Par Value

Par value performs two distinct jobs in a bond's cash flow schedule. First, it is the multiplicand for the coupon: the annual coupon amount equals the stated coupon rate times par value, and each periodic payment equals that annual amount divided by the number of coupon periods per year. A 4% semiannual bond with $1,000 par pays $20 twice a year, indefinitely fixed regardless of what the bond trades for. Second, par is the redemption amount delivered at maturity, so the final period combines the last coupon with repayment of principal.

Because both legs are anchored to par, the entire promised cash flow stream is set at issuance. Everything that varies afterwards, market price, yield to maturity, accrued interest, flows from discounting those fixed amounts at rates the market chooses, not from any change in the contractual amounts themselves.

Bond prices are quoted as a percentage of par, conventionally per 100 units, which makes issues with different denominations directly comparable. A quote of 96.50 on a $1,000 par bond means a price of $965; a quote of 104 means $1,040. Analysts describe a bond as trading at a discount, at par, or at a premium purely by reference to this 100 benchmark.

The relationship to yield is mechanical. When the coupon rate equals the market discount rate, the present value of the cash flows equals par and the bond prices at 100. When required yield rises above the coupon rate, the fixed coupons are inadequate compensation and the price falls below par; when required yield falls below the coupon rate, the bond prices above par. Over time, a discount bond's price pulls upward and a premium bond's price pulls downward toward par as maturity approaches, the effect known as the constant-yield price trajectory.

Par value shows up in indentures and term sheets as the denomination and redemption amount, in issuance statistics as par amount outstanding, and on the balance sheet as the face of debt issued, with any original issue discount or premium carried separately and amortized to interest expense over the bond's life. Call schedules are also expressed relative to par, for example redeemable at 101 of par after a stated date.

Several structures complicate the picture. Zero-coupon bonds pay no coupon and are issued well below par, delivering their entire return through accretion up to par at maturity. Amortizing bonds and sinking-fund issues repay principal in instalments, so the outstanding par declines through time. Inflation-linked bonds such as US TIPS index the principal to a price index, and coupons are computed on the adjusted amount. Note also that par value in equity contexts is a legal accounting artefact with no economic content, unrelated to a bond's redemption obligation.

At Level I you should move fluently between quoted price, par value and cash amounts. Given a coupon rate, par value and payment frequency, compute each coupon payment and the maturity cash flow. Given a quote such as 98.75 and a $100,000 par position, compute the flat price paid, then add accrued interest to arrive at the full or invoice price. Reverse the direction too: from a dollar price and par, express the quote per 100.

Equally important is the inference chain. If you are told only that a bond trades at a premium, you should immediately conclude that its coupon rate exceeds its yield to maturity, that its current yield lies between the coupon rate and the yield to maturity, and that its price will drift toward par as maturity nears if yields are unchanged. These deductions are frequent exam targets and require no computation.