Chapter 4 Summary
Key Concepts
- 4.1 Bond Terminology
- Bond definition, characteristics, and key terminology.
- 4.2 Calculating the Purchase Price of a Bond on an Interest Payment Date
- Calculating a marketable bond price when the selling date is the interest payment date.
- Calculating premiums and discounts.
- 4.3 Calculating the Yield Rate
- Calculating the yield on the bond to maturity.
- Calculating the yield realized by an investor if a bond is purchased and sold before maturity.
- 4.4 Bond Schedules
- How to amortize a bond premium or accrue a bond discount.
- 4.5 Quotation of Bonds
- Calculating a marketable bond price when the selling date is a noninterest payment date.
- Calculating the quoted price of a bond.
- 4.6 Sinking Funds
- Sinking funds and their purposes.
- How to construct complete ordinary sinking fund schedules.
- How to construct partial ordinary sinking fund schedules.
- Other sinking fund calculations.
Glossary of Terms
Accrued Interest. The amount of interest that the bond has earned but has not yet paid out since the previous interest payment date.
Bond. A debt that is secured by a specific corporate asset and that establishes the issuer’s responsibility toward a creditor for paying interest at regular intervals and repaying the principal at a fixed later date.
Book Value of the Debt. The difference between the principal amount owing on the bond and the accumulated balance in the sinking fund at any point in time.
Capital Gain. The amount by which the current value of an asset exceeds the original purchase price.
Capital Loss. The amount by which the current value of an asset falls short of the original purchase price.
Coupon Rate. Also known as the bond rate or nominal rate, this is the nominal interest rate paid on the face value of the bond.
Debenture. A debt that is not secured by a specific corporate asset and that establishes the issuer’s responsibility toward a
creditor for paying interest at regular intervals and repaying the principal at a fixed later date.
Discount. The amount by which a bond’s selling price falls short of its face value.
Face Value. Also called the par value or denomination of the bond, this is the principal amount of the debt that the investor lent to the bond-issuing corporation.
Issue Date. The date that a bond is issued and available for purchase by creditors.
Market Quotation. The purchase price expressed as a percentage of face value.
Market Rate. This is the prevailing nominal rate of interest in the open bond market.
Maturity Date. Also known as the redemption date or due date, this is the day upon which the redemption price will be paid to the bondholder (along with the final interest payment), thereby extinguishing the debt.
Periodic Cost of the Debt. The periodic total of the interest payments and the sinking fund payments.
Premium. The amount by which a bond’s selling price exceeds its face value.
Purchase Price. Also known as the cash price or flat price, this is the amount of money an investor must directly pay out to acquire the bond. It represents the total of the market price and the accrued interest.
Quoted Price. This is the actual value of the bond excluding any accrued interest.
Redemption Price. Also called the redemption value or maturity value, this is the amount the bond issuer will pay to the bondholder upon maturity of the bond.
Selling Date. This is the date that a bond is actively traded and sold to another investor through the bond markets.
Sinking Fund. A special account into which an investor, whether an individual or a business, makes annuity payments such that sufficient funds will be on hand by a specified date to meet a future savings goal or debt obligation.
Sinking Fund Schedule. A table that shows the sinking fund contribution, interest earned, and the accumulated balance for every payment in the annuity.
Yield to Maturity. A bond’s overall rate of return when purchased at a market price and held until maturity. It includes both the semi-annual interest that the bondholders earn on their investment along with the gain or loss resulting from the difference between the market price and the redemption price.
Formula & Symbol Hub
Symbols Used
- [latex]BAL[/latex] = Principal balance
- [latex]BV[/latex] = Book value
- [latex]FV[/latex] = Face value of bond
- [latex]PMT[/latex] = Annuity payment amount
- [latex]N[/latex] = Number of annuity payments
- [latex]I/Y[/latex] = Nominal interest rate
- [latex]P/Y[/latex] = Number of payments per year or payment frequency
- [latex]C/Y[/latex] = Number of compounds per year or compounding frequency
Formulas Used
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Formula 4.1 – Bond Payment
[latex]\text{Payment}=\mbox{Face Value} \times \mbox{periodic bond rate}[/latex]
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Formula 4.2 – Purchase Price on an Interest Payment Date
[latex]\text{Purchase Price}=\mbox{Present Value of Face Value}+\mbox{Present Value of Bond Payments}[/latex]
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Formula 4.3 – Premium (Bonds)
[latex]\text{Premium}=\mbox{Purchase Price}-\mbox{Face Value}[/latex]
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Formula 4.4 – Discount (Bonds)
[latex]\text{Discount}=\mbox{Face Value}-\mbox{Purchase Price}[/latex]
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Formula 4.5 – Quoted Price (Bonds)
[latex]\mbox{Flat Price}-\mbox{Accrued Interest}[/latex]
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Formula 4.6 – Quoted Price as a Percentage of Face Value
[latex]\frac{\mbox{Quoted Price}}{\mbox{Face Value}} \times 100\%[/latex]
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Formula 4.7 – Periodic Cost of Debt
[latex]\mbox{Sinking Fund Payment}+\mbox{Periodic Interest Payment}[/latex]
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Formula 4.8 – Book Value
[latex]\mbox{Loan Amount}-\mbox{Balance}[/latex]
Calculator
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Date Function
- 2nd DATE to access.
- Enter two of the three variables ([latex]DT1[/latex], [latex]DT2[/latex], [latex]DBD[/latex]) by pressing ENTER after each input and using the up arrow and down arrow to scroll through the display. The variables are:
- [latex]DT1[/latex] = The starting date of the transaction
- [latex]DT2[/latex] = The ending date of the transaction
- [latex]DBD[/latex] = The days between the dates, counting the first day but not the last, which is the time period of the transaction.
- [latex]ACT / 360[/latex] = A setting for determining how the calculator determines the [latex]DBD[/latex]. In Canada, you should maintain this setting on [latex]ACT[/latex], which is the actual number of days. In other countries, such as the United States, they treat each year as having [latex]360[/latex] days (the [latex]360[/latex] setting) and each month as having [latex]30[/latex] days. If you need to toggle this setting, press 2nd SET.
- Enter all dates in the format of MM.DDYY, where MM is the numerical month, DD is the day, and YY is the last two digits of the year. DD and YY must always be entered with both digits.
- Press [latex]CPT[/latex] on the unknown (when it is on the screen display) to compute the answer.
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Amortization Worksheet for Bond Schedules
- To use the amortization worksheet for a bond schedule:
- Enter all seven of the time value of money variables accurately ([latex]N[/latex], [latex]I/Y[/latex], [latex]PV[/latex], [latex]PMT[/latex], [latex]FV[/latex], [latex]P/Y[/latex], and [latex]C/Y[/latex]). Because money is received by the bond holder, [latex]PMT[/latex] and [latex]FV[/latex] are positive. Because the purchase price is paid out by the bond holder, [latex]PV[/latex] is negative.
- Press 2nd AMORT.
- Enter a value for [latex]P1[/latex], press ENTER and then the down arrow.
- Enter a value for [latex]P2[/latex], press ENTER and then the down arrow. Note that the higher the numbers entered in [latex]P1[/latex] or [latex]P2[/latex], the longer it will take the calculator to compute the outputs. It is possible that the calculator will go blank and take a few moments before displaying the outputs.
- Press the down arrow to scroll through [latex]BAL[/latex], [latex]PRN[/latex], and [latex]INT[/latex] to read the output. The [latex]BAL[/latex] number is the book value entry of the bond schedule. The [latex]PRN[/latex] number is the amortized premium or accumulated discount entry of the bond schedule. The [latex]INT[/latex] number is the interest on the book value at yield entry of the bond schedule.
- To use the amortization worksheet for a bond schedule:
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Amortization Worksheet for Sinking Fund Schedules
- To use the amortization worksheet for a sinking fund schedule:
- Enter all seven of the time value of money variables accurately ([latex]N[/latex], [latex]I/Y[/latex], [latex]PV[/latex], [latex]PMT[/latex], [latex]FV[/latex], [latex]P/Y[/latex], and [latex]C/Y[/latex]). If [latex]PMT[/latex] was computed, you must re-enter it rounded up to the next cent while retaining the correct cash flow sign convention. Because money is invested into the account, [latex]PMT[/latex] is negative. Because the money is withdrawn from the fund, [latex]FV[/latex] is positive.
- Press 2nd AMORT.
- Enter a value for [latex]P1[/latex], press ENTER and then the down arrow.
- Enter a value for [latex]P2[/latex], press ENTER and then the down arrow. Note that the higher the numbers entered in [latex]P1[/latex] or [latex]P2[/latex], the longer it will take the calculator to compute the outputs. It is possible that the calculator will go blank and take a few moments before displaying the outputs.
- Press the down arrow to scroll through [latex]BAL[/latex], [latex]PRN[/latex], and [latex]INT[/latex] to read the output. The [latex]BAL[/latex] number is the balance entry of the sinking fund schedule. The [latex]PRN[/latex] number is the increase entry of the sinking fund schedule. The [latex]INT[/latex] number is the interest entry of the sinking fund schedule.
- To use the amortization worksheet for a sinking fund schedule:
Attribution
“7.8 Chapter Summary” from Business and Financial Mathematics by Valerie Watts is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.
“Chapter 14 Summary” from Business Math: A Step-by-Step Handbook (2021B) by J. Olivier and Lyryx Learning Inc. through a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License unless otherwise noted.
