Bond pricingIt is important to be able to work out the YTM from the price of a bond.What is the yield to maturity on a 3-year bond with 10% annual coupons, a par value of 100, and a current price of 107.87?8.00%10.00%7.00%9.00%
Question
Bond pricingIt is important to be able to work out the YTM from the price of a bond.What is the yield to maturity on a 3-year bond with 10% annual coupons, a par value of 100, and a current price of 107.87?8.00%10.00%7.00%9.00%
Solution
The yield to maturity (YTM) of a bond can be calculated using the formula:
YTM = [C + (F - P)/n] / [(F + P)/2]
Where: C = annual coupon payment (in dollars, not a percent) F = face value of the bond P = purchase price of the bond n = years until maturity
Given: C = 10% of the face value = 10% of 100 = 10 F = 100 P = 107.87 n = 3
Substituting these values into the formula:
YTM = [10 + (100 - 107.87)/3] / [(100 + 107.87)/2]
Solving the equation will give you the YTM as a decimal. Multiply by 100 to get the percentage.
Please note that this formula assumes that the bond is held until maturity and that all payments are reinvested at the same rate as the bond's current yield. In reality, these assumptions may not hold and the actual yield may be different.
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