Yield to Maturity

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Thomas Shyr

Yield to Maturity (YTM) refers to the expected rate of return a bondholder will receive if they hold a bond all the way until maturity while reinvesting all coupon payments at the bond yield. It should not be confused with holding period return, as the two often differ. Yield to maturity is generally given in terms of Annual Percentage Rate (APR), and it is an estimation of future return, as the rate at which coupon payments can be reinvested at is unknown. However, for zero coupon bonds, the yield to maturity and the rate of return are equivalent since there are no coupon payments to reinvest.

Another way of putting it is that the yield to maturity is the rate of return that makes the present value (PV) of the cash flow generated by the bond equal to the price. Yield to maturity is widely used by investors as a way to compare bonds with different face values, coupon payments, and time till maturity.

Yield to Maturity Terminology

• Face Value, also known as the "par value", is the amount a bond holder will be paid when it matures. For example, a zero coupon bond with a $1000 face value and one year to maturity means that in exactly one year, the bond holder is entitled to $1000 from the issuer.
• Coupon rate is the interest paid on a bond, expressed as a percentage of the face value of the bond. Coupon payments take the form of an annuity. Most government issued bonds such as U.S. Treasury Bonds pay coupons semi-annually. If a bond does not ever pay any coupons between the issue date and maturity, it is called a zero coupon bond. A short example helps explain how coupons work. Suppose you buy a 2 year bond, face value $100 with a coupon rate of 5% paid semi-annually. Every six months you will receive a coupon payment of $5.00 (5% of $100) for a total of 4 payments. After 2 years, you receive $5.00 as the final coupon, as well as the $100 face value of the bond.
• Present Value (PV) is today's value of a set of cash

flows set to occur in the future. Theoretically, the price you pay for a bond should equal its present value, since you are giving up money today to be repaid at a later date.

• Discount Rate is a component used in calculating present value, and is also related to calculating yield to maturity. The yield to maturity is exactly the discount rate that makes the present value of all future cash flows equal to the price of the bond today. In other words, the price of the bond is equal to all future cash flows discounted by the yield to maturity.

Calculating yield to maturity

This is the general formula for calculating yield to maturity for a coupon paying bond. The variable 'n' denotes the number of periods, i.e. 4 year bond paying semi-annual bonds would have 9 periods. Solving for a YTM that satisfies this equation may be difficult without a computer program or an advanced calculator.

[[Image:YTMAnnuity.jpg‎|650px|right|thumb|Using an annuity formula, the calculation becomes much simpler. Ag to maturity can be prohibitively difficult and time consuming without either a computer program or advanced calculator.

Fortunately, most bonds pay coupons on a fixed schedule (generally quarterly, semi-annually, or annually). As a result, its coupon payments take the form of an annuity, whose present value is easier to calculate. In practice, bonds paying coupons will pay them according to a fixed schedule, allowing investors to estimate yield to maturity using an annuity table.

Calculating YTM when FV, PV, CR and the number of period (n) are given;

CP=FV*CR

YTM=(CP+(FV-PV)/n)/(FV+2PV)/3