Valuation of Bonds

A bond is a written contract between a borrower (the issuer) and a lender (the bondholder). Through it the issuer promises to repay a fixed sum on a stated future date and, until that date, to pay interest at an agreed rate at equal time intervals. Paying the bond back at the end is called redemption.

A bond carries a few standard terms. Its face value (also called par value) is the amount marked on the bond — the price at which it is issued to investors and, normally, the amount returned at maturity. The redemption price is what the issuer actually pays on the maturity date; when the bond is redeemed at par this equals the face value. If the bond trades in the market below its face value it is said to sell at a discount; if it trades above face value it sells at a premium.

Bond valuation means working out the fair price of a bond. Like any investment, a bond's theoretical fair value is the present value of the stream of cash flows it is expected to produce, so we discount those future flows back to today using a suitable discount rate.

The nominal rate of interest, better known as the coupon rate, is the rate at which the bond pays interest. It is the coupon payment $C$ expressed as a fraction of the face value $F$:

The current yield measures the coupon against the current market price $P_0$ rather than the face value:

The yield to maturity (YTM) is the single discount rate that makes the bond's price equal to the present value of all its cash flows — in effect the internal rate of return you earn if you buy the bond at price $P_0$, hold it to maturity, and redeem it at par. Because YTM can be used to price a bond, prices are often quoted as a YTM.

These three measures are linked in a fixed order that depends on how the bond is priced:

Present value approach (bonds with a maturity period). When a bond has a maturity date, its value is the present value of every periodic interest payment plus the present value of its redemption amount. Comparing this present value with the market price tells us whether the bond is overvalued or undervalued. …