Equities & Derivatives Calculators

Options pricing with the Black-Scholes-Merton model — live Greeks, an implied-volatility solver, and payoff at expiry, worked step by step

Binomial option pricing on a Cox-Ross-Rubinstein lattice — European and American, converging to Black-Scholes, with the early-exercise premium

Monte Carlo option pricing — simulate thousands of random price paths, watch the estimate converge to Black-Scholes, and see the standard error shrink

CAPM expected return — risk-free rate plus beta times the equity risk premium — the return an investment should earn for its market risk

Dividend discount model value from D₁ ÷ (r − g) — the Gordon Growth present value of all future dividends, and why the r − g spread dominates

DCF intrinsic value — projected free cash flows plus a terminal value discounted to today, with how much rests on the terminal assumption

Compute the weighted average cost of capital — the blend of the cost of equity and the after-tax cost of debt by their weights — the discount rate that powers a DCF.

Bond price from yield, or yield to maturity from a market price — with the premium/discount, current yield, and the cash flows behind the number

Sharpe ratio — excess return over the risk-free rate per unit of volatility — the standard measure of risk-adjusted return, shown step by step

Forward and futures pricing by cost-of-carry — spot grown by financing and storage, less income — and whether the market is in contango or backwardation

Option strategy payoff at expiry for spreads, straddles, covered calls, and iron condors — Black-Scholes-priced legs, break-evens, max profit and loss

Option Greeks charted across the underlying price — delta, gamma, vega, theta, and rho, and how they shift as spot moves toward the strike

Bond duration and convexity — Macaulay and modified duration, and how the two together estimate a price change far better than duration alone

Net present value of a cash-flow series at your discount rate — per-period discounting, the profitability index, and a clear accept/reject signal

Internal rate of return — the discount rate at which NPV is zero — solved numerically, with the NPV profile drawn so you can see where it crosses

Perpetuity present value — level or growing, C ÷ r or C ÷ (r − g) — the engine behind dividend-growth valuation and DCF terminal values

Sortino ratio — risk-adjusted return using downside deviation only, so upside volatility isn't penalised — shown side by side with Sharpe

Expected return — the probability-weighted average across scenarios, plus the variance and standard deviation that measure its risk

Market cap from share price and shares outstanding, with the mega/large/mid/small/micro-cap tier — the equity value the market puts on the company

Enterprise value — the true takeover cost: market cap plus debt, preferred, and minority interest, less cash — built from the balance sheet

P/E ratio from share price and EPS (or net income and shares), plus the earnings yield it implies — the most-quoted valuation multiple

PEG ratio — the P/E-to-growth measure that puts a high multiple in context: a 30× P/E is cheap if earnings grow 30% a year

EV/EBITDA — the enterprise multiple that values the whole business against its cash earnings, so debt-heavy and debt-free firms compare equally

P/B ratio comparing market price to accounting book value, with the premium or discount to book — most telling for asset-heavy firms like banks

Return on equity — net income as a percentage of shareholders' equity — the headline measure of the return a company earns on its owners' capital

Return on assets — profit as a percentage of everything the company owns — how efficiently the asset base becomes earnings, unflattered by leverage

Return on invested capital — NOPAT over the capital put to work — the truest test of operating quality, compared against the cost of capital

Return on capital employed — operating profit over long-term capital, assets minus current liabilities — a pre-tax measure for capital-intensive firms

Return on sales — operating income as a percentage of revenue — the margin that captures pricing power and cost control before financing and tax

DuPont analysis — decompose return on equity into profit margin, asset turnover, and financial leverage to see what really drives a company's ROE

Current yield — annual coupon income as a percentage of a bond's market price — and how it sits between the coupon rate and the yield to maturity

Coupon payment per period — face value times coupon rate, split by frequency — plus the annual income and total coupons over the bond's life

Coupon rate recovered from a bond's periodic payment and face value — the fixed rate set at issue that never changes with the market price

Bond equivalent yield — annualize a T-bill's discount yield on a 365-day year so it compares with coupon bonds, alongside the bank-discount quote

Tax-equivalent yield — the pre-tax yield a taxable bond must offer to match a tax-free municipal in your bracket, with a side-by-side check of which wins

Earnings per share — profit for common shareholders over shares outstanding, preferred dividends removed first — the base of the P/E and PEG ratios

EPS growth — total and annualized (compound) growth between two periods — the engine behind the PEG ratio and the test of a high multiple

Graham number — Benjamin Graham's ceiling for a defensive buy, √(22.5 × EPS × book value per share) — plus the margin of safety versus price

Intrinsic value per share via Graham's revised formula — EPS × (8.5 + 2g) discounted by the corporate bond yield — with the margin of safety

Net asset value per share — assets minus liabilities, divided by shares — the figure mutual funds price at, and the benchmark for discounts

Asset turnover — revenue divided by total assets — how efficiently assets become sales, the efficiency lever in the DuPont breakdown of ROE

Inventory turnover — how many times a year inventory is sold and replaced, COGS over average inventory — plus the days-inventory holding period

Receivables turnover — how quickly a company collects what it is owed, credit sales over average receivables — with days sales outstanding

EBITDA margin — core operating profitability before financing, tax, and depreciation — for comparing firms with different capital structures

Retention ratio — the share of earnings kept to reinvest, equal to one minus the dividend payout — the plowback input to sustainable growth

Sustainable growth rate — return on equity times the retention ratio — the fastest a company can grow without new equity or more leverage

Days payable outstanding — how long a company takes to pay suppliers, accounts payable over COGS — the third leg of the cash conversion cycle

Cash conversion cycle — days inventory plus days sales minus days payable — a negative cycle means suppliers are funding the business

Retained earnings rolled forward — beginning balance plus net income minus dividends — the running total of profits kept rather than paid out

The interest rate the yield curve implies for a future period, derived by no-arbitrage from two spot rates. Educational, not investment advice.

PVGO — the present value of growth opportunities: how much of a stock's price is growth expectation, price minus its no-growth earnings value

The Kelly criterion stake that maximizes long-run bankroll growth — full, half, and quarter Kelly with the expected growth rate at each, and a clear no-edge warning.

How volatility pulls compound returns below the average — arithmetic vs geometric mean from summary stats or a real return series, with the long-run dollar gap.

Yield to call on a callable bond — solved from price, call date, and call price by bisection — with the YTM comparison and the yield to worst brokers must quote.

All three free cash flows — simple FCF, cash flow to the firm, and cash flow to equity — with the reconciliation bridge between them and the discount rate each one pairs with.

Bankruptcy risk by the Altman Z-score — all three published variants with exact coefficients, the distress/grey/safe zones, and each ratio's contribution shown.

Jensen's alpha — the return a portfolio earned above its CAPM-required return — from the risk-free rate, beta, and market return, with the full benchmark breakdown.

Risk-adjusted return per unit of market (beta) risk — the Treynor ratio with a market-benchmark comparison, completing the Sharpe and Sortino performance trilogy.

Put-call parity — solve the missing call or put from the other three legs, or check all four quotes for a parity gap and which side is rich. European, no-dividend form.

Markowitz two-asset portfolio return and risk from weights, volatilities, and correlation — with the diversification benefit quantified and the minimum-variance weights solved.

Unlever a comparable firm's equity beta or relever it at a target capital structure with the Hamada equation — the workhorse step of every comps-based cost-of-equity estimate.

Backs the implied volatility out of an observed option price by inverting Black-Scholes — Newton-Raphson on vega with a bisection fallback, no-arbitrage bounds checked first, and the solver's working shown.