sweep uses available cash to repay debt before exit. Less debt at sale means a larger residual for shareholders, holding operating value and other claims fixed.
Buy at $100m EV with $60m debt and $40m sponsor equity. Sweep $10m annually for three years. Exit debt falls to $30m. At $120m exit EV, equity receives $90m, equal to 2.25× invested capital.
Common mistake. Subtracting interest again from a cash flow already defined after interest would understate sweep capacity. Using a constant cash flow also hides the effect of lower debt on later interest.
Open the lessonA coverage covenant requires cash available to exceed scheduled debt service by a stated factor. Work backward from the covenant to size the maximum payment.
At ₹108 crore available cash and a 1.20× minimum coverage ratio, the payment ceiling is ₹90 crore. A proposed payment of ₹100 crore needs a ₹10 crore reduction in that period.
Common mistake. Using gross revenue in place of cash available overstates capacity. Averaging the ratio across periods can hide a breach in a single period.
Open the lessonDifferent depreciation schedules can shift the timing of tax. An earlier tax deduction can create a deferred tax liability.
A machine’s carrying amount is ₹80 lakh and tax base is ₹60 lakh. At 25%, the ₹20 lakh difference gives a ₹5 lakh liability.
Common mistake. Tax expense and tax paid can diverge. A temporary difference is expected to reverse, whereas a permanent difference does not reverse.
Open the lessonStart with the frequency in a relevant comparison group, then update when new evidence distinguishes this case.
Four of 20 comparable firms refinanced within six months. Start with 20% as a descriptive rate before investigating the new borrower.
Common mistake. Counting only firms still listed after six months omits failures and can inflate the historical success rate.
Open the lessonApply a coherent adverse scenario to each position and combine signed impacts. A stress test estimates severity under the scenario.
A currency move costs ₹6 lakh and a bond position loses ₹9 lakh. Combined P&L is −₹15 lakh before liquidity effects.
Common mistake. Adding magnitudes can overstate loss if a position gains. Retain signs and evaluate basis and liquidity separately.
Open the lessonAn exception occurs when realized loss exceeds the forecast threshold. Compare frequency and clustering over a defined window.
Over 250 days, a 99% model expects 2.5 exceptions. Five observed exceptions imply an observed rate of 2%, which merits investigation.
Common mistake. Expected count is an average across samples, not an automatic pass/fail rule for one sample.
Open the lessonCompare the buyer’s earnings per share before and after the deal. Accretion measures the change in this ratio, while value depends on what you pay and earn.
Buyer has $60m earnings and 30m shares, so EPS is $2. Add $12m target earnings and $3m synergy, with 5m new shares. $75m ÷ 35m ≈ $2.14, or 7.14% accretion.
Common mistake. EPS accretion can come from relative multiples or accounting. It does not establish positive NPV.
Open the lessonPrimary shares raise money for the issuer. Secondary shares transfer proceeds to selling holders.
At $20, 4m new shares and 2m existing shares produce a $120m gross offering. With $5m issuer costs, the company receives $75m net.
Common mistake. Using total deal size as issuer cash raised treats selling holders’ proceeds as company funds.
Open the lessonMeasure each stage on a consistent cohort. Approval improvements only add value when payments reach capture and settlement.
Of 10,000 attempts, 9,000 are approved. Of those, 8,550 are captured and settle. End-to-end rate is 85.5%.
Common mistake. A rise in approval rate can hide a drop in later-stage conversion or an increase in fraud.
Open the lessonIn a one-step arbitrage-free tree, use a pricing weight that makes the expected stock value grow at the risk-free rate.
Stock is $100, up is $120, down is $80, strike is $100 and R = 1.05. q is 0.625. Call value is $12.50 ÷ 1.05 ≈ $11.90.
Common mistake. Substituting a subjective up probability into this formula loses the replication argument.
Open the lessonCompare costs that change with the decision. Allocated overhead can remain even if production stops.
Buying changes cost by ₹84 − ₹77 = ₹7 per part, or ₹70,000 more overall. Keep making under these assumptions.
Common mistake. Counting all allocated fixed costs as savings overstates the benefit of outsourcing.
Open the lessonAdd inventory days and collection days, then subtract supplier payment days.
A distributor holds stock for 45 days, collects in 38 and pays suppliers in 30. The cycle is 53 days.
Common mistake. Do not infer the funding amount from days alone. Convert each component with its own daily flow.
Open the lessonStart with operating profit after assumed tax. Add noncash depreciation and deduct investment in equipment and working capital.
EBIT is $40m and assumed tax is 25%. Add $6m depreciation, subtract $12m capex and $4m more working capital. FCFF is $20m.
Common mistake. Subtracting interest mixes operating cash flow with financing cash flow.
Open the lessonTerminal value estimates cash flows beyond the explicit forecast. A small discount-rate-minus-growth spread magnifies assumptions.
Year-six FCFF is $8m, WACC is 10% and growth is 2%. At year five, terminal value is $100m. Discounting five years gives about $62.09m today.
Common mistake. Using the last forecast year’s cash flow without converting to the following year shifts the timing.
Open the lessonA put gives the holder the right to sell at a strike price. The protection costs a premium.
Buy the share for $100 and a $95 put for $3. At expiry spot of $82, the share and put together are worth $95, leaving an $8 loss.
Common mistake. The strike is the floor for expiry proceeds. The premium must still be included in total profit and loss.
Open the lessonCompounding earns a return on the original balance and on returns already retained.
₹50,000 at 8% annually becomes ₹54,000 after one year and ₹58,320 after two. Year two adds ₹4,320.
Common mistake. Adding 8% of the original principal each year models simple interest.
Open the lessonFunding costs can rise faster than interest income. Margin tracks the net interest earned on the average earning asset base.
A fictional bank earns ₹92 crore interest and pays ₹48 crore over a year, with ₹1,100 crore average earning assets. NIM is 4.0%.
Common mistake. Dividing by total closing assets instead of average earning assets changes the measure.
Open the lessonA regression slope summarizes association in the fitted data. It does not by itself identify an intervention’s effect.
Advertising values are 1, 2 and 3 lakh and sales are 7, 9 and 13 lakh. The centered cross-product sum is 6 and the centered squared x sum is 2. Slope is 3.
Common mistake. The slope has units. Here it is lakh of fitted sales per lakh of advertising.
Open the lessonA sustainability-linked bond can change its coupon if a defined performance target is missed. Read the contract before counting cash flows.
On ₹200 crore principal, a 25 basis-point step adds ₹0.50 crore per affected year. A 7.00% coupon becomes 7.25%.
Common mistake. Do not apply the step-up to years before the contract activates it.
Open the lesson