Price of Bond Calculator With Ytm

Bond Price Formula:

\[ P = \sum_{t=1}^{n} \frac{C}{(1 + ytm / m)^t} + \frac{F}{(1 + ytm / m)^n} \]

Face Value (F):

currency units

Coupon Rate:

decimal

Yield to Maturity (ytm):

decimal

Years to Maturity:

years

Payments per Year (m):

Bond Price (P):

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1. What is the Bond Price Formula?

The bond price formula calculates the present value of all future cash flows from a bond, including coupon payments and the face value at maturity. It uses yield to maturity (YTM) as the discount rate to determine the fair price of a bond in the market.

2. How Does the Calculator Work?

The calculator uses the bond price formula:

\[ P = \sum_{t=1}^{n} \frac{C}{(1 + ytm / m)^t} + \frac{F}{(1 + ytm / m)^n} \]

Where:

\( P \) — Bond price (currency units)
\( C \) — Periodic coupon payment = (coupon rate × F) ÷ m (currency units)
\( ytm \) — Yield to maturity (decimal)
\( m \) — Payments per year (unitless)
\( t \) — Period number (unitless)
\( F \) — Face value (currency units)
\( n \) — Total number of periods = years × m (unitless)

Explanation: The formula discounts all future cash flows (coupon payments and face value) to their present value using the yield to maturity as the discount rate.

3. Importance of Bond Price Calculation

Details: Bond price calculation is essential for investors to determine fair value, make investment decisions, assess risk-return tradeoffs, and for issuers to price new bond offerings appropriately.

4. Using the Calculator

Tips: Enter face value in currency units, coupon rate and YTM as decimals (e.g., 0.05 for 5%), years to maturity, and select payment frequency. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between bond price and YTM?
A: Bond price and YTM have an inverse relationship. When YTM increases, bond price decreases, and vice versa.

Q2: What happens when coupon rate equals YTM?
A: When coupon rate equals YTM, the bond trades at par (price equals face value).

Q3: How does payment frequency affect bond price?
A: More frequent payments generally increase the bond price slightly due to earlier receipt of cash flows.

Q4: What is the difference between current yield and YTM?
A: Current yield is annual coupon divided by current price, while YTM considers all cash flows and time value of money.

Q5: Can this calculator be used for zero-coupon bonds?
A: Yes, set coupon rate to zero. The formula simplifies to only the present value of the face value.