What Is Yield to Maturity (YTM)?

Yield to maturity (YTM) is the 澳洲幸运5官方开奖结果体彩网:internal rate of return (IRR) that equa♏tes all future cash flows of a bond to its current price. YTM assumes the bond is held until maturity and that an i༺nvestor can reinvest at the same yield.

YTM Formula

A bond's YTM can be calculated using the formula:

YTM = [ C+ (FV - PV) ÷ t ] ÷ [ (FV + PV) ÷ 2 ]

Where:

• C = Coupon Payment
• FV = Face Value
• PV = Present Value/Current Price
• t = Years to Maturity
  

YTM vs. Coupon Rate

Unlike stock investments, bond issuers promise to pay the holder the full face value once it matures. Bonds come with two metrics: YTM and coupon rate. YTM is the total return expected on a bond if it's held until maturity.

The coupon rate is the total amount the bond pays in income to the bondholder for as long as they hold it. The coupon rate is the interest paid annually on the bond's face value. A bond's YTM fluctuates over time while the coupon rate remains fixed.

Calculating YTM

To calculate YTM on a bond priced below par, investors plug in various annual interest rates higher than the coupon rate to find a bond price close to the researched bond price. Calculations of yield to maturity assume that all coupon payments are reinvested at the same rate as the bond's current yield and account for the bond's current market price, par value, coupon interest rate, and term to maturity.

The YTM is a snapshot of the return on a bond because coupon payments cannot always be reinvested at the same interest rate. As interest rates rise, the YTM will increase; as interest rates fall, the YTM will decrease. Investors can approximate YTM by hand or by using a bond yield table, financial calculator, or online 🐽YTM calculator.

The annual rate of a bond m🦹ust be calculated via trial and error. Imagine an investor holds a bond whose par value is $100. The bond:

• It is priced at a discount of $95.92
• Matures in 30 months (2.5 years)
• Pays a semi-annual coupon of 5%

The current yield is calculated using thꦆe formula:

Annual Cash Flow ÷ Market price

Therefore, the current yield is (5% coupon x $100 par value) / $95.92 market price = 5.21%. This is the value to which investors compare the next calculations.

To calculate YTM, the cash flows must be determined first. Every six months (semi-annually), the bondholder receives a coupon payment of ( 5% x $100 ) / 2 = $2.50. Next, we incorporate this data into the formula (30 months = 2.5 years):

YTM = [ C+ (FV - PV) ÷ t ] ÷ [ (FV + PV) ÷ 2 ]

• YTM = [ $2.50 + ($100 - $95.92) ÷ 2.5 ] ÷ [ ($100 + $95.92) ÷ 2 ]
• YTM = [ $2.50 + $4.08 ÷ 2.5] ÷ [$195.92 ÷ 2 ]
• YTM = [ $2.50 + $1.632 ] ÷ [ $97.96 ]
• YTM = [$4.132 ] ÷ [ $97.96 ]
• YTM = .0422, or 4.22%
  

This bond's YTM is less than its coupon rate, so the next step is to estimate rates to learn what its YTM is. Here, we'll use 6%, so the coupon payment would be ( 6% x $100 ) / 2 = $3.00.

• YTM = [ $3.00 + ($100 - $95.92) ÷ 2.5 ] ÷ [ ($100 + $95.92) ÷ 2 ]
• YTM = [ $3.00 + $4.08 ÷ 2.5] ÷ [$195.92 ÷ 2 ]
• YTM = [ $3.00 + $1.632 ] ÷ [ $97.96 ]
• YTM = [ $4.632] ÷ [$97.96]
• YTM = .0473. or 4.73%

Next, we'll try 7%, with a YTM of ( 7% x $100 ) / 2 = $3.50

• YTM = [ $3.50 + ($100 - $95.92) ÷ 2.5 ] ÷ [ ($100 + $95.92) ÷ 2 ]
• YTM = [ $3.50 + $4.08 ÷ 2.5] ÷ [$195.92 ÷ 2 ]
• YTM = [ $3.50 + $1.632 ] ÷ [ $97.96 ]
• YTM = [ $5.132] ÷ [$97.96]
• YTM = 0.0524, or 5.24%

Because 7% has a YTM of more than the 澳洲幸运5官方开奖结果体彩网:current yield and 6% results in🎀 less than the current yield of 5.21%, we know the rate is between 6% and 7%. This is how investors calculate and test several bond prices by plugging various annual interest rates that are higher than the bond's coupon rate:

Taking the interest rate up by one and two percentage points to 6% and 7% yields bond prices of $98 and $95, res✃pectively. Because the bond price in the example is $95.92, the chart indicates that the interest rate is between 6% and 7%.

Having determined the range of rates, investors can take a closer look and make another table showing the prices where YTM calculations produce a series of interest rates incr💮easing in increments of 0.1% instead of 1.0%. Using interest rates with smaller increments, calculated bond prices are as follows:

The present value of this bond is equal to $95.92 when the YTM is at 6.8%. Fortunately, 6.8% corresponds precisely to the bond price, so no further calculations are required. If the investor found that using a YTM of 6.8% in their calculations did not yield the exact bond price, they♕ would continue trials and test interest rates increasing in 0.01% increment꧑s.

Variations of YTM

Yield to maturity ไhas varꦿiations that account for bonds with embedded options:

• Yield to Call (YTC): Assumes the bond will be called and repurchased by the issuer before it reaches maturity and thus has a shorter cash flow period. 澳洲幸运5官方开奖结果体彩网:Yield to Call is calculated, assuming the bond will be called as soon as possible and financially feasible.
• Yield to Put (YTP): Similar to YTC; However, the holder of a put bond can sell the bond back to the issuer at a fixed price based on the terms of the bond. YTP is calculated based on the assumption that the bond will be returned to the issuer as soon as possible and financially feasible.
• Yield to Worst (YTW): A calculation used when a bond has multiple options. If an investor evaluates a bond with both call and put provisions, they would calculate the 澳洲幸运5官方开奖结果体彩网:Yield to Worst based on the option terms that give the lowest yield.
  

Explain Like I'm 5

A bond's maturity date is the date the issuer is required to pay back the bondholder. Yield to maturity is the estimated total return you get from a bond if you hold it until it matures.

Yield to matuꦑrity is calculated usܫing different interest rates to find a bond that offers the best estimated total return at current prices.

The Bottom Line

A bond's yield to maturity is the internal rate of return required for the present value of all future cash flows, including face value and coupon payments, to equal the current bond price. YTM assumes that all coupon payments are reinvested at a yield equal to the YTM and that the bond is held to maturity.