The price of a bond is the present value of an annuity (the interest payments) plus the present value of a single sum (maturity value) or face amount Select one True False
The correct answer and explanation is:
Correct Answer: True
The price of a bond is indeed calculated as the present value of two separate cash flows: the annuity represented by periodic interest payments, and the single sum which is the face value (or maturity value) of the bond to be paid at maturity.
When an investor purchases a bond, they are essentially lending money to the bond issuer. In return, the issuer promises to make periodic interest payments—commonly known as coupon payments—until the bond matures. These payments usually occur annually or semi-annually and remain the same throughout the bond’s life. Because these coupon payments are consistent and fixed, they form an annuity.
At the end of the bond’s term, the issuer repays the face value, also called the par value or maturity value, of the bond. This repayment is a single lump sum. To determine the bond’s price, this future payment must be discounted to its present value.
To find the bond’s current value, or price, both the stream of coupon payments and the single payment of face value must be discounted using the market interest rate, also referred to as the yield to maturity. This discounting process accounts for the time value of money, which states that a dollar received in the future is worth less than a dollar received today.
Therefore, the bond price formula is:
Bond Price = Present Value of Interest Payments (Annuity) + Present Value of Face Value (Single Sum)
This method allows investors to evaluate whether a bond is priced fairly compared to its risk and return. If the market interest rate is higher than the bond’s coupon rate, the bond will sell at a discount. If it is lower, the bond will sell at a premium. This pricing principle is central to bond valuation in financial markets.