Yield to Maturity (YTM) Calculator
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Yield to Maturity (YTM) is the total internal rate of return (IRR) anticipated on a bond if held until its scheduled maturity date. YTM expresses overall bond performance in annual percentage terms, integrating periodic coupon interest payments, secondary market purchase price discounts or premiums, and the time value of money.
Our free Yield to Maturity Calculator computes exact and approximate YTM for both annual and semi-annual coupon bonds.
How to Calculate Yield to Maturity (YTM)
The exact YTM is the discount rate r that sets the present value of all future cash flows equal to the bond’s current market price:
Exact Present Value Formula:
Market Price = Σ [ C / (1 + YTM)^t ] + [ Face Value / (1 + YTM)^n ]
Approximate YTM Formula:
Because solving exact YTM requires iterative trial-and-error, analysts use the standard approximation formula:
Approximate YTM = [ C + ( ( F - P ) / n ) ] / [ ( F + P ) / 2 ]
Sub-Formula Components:
- C (Annual Coupon Payment): Annual coupon interest paid (Coupon Rate × Face Value).
- F (Face / Par Value): Principal value repaid at maturity (typically $1,000).
- P (Current Price): Current secondary market purchasing price of the bond.
- n (Years to Maturity): Remaining years until bond redemption.
Bond Price & YTM Relationships
A bond’s yield to maturity directly dictates whether it trades at a discount, par, or premium relative to face value:
| Bond Trading Status | Market Price vs Par Value | YTM vs Coupon Rate |
|---|---|---|
| Discount Bond | Price < Par Value (e.g., $950) | YTM > Coupon Rate |
| Par Bond | Price = Par Value ($1,000) | YTM = Coupon Rate |
| Premium Bond | Price > Par Value (e.g., $1,080) | YTM < Coupon Rate |
Step-by-Step Calculation Example
An investor purchases a corporate bond with the following metrics:
- Face Value (F): $1,000
- Current Purchase Price (P): $950
- Annual Coupon Rate: 6.0% (Coupon C = $60/year)
- Years to Maturity (n): 5 years
Step 1: Calculate Annual Price Gain Component
( F - P ) / n = ( $1,000 - $950 ) / 5 = $10 per year
Step 2: Calculate Average Price Base
( F + P ) / 2 = ( $1,000 + $950 ) / 2 = $975
Step 3: Compute Approximate YTM
Approximate YTM = ( $60 + $10 ) / $975 = $70 / $975 = 7.18%
Frequently Asked Questions (FAQ)
What underlying assumptions does YTM make?
YTM assumes that the bond is held until its final maturity date and that all interim coupon cash flows are reinvested immediately at a interest rate equal to the YTM itself.
What is the difference between Current Yield and YTM?
Current Yield only measures annual coupon income divided by market price (C / P). Yield to Maturity incorporates coupon payments, principal gain/loss from discount or premium price convergence, and compounding over time.
How does semi-annual coupon compounding affect YTM?
Most US Treasury and corporate bonds pay coupons semi-annually. To calculate semi-annual YTM, divide the annual coupon by 2, double the periods (2n), solve for the periodic rate, and multiply by 2 to state the Bond Equivalent Yield (BEY).