Fixed Income Valuation & Yield Lab

Yield to Maturity (YTM) & Bond Pricing Calculator

Calculate exact Yield to Maturity (YTM), current yield, clean vs. dirty price, capital gains at maturity, and price-yield sensitivity curves in an interactive fixed income lab.

Bond Parameters Sensitivity Matrix Valuation Formulas FAQ

Preset Bond Scenarios

Load standard fixed income market benchmarks.

Interactive Bond Engine

Bond Terms & Market Price Inputs

📜 Security Specifications

💵 Quoted Market Price & Settlement

Pricing Status: Discount Bond
Total Dirty Price: $937.50
% of Par Value: 92.50%
Yield to Maturity (YTM)
6.05%
Annualized IRR (Semiannual Compounded)
Current Yield
5.41%
Annual Coupon / Quoted Clean Price
Total Cash Flows to Maturity
$1,500.00
Coupons ($500.00) + Principal ($1,000)
Capital Gain / (Loss) at Par
+$75.00
Par Value ($1,000) - Clean Price ($925)

Return Attribution Decomposition

Yield Components & Yield Curve Position

Nominal Coupon Rate 5.00% Fixed contractual annual rate on Par
Current Cash Flow Yield 5.41% Immediate annual coupon income yield
Annualized Capital Accretion +0.64% Price discount amortized over 10 yrs
Total Effective Annual YTM (EAY) 6.14% (1 + YTM/k)^k - 1 annual compounding
Periodic Payment per Cycle $25.00 20 Semiannual payments

Newton-Raphson Iteration Progress

Numerical Root-Finding Convergence

Bond pricing polynomials cannot be factored algebraically. The engine computes derivative slopes to reach exact convergence in milliseconds.

Iteration Trial Yield Implied PV Pricing Error

Fixed Income Sensitivity Analysis

Price Sensitivity Matrix Across Yields & Maturities

Dollar Bond Price per $1,000 Par

Demonstrates the non-linear convexity of bond pricing across varying market discount rates and remaining maturities.

Discount Rate (YTM) 3 Years 5 Years 10 Years (Current) 20 Years 30 Years

Core Concepts

Understanding Bond Yield Metrics

Investors must distinguish between the three primary yield measures when evaluating fixed-income instruments:

  • Coupon Rate: The stated annual interest rate on the bond's face value. Fixed at issuance.
  • Current Yield: Measures the annual cash return on current market price (Coupon / Price). It ignores price amortization and terminal par repayment.
  • Yield to Maturity (YTM): The total expected return reflecting periodic coupon interest, coupon reinvestment, and capital gain/loss at par redemption.
  • Effective Annual Yield (EAY): The true compound annual yield accounting for intra-year compounding cycles: EAY = (1 + y/k)^k - 1.

For interest rate risk sensitivity and duration, see the companion Bond Duration & Convexity Lab.

Mathematical Formulation

Bond Valuation & Newton-Raphson Equations

Price = ∑ [ C / ( 1 + y / k )^t ] + M / ( 1 + y / k )^(n × k)

Current_Yield = Annual_Coupon / Market_Price

Newton-Raphson Step: y_(i+1) = y_i - [ f(y_i) - Price ] / f'(y_i)

f'(y) = - ∑ [ (t/k) × C / (1 + y/k)^(t+1) ] - (n) × M / (1 + y/k)^(n×k+1)

Effective Annual Yield (EAY) = ( 1 + y / k )^k - 1

Model corporate equity cost of capital in the CAPM Lab.

FAQ

Yield to Maturity & Bond Pricing Questions

What is Yield to Maturity (YTM)?

Yield to Maturity (YTM) is the total annualized rate of return anticipated on a bond if it is held until maturity. It represents the internal rate of return (IRR) where the present value of all future coupon payments and the principal par repayment exactly equals the current market price of the bond.

How does Yield to Maturity differ from Current Yield and Coupon Rate?

The Coupon Rate is the fixed annual interest paid as a percentage of par. Current Yield equals annual coupon income divided by the current market purchase price. YTM is comprehensive: it accounts for coupon income, current purchase price, time value of money, reinvestment at the YTM rate, and capital gain or loss realized when the bond matures at par.

Why must YTM be solved using numerical iteration such as Newton-Raphson?

Because the bond pricing formula is a high-degree polynomial equation P = sum(C / (1+y)^t) + M / (1+y)^n, there is no closed-form algebraic formula to isolate y (yield). Financial algorithms use the Newton-Raphson method or secant root-finding to iteratively converge to the exact yield to within 0.0001% precision.

What is the difference between Clean Price and Dirty Price?

Clean Price is the agreed quoted market price of the bond excluding accrued interest. Dirty Price (or invoice price) is the total cash paid by the buyer to the seller: Dirty Price = Clean Price + Accrued Interest earned since the last coupon payment date.

When does a bond trade at a premium, discount, or par?

When YTM is greater than the coupon rate, the bond trades at a Discount (below par). When YTM is less than the coupon rate, the bond trades at a Premium (above par). When YTM equals the coupon rate, the bond trades exactly at Par.

Continue Exploring Corporate Finance & Valuation Tools

Explore our Cash Flow & Break-Even Hub, measure interest rate risk in the Bond Duration & Convexity Lab, evaluate capital structure in the Levered Beta & Hamada Lab, model DCF valuations in the FCFF vs. FCFE Valuation Lab, or check firm solvency in the Altman Z-Score Lab.