Contents
Time Value of Money
Annuities
Perpetuities
Kinds of Interest Rates
Future Value of an Uneven Cash flow
Probability Distribution
Standard Deviation
CAPM
Security Market Line
Bond Valuation
Stock Valuation
Cost of Capital
The Balance Sheet
Financial Terms
Scientific Terms
Disclaimer




Bond Valuation

Bond When a company (or government) borrows money from the public or banks (bondholders) and agrees to pay it back later
Par Value The amount of money that the company borrows. Usually it is $1,000.
Coupon Payments This is like interest. The company makes regular payments to the bondholders, like every 6 months or every year.
Indenture The legal stuff. A written agreement between the company and the bond holder. They talk about how much the coupon payments will be, and when the money (par value) will be paid back to the bondholder.
Maturity Date Date when the company pays the par value back to the bondholder.
Market Interest Rate This changes everyday.


The thing about bonds is that the interest rate (coupon payments) is fixed. It doesn't change. And bonds last a long time. Like 10 years or whatever. So in the meantime, the market interest rate (the interest rates in general) go up and down. OK, well, if the coupon payments are for 10% and then the market interest rates fall from 10% to 8%, then that bond at 10% is valuable, right. It is paying 10% while the overall interest rate is only 8%. Exactly how much is it worth? You mean 'what is the present value of a bond?'

The Present Value of a Bond = The Present Value of the Coupon Payments (an annuity) + The Present Value of the Par Value (time value of money)

Example

  • Par Value = $ 1,000
  • Maturity Date is in 5 years
  • Annual Coupon Payments of $100, which is 10%
  • Market Interest rate of 8%

The Present Value of the Coupon Payments (an annuity) = $399.27

The Present Value of the Par Value (time value of money) =$680.58

The Present Value of a Bond = $ 399.27 + $ 680.58 = $1,079.86


Detailed Explanation


Bonds are a form of debt instrument issued by companies, governments, and other organizations to raise funds from investors. In essence, bonds represent a promise by the issuer to pay the investor a specified interest rate for a certain period of time, with the principal amount returned to the investor at the end of the bond's term. However, not all bonds are created equal, and the terms of a bond can vary depending on the needs and objectives of the issuer and investor. In this chapter, we will explore the different types of bonds, including fixed-rate, floating-rate, and zero-coupon bonds.

Fixed-rate bonds are the most common type of bond, and they are issued with a predetermined interest rate that remains fixed throughout the life of the bond. This interest rate is often referred to as the coupon rate, and it is based on the creditworthiness of the issuer, prevailing interest rates, and the term of the bond. For example, a company might issue a 10-year bond with a coupon rate of 4%. This means that the company will pay the bondholder an annual interest payment of 4% of the face value of the bond for the next 10 years.

One of the key benefits of fixed-rate bonds is that they provide a predictable stream of income for investors, as the interest payments remain constant throughout the life of the bond. This makes them particularly attractive to investors who are looking for a reliable source of income. Additionally, fixed-rate bonds are generally less risky than other types of bonds, as the interest rate remains fixed regardless of changes in market conditions.

However, fixed-rate bonds also have some drawbacks. One of the main drawbacks is that they are subject to interest rate risk, which is the risk that the bond's value will decrease if interest rates rise. For example, if interest rates rise from 4% to 6%, the 4% coupon rate on the 10-year bond described above will become less attractive to investors, as they can now earn a higher return elsewhere. As a result, the value of the bond will decrease, which can lead to capital losses for the investor if they sell the bond before it matures.

Floating-rate bonds are a type of bond where the interest rate is not fixed, but rather adjusts periodically based on a benchmark interest rate. This benchmark rate is typically tied to the prevailing market interest rates, such as the London Interbank Offered Rate (LIBOR) or the U.S. Treasury bill rate. The interest rate on a floating-rate bond is usually quoted as a spread over the benchmark rate. For example, a company might issue a 5-year floating-rate bond with a coupon rate of LIBOR + 2%. This means that the interest rate on the bond will be equal to the LIBOR rate plus 2%.

One of the main advantages of floating-rate bonds is that they offer protection against interest rate risk, as the interest rate adjusts to changes in market conditions. This makes them particularly attractive to investors who are concerned about rising interest rates. Additionally, floating-rate bonds often offer higher yields than fixed-rate bonds, as investors are compensated for taking on the risk of fluctuating interest rates.

However, floating-rate bonds also have some disadvantages. One of the main disadvantages is that they are subject to credit risk, which is the risk that the issuer will default on the bond. This risk is particularly pronounced in the case of floating-rate bonds issued by companies with low credit ratings, as they may have difficulty making interest payments if their financial condition deteriorates. Additionally, the interest rate on a floating-rate bond may not adjust as quickly as market interest rates, which can lead to mismatches between the bond's interest rate and prevailing market rates.

Zero-coupon bonds are a type of bond that does not pay periodic interest payments to the bondholder. Instead, the bond is issued at a discounted price and the bondholder receives the full face value of the bond when it matures. Zero-coupon bonds are also known as discount bonds or deep discount bonds, and they are commonly used by issuers who want to raise funds without incurring the expense of paying regular interest payments to bondholders.

When a zero-coupon bond is issued, the issuer sets the maturity date and the face value of the bond, which is the amount that the bondholder will receive when the bond matures. The bond is then sold to investors at a price that is less than the face value, and the difference between the face value and the purchase price represents the bond's interest income.

For example, suppose a company issues a 10-year zero-coupon bond with a face value of $10,000. The bond is sold to investors at a price of $7,000, which is a discount of $3,000 from the face value. At maturity, the bondholder will receive the full face value of $10,000, which represents a return of $3,000 or 42.86% on their investment over the 10-year period.

Zero-coupon bonds are often sold at a deep discount to their face value, as the lack of periodic interest payments means that investors must wait until the bond matures to receive any return on their investment. The discount rate applied to the bond will depend on a number of factors, including prevailing market interest rates, the creditworthiness of the issuer, and the length of time until the bond matures.

One of the main advantages of zero-coupon bonds is their simplicity. Unlike other types of bonds, there are no periodic interest payments to keep track of, which makes them an attractive investment option for investors who want a straightforward investment vehicle. Additionally, because zero-coupon bonds do not pay periodic interest, they are not subject to reinvestment risk, which is the risk that an investor will be unable to reinvest their interest income at a comparable rate to their original investment. Another advantage of zero-coupon bonds is their tax efficiency. Because the bondholder does not receive any periodic interest payments, they do not have to pay income tax on those payments. Instead, the bondholder is only taxed on the capital gains that they receive when the bond matures. This can be particularly beneficial for investors who are in a high tax bracket, as they can defer paying taxes on their investment until the bond matures and they receive the full face value.

Despite their advantages, zero-coupon bonds also have some drawbacks. One of the main drawbacks is that they are subject to interest rate risk, which is the risk that changes in market interest rates will affect the value of the bond. Because zero-coupon bonds do not pay periodic interest, they are particularly sensitive to changes in interest rates, as the discount rate used to price the bond will be affected by changes in prevailing market rates. Additionally, because zero-coupon bonds do not pay periodic interest, they may not be suitable for investors who require a regular stream of income from their investments. This can be a disadvantage for retirees or other investors who are relying on their investments to generate income to meet their living expenses.

Yields are one of the most important factors that investors consider when making investment decisions. They represent the return that investors can expect to receive on their investments, and are influenced by a variety of factors, including inflation, economic conditions, and interest rates. In this section, we will discuss three important concepts related to yields: nominal yield, real yield, and yield curve.

Nominal yield also known as coupon yield, is the stated rate of interest that a bond pays to its investors. It is expressed as a percentage of the bond's face value, and represents the amount of annual interest income that the investor will receive from the bond. For example, if a bond has a face value of $1,000 and a coupon rate of 5%, the bondholder will receive $50 in annual interest income. Nominal yields are fixed at the time that the bond is issued and remain constant throughout the life of the bond. This means that if an investor purchases a bond with a 5% nominal yield and holds it to maturity, they will receive a fixed annual return of 5% on their investment.

Real yield also known as inflation-adjusted yield, takes into account the effects of inflation on a bond's returns. Inflation erodes the purchasing power of money over time, which means that a fixed nominal yield may not be sufficient to provide investors with a positive real return. To calculate real yield, the nominal yield is adjusted for inflation using the Consumer Price Index (CPI) or another measure of inflation. The resulting real yield represents the bond's return after accounting for the effects of inflation. For example, suppose a bond has a nominal yield of 5% and the inflation rate is 2%. The real yield would be calculated as follows:


Real Yield = Nominal Yield - Inflation Rate
Real Yield = 5% - 2%
Real Yield = 3%

This means that the bondholder would receive a real return of 3% after accounting for the effects of inflation.

The yield curve is a graph that plots the yields of bonds with different maturities against their respective maturities. It provides investors with a visual representation of the relationship between interest rates and time to maturity. There are three main types of yield curves: normal, inverted, and flat. A normal yield curve is upward sloping, with longer-term bonds offering higher yields than shorter-term bonds. This is because longer-term bonds are exposed to greater interest rate risk, which means that investors require a higher yield to compensate for this risk. An inverted yield curve, on the other hand, is downward sloping, with shorter-term bonds offering higher yields than longer-term bonds. This is a rare occurrence and is often viewed as a signal of an impending economic downturn. A flat yield curve occurs when the yields of bonds with different maturities are relatively similar. This can indicate that investors expect interest rates to remain stable in the future. The yield curve is closely watched by investors, as it can provide valuable information about future economic conditions. For example, a steeply upward-sloping yield curve may signal that investors expect economic growth to continue in the future, while a flat or inverted yield curve may indicate that investors are concerned about a potential economic downturn.



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Mark McCracken

Author: Mark McCracken is a corporate trainer and author living in Higashi Osaka, Japan. He is the author of thousands of online articles as well as the Business English textbook, "25 Business Skills in English".

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