consider an annual coupon bond with 4% coupon rate, $1,000 face value and 15 year term. how much is this bond worth if its yield to maturity is 3%? round to the nearest dollar.
The value of a bond is determined by discounting its future cash flows (coupon payments and face value) to the present using the yield to maturity (YTM) as the discount rate. In this case, the bond has a 4% coupon rate, meaning it pays $40 ($1,000 x 4%) in coupon payments annually.
To calculate the value of the bond, we need to discount these coupon payments and the face value ($1,000) using the yield to maturity rate of 3%. The bond has 15 years remaining until maturity, so we’ll discount each cash flow for each year.
The formula to calculate the present value of a bond is:
PV = (C / (1 + r)^1) + (C / (1 + r)^2) + … + (C / (1 + r)^n) + (F / (1 + r)^n)
Where:
PV = Present Value
C = Coupon payment
r = Yield to maturity rate
n = Number of years
In this case, plugging in the numbers:
PV = (40 / (1 + 0.03)^1) + (40 / (1 + 0.03)^2) + … + (40 / (1 + 0.03)^15) + (1000 / (1 + 0.03)^15)
Calculating this sum, we find that the bond is worth approximately $1,140 when the yield to maturity is 3%.