Suppose you have a $1,000 face value bond with 12 years to maturity, a coupon rate of 6% and a yield to maturity of 8%. If the bond makes semiannual payments, what is it's price today?
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To calculate the price of a bond, you can use the present value formula. The present value of a bond is the sum of the present values of its future cash flows, which are the coupon payments and the face value payment at maturity.
In this case, the bond has a face value of $1,000, a coupon rate of 6%, and a yield to maturity of 8%. Since the bond makes semiannual payments, it will have 24 (12 years * 2) coupon payments.
To calculate the present value of each coupon payment, you need to use the formula:
Present Value = Coupon Payment / (1 + Yield to Maturity / 2) ^ (number of periods)
In this case, the coupon payment is 6% of the face value, so it will be $1,000 * 6% / 2 = $30.
Let's calculate the present value of each coupon payment:
PV_coupon = $30 / (1 + 8% / 2) ^ (1)
= $30 / (1 + 4%)
= $30 / 1.04
= $28.85 (rounded)
Now, let's calculate the present value of the face value payment at maturity:
PV_face_value = $1,000 / (1 + 8% / 2) ^ (12 * 2)
= $1,000 / (1 + 4%) ^ 24
= $1,000 / (1.04) ^ 24
= $1,000 / 1.8384
= $543.49 (approx.)
Finally, to calculate the price of the bond today, you need to sum the present values of the coupon payments and the face value payment at maturity:
Price = PV_coupon * number of coupon payments + PV_face value
= $28.85 * 24 + $543.49
= $692.40 + $543.49
= $1,235.89
Therefore, the price of the bond today is approximately $1,235.89.