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Hamada Equation Levered / Unlevered Beta Calculator

The **Hamada equation** (Hamada 1972) is the corner-stone Modigliani-Miller-with-taxes result that links a firm's *levered (equity) beta* β_L — the same beta you get by regressing the stock against the market — to its *unlevered (asset) beta* β_U via the capital structure D/E and the marginal corporate tax rate t: β_L = β_U · [1 + (1 − t) · D/E]. **Standard valuation workflow**: (1) pick a peer set of *pure-play* comparable firms; (2) unlever each firm's β_L by its own D/E and t to obtain β_U; (3) take the median as the industry asset beta; (4) re-lever β_U using the *target firm's* D/E and t to recover its β_L, then plug into CAPM for the cost of equity. Enter β, D/E and t (%); the tool converts in either direction and reports the lever factor, debt share and equity share.

Industry presets (Damodaran 2024)

Result

Levered β_L

Unlevered β_U

Lever factor 1 + (1 − t) · D/E
Debt share D/(D+E)
Equity share E/(D+E)

Formula: β_L = β_U · [1 + (1 − t) · D/E]; assumes β_D = 0 (risk-free debt).

Standard CAPM / WACC step: unlever peer-group betas to β_U, then relever to the target firm's D/E and tax rate.

Formula

Relever: β_L = β_U · [1 + (1 − t) · D/E] Unlever: β_U = β_L / [1 + (1 − t) · D/E] Lever factor: LF = 1 + (1 − t) · D/E Capital structure: debt share = D / (D + E) equity share = E / (D + E) Assumption: β_D = 0 (debt beta is zero; the interest tax shield is discounted at the cost of debt).

Frequently asked

My peers issue high-yield debt with non-zero β_D. How do I handle this in Hamada?

**Standard Hamada assumes β_D = 0**, which is reasonable for investment grade but understates risk for high-yield issuers (BB- and lower), where β_D can run 0.2–0.4 and ignoring it *overstates β_U* by ~5–15 %. **The exact form** (Modigliani-Miller 1963) is β_L = β_U + (β_U − β_D) · (1 − t) · D/E. **Workflow**: (1) for investment-grade peers, keep Hamada with β_D = 0; (2) for distressed / high-yield, approximate β_D ≈ credit spread / market ERP — e.g. 500 bps spread, 5 % ERP → β_D ≈ 1.0; (3) the rigorous formula is β_D = covariance(r_D, r_m) / variance(r_m), but secondary corporate-bond liquidity introduces large estimation error. **Bottom line**: Hamada is fine for IG peers; once leverage tops ~50 % or the credit is sub-investment-grade, switch to the full MM formula with explicit β_D.

Should D/E use book debt or market debt?

**Equity (E) is always market cap**; *debt (D)* depends on context. **Damodaran's guidance**: (1) investment-grade firm, actively-traded bonds → use D at market value (Bloomberg or TRACE *clean price*); (2) private debt, bank loans, no trading quotes → book value is the practical proxy (typically understates by 1–5 %; up to 30 % if the firm is near distress); (3) **mixed practice**: combine market-value bonds with book-value bank debt. **Frequent mistakes**: (a) using *book equity* — flatly wrong; CAPM β reflects sensitivity to *market* returns; (b) adding only "short + long-term debt" — usually fine but include *capital and operating leases (ASC 842)* and pension underfunding; (c) ignoring *off-balance-sheet leverage* via SPVs and securitisation; (d) US GAAP vs IFRS classify debt slightly differently — reconcile for cross-border comparisons.

In an LBO the post-deal D/E jumps from 0.5 to 4.0, so β_L spikes. Does that justify a higher IRR estimate?

**Yes — but separate *cost of equity* from *target IRR*.** (1) **CAPM cost of equity**: with β_U = 0.8, t = 25 %, ERP = 5 %, r_f = 4 %: (a) pre-LBO β_L = 0.8 · (1 + 0.75 · 0.5) = 1.10, r_E = 4 + 1.10 · 5 = 9.5 %; (b) post-LBO β_L = 0.8 · (1 + 0.75 · 4.0) = 3.20, r_E = 4 + 3.20 · 5 = 20 %! (2) **PE target IRRs** are typically 20–25 % — that is *cost of equity + alpha*, not pure alpha. A high LBO IRR is therefore mostly *leverage risk premium*, not skill. (3) **Narrative caution**: a sponsor advertising "25 % annual returns" sounds compelling, but if levered β implies a 22 % cost of equity, the *real alpha* is only 3 % — comparable to public growth equity. (4) **De-levering path**: LBOs typically pay down debt over 5–7 years, D/E reverts towards 1.0, and β_L plus cost of equity decline. Correct valuation models the *time-varying WACC* across the holding period, not a single constant.

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Black-Scholes Option Price Calculator

Enter spot price, strike, time to expiry, risk-free rate, volatility and optional dividend yield; the tool applies the Black-Scholes-Merton 1973 model to return the European call and put prices, d₁ / d₂ and the full set of Greeks (Delta, Gamma, Vega, Theta, Rho) — the standard reference for option pricing, sanity-checking quotes and exploring implied volatility.

Tiered Sales Commission Calculator

Enter cumulative sales and 1–5 tiered commission rates (e.g. 5 % on the first 100 k, 6 % on the next, 8 % above) and the tool returns total commission, marginal and effective rates, plus the contribution of each tier — used by sales reps, sales managers and year-end payroll.

Customer Lifetime Value Calculator (CLV / LTV)

Enter average order value, purchase frequency, gross margin, churn (or expected lifetime) and discount rate; the tool applies the steady-state formula CLV = (AOV × Freq × Margin) / (Churn + Discount) to give the net present value of one customer over their entire relationship — the standard SaaS, subscription, retail and e-commerce metric.

Average True Range Calculator (ATR)

Paste the high, low and close for the last N bars; the tool applies Wilder's True Range max(H − L, |H − C_prev|, |L − C_prev|) and his RMA smoothing to give ATR — the standard volatility measure for sizing futures, FX and crypto stops and positions.

Dividend Reinvestment Plan (DRIP) Calculator

Enter starting shares, share price, annual dividend yield (DPS / price), expected annual price growth and horizon; the tool runs the year-by-year compounding loop — each dividend is fully reinvested into new shares, which earn the next round of dividends — and reports the final share count, market value, cumulative dividends and annualised CAGR. The standard analysis tool for long-term dividend reinvestment in stocks such as SPY, AAPL and KO.

Holding Period Return (HPR) Calculator

Enter buy price, sell price, total cash received during the holding period (dividends / coupons / distributions) and the length of the period; the tool computes the holding-period return (HPR) and the annualised HPR — works for stocks, bonds, ETFs and funds and shows the complete picture of capital gain plus cash distributions.

Personal Net Worth Calculator

Enter assets (cash, investments, property, vehicles, other) and liabilities (mortgage, credit cards, student loans, car loans, other); the tool returns total assets, total liabilities and net worth, plus the debt-to-asset ratio (DTA) and liquid-to-debt ratio commonly used to gauge financial health.

Cash-on-Cash Return Calculator

Enter the annual pre-tax cash flow from a property or investment and the actual cash you invested (down payment plus closing costs); the tool returns CoC = annual_cash_flow ⁄ total_cash_invested — real-estate investors' standard benchmark for cash-on-cash efficiency.

Car Loan Monthly Payment Calculator

Enter the car price, down payment, annual interest rate and loan term; the tool applies the standard amortization formula to give the monthly payment, total interest, total repayment, and a 12-month principal/interest split.

Safety Stock & Reorder Point Calculator

Enter the average daily demand, demand standard deviation, lead time and target service level; the tool applies Safety Stock = Z × σ_d × √L and ROP = d̄ × L + SS to give the reorder point that meets your stock-out tolerance.

Car Lease Monthly Payment Calculator (Depreciation + Money Factor)

Enter the cap cost, residual value, term, money factor and down payment; the tool applies the industry-standard lease formula to split the monthly bill into depreciation, finance charge and pre-tax total.

Loan Extra Payment Savings Calculator (Time & Interest Saved)

Enter the loan principal, annual rate, scheduled monthly payment and the extra you can pay each month; the tool runs month-by-month amortisation to show the time and interest saved, and compares the with- vs without-extra payoff timelines.

Two-Asset Portfolio Variance / Std-Dev Calculator (Markowitz)

Enter two assets' weights, standard deviations and correlation ρ; the tool applies σ²p = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ to give portfolio variance / std-dev, covariance, diversification benefit and the minimum-variance weights — the heart of Markowitz modern portfolio theory.

Interest-Only Mortgage Payment Calculator

Enter loan principal, annual rate, interest-only period and the following amortizing period; the tool gives the interest-only monthly payment, the amortizing monthly payment that kicks in afterwards, total interest paid and the cost gap vs a fully-amortizing loan — useful for mortgage shopping and personal-finance planning.

Forward Exchange Rate Calculator (Covered Interest Rate Parity)

Enter the spot rate, the quote-currency (domestic) and base-currency (foreign) annual interest rates, and the contract days; the tool applies covered interest rate parity F = S × (1 + r_d × t/basis) / (1 + r_f × t/basis) to give the theoretical forward rate, forward points and annualised premium / discount — essential for FX-forward pricing, carry-trade analysis and cross-border settlement.

Mortgage Balloon Payment Calculator

Enter principal, rate, amortising term and actual loan term; the tool calculates the monthly payment using the longer amortisation schedule and the balloon (lump-sum) due at loan maturity, plus total interest and a comparison vs a fully-amortising loan of the same term.

Enterprise Value to EBITDA (EV / EBITDA) Multiple Calculator

Enter equity market cap, total debt, cash, minority interest and preferred stock, plus trailing-12-month EBITDA; the tool returns Enterprise Value, the EV / EBITDA multiple and an industry benchmark band — the cornerstone multiple in M&A, private-equity and value-investing valuation.

Modified Duration Calculator (Bond Price Sensitivity to Yield)

Enter a bond's coupon rate, yield to maturity, remaining years and coupon frequency; the tool returns Macaulay duration, modified duration D* = D_M / (1 + y/k), convexity, DV01 and the approximate price change for ±1% yield moves — the standard interest-rate-risk metric for fixed-income portfolios.

Earned Value Management (EVM) Calculator (CPI, SPI, EAC, ETC, VAC)

Enter Planned Value (PV), Actual Cost (AC), Earned Value (EV) and Budget at Completion (BAC); the tool instantly returns the PMI / PMBOK-standard Cost Performance Index (CPI), Schedule Performance Index (SPI), Cost / Schedule Variance (CV / SV), Estimate at Completion (EAC), Estimate to Complete (ETC), Variance at Completion (VAC) and To-Complete Performance Index (TCPI) — the core indicators a PMP / PRINCE2 project manager uses to track project health.

Rent vs Buy Total-Cost Comparison

Enter property price, down payment, mortgage rate, expected property appreciation, current rent, rent growth, alternative investment return and intended holding period; the tool computes the NPV of renting vs buying and identifies the break-even year — a universal framework without country-specific tax handling.

Graham Number Calculator (Value-Investing Fair Price √(22.5 × EPS × BVPS))

Enter earnings per share (EPS) and book value per share (BVPS); the tool applies Benjamin Graham's classic formula √(22.5 × EPS × BVPS) to estimate the theoretical fair-value ceiling for a defensive stock pick — the entry-level screen used by value investors and equivalent to the combined P/E ≤ 15 and P/B ≤ 1.5 Graham criteria.

Effective Annual Rate (EAR / APY) Calculator

Enter the nominal annual rate (APR) and the number of compounding periods per year n; the tool returns EAR = (1 + APR/n)ⁿ − 1 (the same as US APY), the apples-to-apples annualised rate used to compare credit cards, CDs, loans and bonds. Continuous compounding uses e^APR − 1.

Fisher Equation Real Rate Calculator

Enter the nominal rate (or return) and the inflation rate; the tool applies the Fisher equation r_real = (1 + r_nom) / (1 + π) − 1 and contrasts it with the common approximation r_real ≈ r_nom − π — the standard way to compare investment returns, deposit rates, mortgages and pay rises against inflation.

Reverse Sales Tax / VAT Calculator (Extract Pre-Tax Price)

Enter the tax-inclusive total and the tax rate (GST / VAT / sales tax); the tool extracts the pre-tax amount net = gross / (1 + rate), the tax tax = gross − net and the effective rate — the everyday tool for receipts, expense claims, cross-border shopping and bookkeeping.

Earnings Yield Calculator (EPS / Price = 1 / P/E)

Enter EPS and stock price (or the P/E ratio directly); the tool applies Earnings Yield = EPS / Price = 1 / (P/E) for the percentage earnings yield and compares against the 10-year Treasury yield to surface the *Fed-model* equity risk premium — a quick yardstick for stock-vs-bond valuation and long-horizon asset allocation.

Stock Average Cost Basis Calculator (Weighted Average / DCA)

Enter your share lots (quantity + price each); the tool applies the weighted-average formula Σ(qᵢ · pᵢ) / Σqᵢ to return the average cost basis, total invested, total shares held, and the unrealised P&L (absolute and percentage) at the current market price — the most basic tool for retail investors averaging down, dollar-cost-averaging or planning an exit.

Bond Accrued Interest Calculator (30/360 / Actual/Actual)

Enter par value, coupon rate, last coupon date, settlement date and coupon frequency; the tool applies either the 30/360 or Actual/Actual day-count convention to return the interest accrued from the last coupon to the settlement date (the dirty − clean price spread) — a core tool for secondary-market trading, price-quote conversion and bond accounting.

Credit Card Utilization Calculator

Enter outstanding balance and credit limit; the tool returns the utilisation ratio and flags the credit-score impact band (< 10 % excellent, 10–30 % healthy, 30–50 % marginal, > 50 % damaging) — the standard health check before any loan or mortgage application.

Rule of 114 (Years to Triple Your Money)

Enter an annual rate of return; the tool uses the Rule of 114, t ≈ 114 / r, to estimate the years for an investment to triple — the companion to the better-known Rule of 72 (doubling) and a quick mental-maths tool for retirement and long-term compounding planning.

Freelance Target Hourly Rate Calculator

Enter your target take-home income, the share of hours that are billable, annual business expenses and your tax rate; the tool back-solves the hourly rate you must charge to cover everything and still hit the target — essential pricing tool for freelancers, designers, developers, coaches and consultants.

Rule of 78 Loan Interest Allocator

Some older or sub-prime loans use the Rule of 78 (sum-of-digits) to allocate total interest by month in *reverse* order — meaning early payments are heavily interest-loaded and early payoff barely saves any interest. Enter principal, APR and term in months; the tool tabulates per-month interest/principal split and quantifies the front-loaded interest penalty vs straight-line allocation.

Floor Area Ratio (FAR / Plot Ratio) Calculator

Enter the site area, allowable floor area ratio (FAR / plot ratio) and site coverage cap; the tool returns the maximum gross floor area (GFA), the per-floor footprint cap and the implied number of storeys — the standard pre-feasibility tool for property developers, investors and self-build owners.

Continuous Compounding Calculator (A = P · e^(rt))

Enter principal, annual rate and term; the tool applies the continuous compounding formula A = P · e^(rt) to return the future value, total interest, equivalent effective annual rate (EAR = e^r − 1) and growth multiplier — the standard model behind option pricing (Black-Scholes), academic finance and the theoretical upper bound of compound growth.

Biweekly Mortgage Savings Calculator

Compare a standard monthly mortgage with a biweekly accelerated plan (half a monthly payment every two weeks = 26 half-payments = 13 monthly equivalents per year); the tool reports total interest saved, months shaved off the term, and the new payoff date — the calculator banks use to pitch their biweekly programs.

Life Insurance Coverage Calculator (DIME Method)

Apply the industry-standard DIME method (Debt + Income × years to replace + Mortgage balance + Education funding) to estimate the life-insurance coverage your household needs — a universal rule-of-thumb that is more accurate than the simplistic "10× annual salary" heuristic.

Latte Factor Calculator (True Cost of Small Daily Spending)

Enter a small daily expense (coffee, soda, takeaway lunch, etc.), how often, and an expected investment return; the tool shows the cumulative amount over 10 / 20 / 30 years if that money were *invested instead* — David Bach's "Latte Factor" framing that makes it concrete how much your daily $5 habit actually costs at retirement.

Crypto LP Impermanent Loss Calculator

Enter the price-ratio change k since entering a Uniswap V2-style liquidity pool; the tool returns impermanent loss IL = 2√k ÷ (1 + k) − 1 (loss vs HODL, in %) — the standard risk-quantification tool for DeFi liquidity providers and AMM yield farmers.

Coast FIRE Number Calculator

Enter target retirement age, target FIRE nest egg and expected real return; the tool uses PV = FV / (1 + r)^n to return your **Coast FIRE number** — how much you need to have saved today so that, with zero further contributions, compounding alone reaches the target by retirement.

Drawdown Recovery Gain Calculator (% gain needed to break even from a loss)

Enter your loss percentage (e.g. −25 %); the tool returns the gain required to break even — gain = L /(1 − L). A 25 % loss needs a 33 % gain to recover; a 50 % loss needs 100 %. The result is shown alongside a 10–90 % loss table so you can see how recovery requirements explode with deeper drawdowns.

Margin Call Price Calculator

Enter your purchase price, initial margin and maintenance margin, and the tool returns the stock price at which a broker margin call is triggered — P_call = P_buy × (1 − IM) / (1 − MM). Works for any long-equity margin account.

Solar Panel Payback Period Calculator

Enter the system cost (after rebates), daily kWh production, and your current electricity rate; the tool returns annual savings, simple payback years, 25-year lifetime savings and simple ROI — useful for residential and commercial solar PV investment decisions.

Investment Fee Drag Calculator (MER / TER Impact)

Enter your initial investment, gross annual return, fund expense ratio (MER / TER, % p.a.) and time horizon; the tool compares the with-fees and zero-fee final values, the total fees paid and the annualized return drag — quantifying why low-cost ETFs and index funds matter for long-horizon investors.

Cash Runway Calculator (Months Until Cash Runs Out)

Enter your cash balance, monthly burn rate and an optional monthly burn-growth rate; the tool returns runway in months and the projected zero-cash date — a staple metric for startups, sabbaticals and career-break planning.

Portfolio Rebalance Calculator

Enter the current values and target percentages of 2–4 assets; the tool returns the buy / sell amount needed to bring each back to its target allocation, with an optional *cash-injection (no-sell) mode* to avoid taxable disposals — useful for 60/40 stock-bond, three-fund and FIRE allocations.

Mortgage Amortization Schedule

Enter loan amount, annual rate and term to generate a full month-by-month split of principal vs. interest plus remaining balance, with annual subtotals.

Credit Card Minimum Payment Payoff Calculator

Enter your card balance, APR and minimum-payment rule (percent of balance or fixed floor) to see how many months / years it would take to clear and how much total interest you pay — the answer is usually alarming.

Reverse Discount Calculator (Original Price from Sale Price)

Seen "$560 after 30 % off" and need the original price? Enter the sale price and discount percentage to back-solve the original price, the amount saved and the share you actually paid — handy for online-shopping comparison, refunds and bookkeeping.

Real Hourly Wage Calculator

Inspired by Your Money or Your Life — subtract commute time, work meals, work clothes, child-care and other job-only costs from your gross pay to see your real take-home per hour of life spent. The result is often 30–50 % lower than your nominal hourly rate.

Savings Rate & Years to Financial Independence Calculator

Enter your monthly take-home pay and how much of it you save; read the savings rate percentage instantly. Using the standard 4% safe-withdrawal framework, the tool estimates how many years to financial independence (FI) if you keep spending at your current level.

Effective Tax Rate Calculator

Enter your gross income and the total tax you actually paid; read the effective tax rate as a percentage and compare it to your marginal bracket. Also shows net take-home, average tax per month and how many of your working days went to taxes.

Mortgage Recast Savings Calculator

Enter your current remaining principal, rate, remaining term and the lump-sum prepayment; using the original rate and remaining term, the tool re-amortises the loan and shows the new monthly payment and total interest savings.

Apartment Rent Affordability Calculator

Using the universal "30 % gross-income rule" and landlords' "40× annual rent" qualifier, enter your gross monthly income to see recommended max rent and the max rent a landlord will typically approve.

Marginal vs Effective Tax Rate Calculator

Enter taxable income and your jurisdiction's progressive tax brackets (up to 7 tiers); the tool returns total tax, marginal rate (top bracket touched) and effective rate (total tax ÷ income) — works for any country's progressive tax system.

Meeting Cost Calculator

Enter headcount, average hourly rate (or monthly salary equivalent) and meeting length; the tool returns how much the meeting actually costs and a per-minute burn-rate to help decide whether to extend by another 30 minutes.

Years to Financial Independence Calculator (FIRE)

Enter take-home income, savings rate, expected real return and safe withdrawal rate (SWR). Uses Mr. Money Mustache's "Shockingly Simple Math" formula to return years to financial independence (FI) and the target portfolio size.

Currency Cross-Rate Calculator

Enter two quotes against USD (or a shared base) — instantly returns the X/Y and Y/X cross rate, with optional bid/ask spread.

Down Payment Savings Timeline Calculator

Enter your down-payment goal, current savings, monthly contribution and savings APR to find the months, years and target date — along with the total you contributed and the interest earned.

Prorated Rent Calculator (Partial Month)

Enter monthly rent and the move-in or move-out date to compute partial-month rent owed, prorated by days occupied — useful when taking possession mid-month or leaving before month-end.

Loyalty Points / Airline Miles Cash Value Calculator

Enter your points / miles balance, the cents-per-point redemption rate and any redemption fee to see the net cash value and your effective conversion rate.

Vacation Daily Budget Allocator

Enter total trip budget, number of days, and the percentage split between lodging / food / transport / activities to get a daily cap and per-category daily amounts.

Charity Donation Tax Savings Calculator

Enter your donation amount and marginal tax rate to find the tax saved and the real net cost of giving.

Rule of 69 (Continuous Compounding Doubling Time) Calculator

Enter an annual rate to estimate the time it takes to double an investment under continuous compounding via 69 ÷ r, alongside the exact ln 2 ÷ r benchmark and a comparison to the Rule of 72.

Engagement Ring Budget Calculator (Common Rules)

Enter your annual (or monthly) salary and see ring budget ranges using the classic 1-, 2- and 3-month salary rules, plus a custom-percentage option.

Home Closing Cost Estimator (2–5 % of Sale Price)

Enter sale price, loan amount and a typical regional percentage to estimate total closing costs — lawyer, title insurance, appraisal, taxes, recording and miscellaneous.

Credit Card Processing Fee Calculator (% + Fixed)

Enter transaction amount, processing percentage (e.g. 2.9 %) and per-transaction fixed fee (e.g. $0.30) to get merchant fee and net receivable; gross-up mode also solves "to net X, what do I charge?"

Recipe Cost / Cost per Serving Calculator

List each recipe ingredient with its purchase amount, purchase price and amount used in the recipe — get each ingredient's actual cost, the total recipe cost and the cost per serving for menu pricing or household budgeting.

Net Profit Margin Calculator

Enter revenue and net income to instantly compute the net profit margin % — the core profitability ratio measuring how much net profit a business keeps from every dollar of sales.

Altman Z-Score Bankruptcy Predictor

Enter working capital, retained earnings, EBIT, market equity and sales (as % of total assets) — get the Altman 1968 Z-Score and the bankruptcy risk zone (safe / grey / distress).