Yield to Maturity Calculator

Calculate the total return anticipated on a bond if held until maturity

Bond Details

Face Value ($)

Current Price ($)

Coupon Rate (%)

Years to Maturity

Coupon Payments Annually Semi-Annually Quarterly Monthly

Yield to Maturity Results

Yield to Maturity

-

%

Annualized total return

Total Coupon Payments

-

$

Interest payments over bond life

Total Profit

-

$

Coupons + capital gain/loss

Bond Cash Flows

Chart will appear after calculation

Cash Flow Schedule

Period	Date	Coupon Payment	Principal	Total Payment

Bond Analysis

Price vs. Value

Price analysis will appear here...

Market Comparison

Market comparison will appear here...

This calculator provides estimates only. Bond prices fluctuate with market conditions. Print Results

1. What is Yield to Maturity (YTM)?

Yield to Maturity (YTM) is the total expected return on a bond if held until maturity, accounting for:
✔ Current market price
✔ Face value (par value)
✔ Coupon payments
✔ Time remaining until maturity

YTM is expressed as an annualized percentage rate and helps investors compare bonds with different maturities and coupon rates.

---

2. Key Components of a YTM Calculator

A YTM calculator requires the following inputs:

Input	Description	Example
Bond Price (P)	Current market price of the bond (may be at a discount or premium).	$950 (discount bond)
Face Value (FV)	The bond's redemption value at maturity (usually $1,000).	$1,000
Coupon Rate (C)	Annual interest payment as a percentage of face value.	5% ($50/year)
Coupon Frequency	How often interest is paid (annual, semi-annual, quarterly).	Semi-annual
Years to Maturity (t)	Time remaining until bond maturity.	5 years

---

3. How to Calculate YTM (Formula & Example)

Since YTM involves solving for the interest rate in the present value of cash flows, it is typically calculated using trial-and-error or financial calculators (no closed-form formula exists).

Approximate YTM Formula (Estimation)

$$\text{YTM}\approx \frac{C+\frac{(FV-P)}{t}}{\frac{(FV+P)}{2}}$$

Where:

• $C$ = Annual coupon payment

• $FV$ = Face value

• $P$ = Current bond price

• $t$ = Years to maturity

Example:

• Bond Price ($P$) = $950

• Face Value ($FV$) = $1,000

• Coupon Rate = 5% → Annual Coupon ($C$) = $50

• Years to Maturity ($t$) = 5

$$\text{YTM}\approx \frac{50+\frac{(1000-950)}{5}}{\frac{(1000+950)}{2}}=\frac{50+10}{975}\approx \ast \ast 6.15$$

(Note: This is an approximation. The exact YTM requires iterative methods.)

Exact YTM Calculation (Using Bond Cash Flows)

The precise YTM is the discount rate that equates the bond's present value (PV) of future cash flows to its current price.

$$P=\sum _{k=1}^n\frac{C}{(1+YTM{)}^k}+\frac{FV}{(1+YTM{)}^n}$$

Where:

• $n$ = Total number of periods

• $C$ = Coupon payment per period

Solved using:

• Financial calculators (TI BA II+, HP 12C)

• Excel’s =YIELD() or =IRR() function

• Trial-and-error method

---

4. How to Use a YTM Calculator (Step-by-Step)

1. Enter Bond Details:

   • Current market price ($950)

   • Face value ($1,000)

   • Annual coupon rate (5%)

   • Coupon frequency (semi-annual → $25 every 6 months)

   • Years to maturity (5)

2. Click "Calculate YTM" → Output: 6.38% (exact YTM, semi-annual compounding)

3. Interpretation:

   • If YTM > Coupon Rate → Bond is selling at a discount (good deal).

   • If YTM < Coupon Rate → Bond is selling at a premium (lower yield).

---

5. YTM vs. Current Yield vs. Coupon Rate

Metric	Formula	Purpose
Coupon Rate	Fixed % of face value	Shows bond’s stated interest.
Current Yield	$\frac{\text{Annual Coupon}}{\text{Current Price}}$	Measures income return only.
Yield to Maturity (YTM)	Internal Rate of Return (IRR)	Total return if held to maturity.

Example Comparison:

• Bond Price: $950

• Face Value: $1,000

• Coupon Rate: 5% ($50/year)

• Current Yield: $\frac{50}{950}\approx \ast \ast 5.26$

• YTM: ≈6.38% (higher because it includes capital gain at maturity).

---

6. Factors Affecting YTM

📈 Interest Rates: If market rates rise, YTM increases (bond prices fall).
📉 Credit Risk: Higher default risk → Higher YTM (compensates investors).
⏳ Time to Maturity: Longer maturity → Higher sensitivity to rate changes.
💵 Bond Price: Discount bonds have higher YTM than premium bonds.

---

7. Limitations of YTM

⚠ Assumes Reinvestment at YTM: Coupons must be reinvested at the same rate (rare in reality).
⚠ Ignores Default Risk: YTM assumes no bond issuer default.
⚠ Callable Bonds: YTM may not apply if the bond is called early.

---

8. Practical Applications of YTM

✅ Bond Valuation: Helps determine if a bond is overpriced or underpriced.
✅ Portfolio Management: Compares bonds with different maturities & coupons.
✅ Investment Strategy: Identifies high-yield bonds for better returns.

---

9. Free YTM Calculators & Tools

🔹 Investopedia YTM Calculator
🔹 SEC’s Official YTM Calculator
🔹 Excel Formula: =YIELD(settlement, maturity, rate, pr, redemption, frequency)