Why the Three Amounts Must Be Kept Separate
A callable bond can have several different dollar amounts associated with it. Par value is the reference amount used to state the bond’s face value and, usually, calculate its coupons. Scheduled maturity redemption is the amount the issuer is contractually to pay if the bond remains outstanding to maturity. A call price is the amount specified for redemption on an eligible call date. These amounts can be equal, but they need not be.
The distinction matters whenever a bond is redeemed. The redemption cash flow uses the amount specified for that redemption scenario, not automatically par value or the maturity amount. If a coupon is also due on the redemption date, the investor receives that coupon in addition to the redemption amount, unless the contract specifies otherwise. This tutorial assumes the call dates in its examples coincide with coupon dates, so there is no separate accrued-coupon calculation.
A call price may be quoted as a dollar amount or as a percentage of par. If the call price is \(q\%\) of par, then \(K_t=(q/100)F\). The premium is measured against par: \(K_t-F\). It is not calculated by comparing the call price with the investor’s purchase price, and a quoted call price already includes any premium it specifies.
How Redemption Terms Enter the Cash Flow
For a bond with par value \(F\), annual coupon rate \(r\), and \(m\) coupon payments per year, the coupon per payment period is \(C=rF/m\), assuming a level coupon rate and equal payment periods. When a coupon and redemption fall due together, the cash flow on that date is the coupon plus the applicable redemption amount:
This addition follows from the contract’s separate obligations: the coupon pays interest for the coupon period, while the redemption amount repays the bond under the chosen redemption scenario. The premium is already part of \(K_t\) or \(R\); it is not a third cash-flow item to add again.
Record the par value and the coupon rate and frequency. Calculate the coupon due on the relevant date.
For a call, use the call price for that date. For scheduled maturity, use the stated maturity redemption amount.
Multiply the quoted percentage by par to obtain the dollar redemption amount.
Subtract par from the applicable redemption amount, then add the coupon if one is due.
Worked Examples
Worked Example: Semiannual Coupon and a Call Premium
A hypothetical bond has par value \(F=\$1{,}000\), pays coupons semiannually at an annual coupon rate of \(6\%\), and matures in five years. If it remains outstanding to maturity, it redeems for \(105\%\) of par. It may instead be called after three years for \(102\%\) of par. The call date is a coupon date. Find the coupon per period, both redemption premiums, and the total cash flow on each possible redemption date. Method: calculate coupon and redemption terms separately, then combine only the amounts due in each scenario. This avoids confusing the call price with an extra call premium.
Coupon per half-year. There are \(m=2\) coupon payments per year, so \(C=0.06(\$1{,}000)/2=\$30\).
Call scenario. The call redemption amount is \(K_t=1.02(\$1{,}000)=\$1{,}020\). The call premium is \(\$1{,}020-\$1{,}000=\$20\). Because the call date is a coupon date, the cash flow on that date is \(\$1{,}020+\$30=\$1{,}050\).
Scheduled maturity scenario. The maturity redemption amount is \(R=1.05(\$1{,}000)=\$1{,}050\). The maturity redemption premium is \(\$1{,}050-\$1{,}000=\$50\). The final coupon is also \(\$30\), so the maturity-date cash flow is \(\$1{,}050+\$30=\$1{,}080\).
Check. The call-date redemption is \(\$20\) above par, while maturity redemption is \(\$50\) above par. In each scenario, adding one \(\$30\) coupon gives the stated total cash flow. The call premium is not added a second time.
Worked Example: Aggregate Call Cash Flow for Multiple Bonds
A hypothetical investor holds 120 identical bonds, each with par value \(\$1{,}000\). Each bond pays a \(5.4\%\) annual coupon rate in two equal payments per year. On a specified coupon date, the issuer may call the bonds for \(100.75\%\) of par. Calculate the call redemption amount, the call premium, the coupon due, and the aggregate cash flow if all 120 bonds are called that day. Method: calculate amounts per bond first, then multiply by the number of bonds. This avoids applying a per-bond coupon to the aggregate par value and then multiplying again.
Coupon per bond. The semiannual coupon is \(0.054(\$1{,}000)/2=\$27\).
Call redemption amount per bond. The quoted percentage gives \(K_t=1.0075(\$1{,}000)=\$1{,}007.50\). The call premium per bond is \(\$1{,}007.50-\$1{,}000=\$7.50\).
Call redemption amount for 120 bonds. \(120(\$1{,}007.50)=\$120{,}900\). The aggregate call premium is \(120(\$7.50)=\$900\).
Coupon due for 120 bonds. \(120(\$27)=\$3{,}240\). Therefore, the aggregate cash flow on the call date is \(\$120{,}900+\$3{,}240=\$124{,}140\).
Check. Aggregate par is \(120(\$1{,}000)=\$120{,}000\). Adding the \(\$900\) call premium gives the \(\$120{,}900\) redemption amount; adding the separate \(\$3{,}240\) coupon gives \(\$124{,}140\).
Worked Example: Zero-Coupon Bond with a Maturity Premium
A hypothetical zero-coupon bond has par value \(\$5{,}000\). Its scheduled maturity redemption amount is \(112\%\) of par. It is also callable at the end of year 4 for \(\$5{,}250\); scheduled maturity is at the end of year 7. There are no periodic coupons. Find the maturity premium, the year-4 call premium, and the cash flow under each redemption scenario. Method: use the stated redemption amount for each scenario and compare it with par. This avoids assuming that a zero-coupon bond must redeem at par.
Scheduled maturity. The maturity redemption amount is \(R=1.12(\$5{,}000)=\$5{,}600\). The maturity premium is \(\$5{,}600-\$5{,}000=\$600\). With no coupon, the maturity-date cash flow is \(\$5{,}600\).
Year-4 call. The call price is already stated in dollars: \(K_4=\$5{,}250\). Its premium is \(\$5{,}250-\$5{,}000=\$250\). With no coupon due, the year-4 call-date cash flow is \(\$5{,}250\).
Check. The two redemption cash flows differ because their contract terms differ: \(\$5{,}250\) on a year-4 call versus \(\$5{,}600\) at scheduled maturity. There is no coupon to add in either case, and the premiums of \(\$250\) and \(\$600\) are already included in those amounts.
Interpreting Redemption Premiums Correctly
A redemption premium describes how far a redemption amount is above par; it does not describe the bond’s market price or the investor’s gain. For example, a call price of \(102\%\) of par means the issuer pays \(102\%\) of par for redemption, whether an investor originally purchased the bond above or below par. Purchase price is a separate amount.
The maturity amount and call price are also scenario-specific. A bond might mature at a premium but be callable earlier at a smaller premium, as in the first worked example. If a bond is called, use the call price applicable to that call date. Do not substitute its scheduled maturity redemption amount merely because that amount is stated elsewhere in the terms.
| Term | What it measures | How it enters a redemption-date cash flow |
|---|---|---|
| Par value | Reference face amount; commonly used to calculate coupons | Used to convert percentage quotes and measure premiums, but not automatically the redemption amount |
| Scheduled maturity redemption | Amount due if the bond remains outstanding to maturity | Added to any coupon due at maturity |
| Call price | Amount due if redeemed on a specified eligible call date | Added to any coupon due on that call date |
| Redemption premium | Applicable redemption amount minus par | Already included in the redemption amount; do not add it again |
Common Exam Trap
Suppose par is \(\$1{,}000\), the call price is \(103\%\) of par, and a coupon of \(\$25\) is due on the call date. The incorrect calculation is to treat the \(3\%\) call premium as a separate payment after the call price:
Here, \(\$30\) is the supposed separate premium, but it is already included in the \(103\%\) call price. The correct calculation converts the quoted price once, then adds only the coupon:
Another frequent error is to use par as the redemption payment whenever the terms mention par. Par is the benchmark for measuring the premium; the contract’s scenario-specific redemption term determines the actual principal payment.
Check Your Understanding
For each problem, distinguish the redemption amount from the coupon and report the requested cash flow or premium.
- A hypothetical bond has par \(\$2{,}500\), an annual coupon rate of \(4.8\%\) paid quarterly, and a call price of \(101.2\%\) of par on a coupon date. Find the coupon per quarter, call premium, and total call-date cash flow. (Answer: coupon \(\$30\); call premium \(\$30\); total cash flow \(\$2{,}560\))
- A bond portfolio has aggregate par \(\$60{,}000\), pays a \(6\%\) annual coupon rate semiannually, and is called for \(99.5\%\) of par on a coupon date. Find the aggregate call premium and total cash flow on the call date. (Answer: call premium \(-\$300\), a discount; total cash flow \(\$61{,}500\))
- A hypothetical bond has par \(\$9{,}000\), pays a \(5\%\) annual coupon once per year, matures for \(107\%\) of par, and can be called on a coupon date for \(\$9{,}180\). Find both redemption premiums and the total cash flow for each scenario. (Answer: maturity premium \(\$630\), maturity cash flow \(\$10{,}080\); call premium \(\$180\), call cash flow \(\$9{,}630\))
- An investor holds 75 bonds, each with par \(\$2{,}000\), paying a \(3.6\%\) annual coupon rate semiannually. All are called on a coupon date for \(101.5\%\) of par. Find the aggregate redemption amount, aggregate call premium, and total cash flow. (Answer: redemption amount \(\$152{,}250\); call premium \(\$2{,}250\); total cash flow \(\$154{,}950\))
- A hypothetical zero-coupon issue consists of 40 bonds, each with par \(\$2{,}500\). The issue is callable for \(104.25\%\) of par and matures for \(109\%\) of par. Find the aggregate call and maturity redemption amounts and their respective premiums. (Answer: call amount \(\$104{,}250\), call premium \(\$4{,}250\); maturity amount \(\$109{,}000\), maturity premium \(\$9{,}000\))