It 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?

To calculate the yield to maturity (YTM) on a bond, we need to follow these steps:

Step 1: Determine the annual coupon payment In this case, the bond has a 10% annual coupon rate and a par value of 100. Therefore, the annual coupon payment is calculated as 10% of 100, which is 10.

Step 2: Determine the number of coupon payments Since the bond has a 3-year maturity, there will be three coupon payments.

Step 3: Determine the present value of the bond's future cash flows To calculate the present value of the bond's future cash flows, we need to discount each coupon payment and the final principal payment back to the present value.

Using a financial calculator or spreadsheet software, we can calculate the present value of the bond's future cash flows as follows:

PV = (C / (1 + r)^1) + (C / (1 + r)^2) + (C / (1 + r)^3) + (F / (1 + r)^3)

Where: PV = Present value of the bond's future cash flows C = Coupon payment r = Yield to maturity (YTM) F = Par value of the bond

In this case, C = 10, F = 100, and the current price of the bond is 107.87. We need to solve for r.

Step 4: Solve for YTM Using the present value formula, we can substitute the known values and solve for YTM:

107.87 = (10 / (1 + r)^1) + (10 / (1 + r)^2) + (10 / (1 + r)^3) + (100 / (1 + r)^3)

To solve this equation, we can use trial and error, or we can use financial calculators or spreadsheet software to find the YTM. In this case, the YTM is approximately 6.5%.

Therefore, the yield to maturity on the 3-year bond with 10% annual coupons, a par value of 100, and a current price of 107.87 is approximately 6.5%.