C = the coupon payment, or the amount paid in interest to the bond holder each year. F = the face value, or the full value of the bond. P = the price the investor paid for the bond. n = the number of years to maturity.
Use the formula: ($100+(($1,000−$920)/10))/($1,000+$920)/2{\displaystyle ($100+(($1,000-$920)/10))/($1,000+$920)/2} Using this calculation, you arrive at an approximate yield to maturity of 11. 25 percent.
Use the formula P=C∗((1−(1/(1+i)n))/i)+M/((1+i)n){\displaystyle P=C*((1-(1/(1+i)^{n}))/i)+M/((1+i)^{n})}, where, P = the bond price, C = the coupon payment, i = the yield to maturity rate, M = the face value and n = the total number of coupon payments. If you plug the 11. 25 percent YTM into the formula to solve for P, the price, you get a price of $927. 15. A lower yield to maturity will result in a higher bond price. The bond price you get when you plug the 11. 25 percent interest figure back into the formula is too high, indicating that this YTM estimate may be somewhat low.
For example, suppose your purchased a $100 bond for $95. 92 that pays a 5 percent interest rate every six months for 30 months. Every six months you will receive a coupon payment of $2. 50 ($100∗. 05∗. 5=$2. 50{\displaystyle $100*. 05*. 5=$2. 50}). If there are 30 months until maturity, and you receive a payment every six months, that means you will receive 5 coupon payments. Plug the information into the formula 95. 92=2. 5∗((1−(1/(1+i)5))/i)+100/((1+i)5){\displaystyle 95. 92=2. 5*((1-(1/(1+i)^{5}))/i)+100/((1+i)^{5})}. Now, you have to solve for i using trial and error, plugging in different values for i until you get the correct price.
Remember, though, you’re plugging in an estimated i for semi-annual payments. That means you’ll effectively want to divide the annual interest rate by 2. In the above example, begin by taking the annual interest rate up by one point to 6 percent. Plug half of that (3 percent, because payments are semi-annual) it into the formula, and you get a P of $95. This is too high, since the purchase price is $95. 92. Talk the annual interest rate up by one more point to 7 percent (or 3. 5 percent on a semi-annual basis). Plug it into the formula, and you get a P of $95. This is too low, but you now know that the precise yield to maturity is somewhere between 6 and 7 percent or between 3 and 3. 5 percent on a semi-annual basis.
For example, when you plug in 6. 9 percent (3. 45 percent semi-annual), you get a P of 95. 70. You’re getting close, but it’s not exactly correct yet. Decrease it by one tenth of a point to 6. 8 percent (3. 4 percent semi-annual), plug that into the formula and you get $95. 92. Now you have arrived at the exact price you paid for the bond, so you know that your precise yield to maturity is 6. 8 percent.
Yield to call (YTC) calculates the yield rate between the present and the call date of a bond. [10] X Research source Yield to put (YTP) calculates the yield rate until the issuer puts the bond. [11] X Research source
