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An+overview+of+interest+rate+and+bond+valuation

An+overview+of+interest+rate+and+bond+valuation
An+overview+of+interest+rate+and+bond+valuation

An overview of interest rate and bond valuation

Interest rate fundamentals

When funds are obtained by selling ownership interest, as in the sale of stock, the cost to the issuer of the funds is commonly called the required return.

The real rate of interest is the rate that has not been adjusted for inflation, liquidity preferences, or risk. The real rate of interest is the most basic cost of money. The nominal rate of interest is the actual rate of interest charged by the supplier of funds and paid by the demander.

The nominal rate of interest, r, consists of the real rate of interest, r*, plus an inflation premium, IP, and a risk premium, RP, that covers such things as default risk and contractual provisions.

Nominal Rate of Interest

r = r* + IP + RP

where:

r = nominal rate of interest

r* = real rate of interest

IP = inflation premium

RP = risk premium

The risk free-rate of interest, RF, is the required return on a risk-free asset. The risk-free rate consists of the real rate of interest plus an inflation premium. The rate on the three-month Treasury bill (T-bill) is considered to be the risk-free rate of return.

Risk-Free Rate of Return

RF = r* + IP

where:

RF = risk-free rate of interest

The real rate of interest is 4% Zui bank has the inflation expectation of 6% and risk premium of 4%. Estimate the risk free rate of return

RF= r?+RP

= 4%+ 6 %

= 10 %

Term Structure of Interest Rates

The term “structure of interest” relates the interest rate to the yield to maturity.

The yield curve is a graph of the term structure of interest rates. It is a graphical representation of the yield

to maturity of a security (y-axis) and the time to maturity (x-axis). The yield curve can take on three different shapes: upward-sloping, flat, or downward-sloping.

There are three generally cited theories that help to explain the shape of the yield curve.

1. The expectations hypothesis reflects investor’s expectations about future interest rates. The hypothesis is based on inflationary expectations. Expectations of higher future rates of inflation will result in higher long-term interest rates. The opposite is

true for expected lower rates of inflation. If investors believe that inflation rates will be lower in the future, then long-term interest rates will be lower than short-term rates.

An upward sloping yield curve implies which of the following according to the expectation theory?

1. The interest rates are expected to decline in the future.

2. The interest rates are expected to increase in the future.

3. The interest rates are expected to remain stable in the future.

4. The interest rates are expected to decline first, then increase.

2. Liquidity preference theory suggests that investors require a premium for tying up funds for long periods of time. This premium is due to the reduced liquidity of long-term funds. To avoid having to repeatedly renew short-term debt, borrowers are willing to pay a premium to obtain long-term funds. This helps to explain why the normal yield curve is upward-sloping.

3. Market segmentation theory is based on the law of supply and demand. The theory suggests that the market for loans is segmented by the length of maturity for different funds and that the supply and demand for loans within each segment determine the interest rate.

Which theory states that the yield curve should normally be upward-sloping because investors are risk-averse and prefer shorter-term securities?

1. Liquidity preference theory

2. Expectations theory

3. Efficient market theory

4. Market segmentation theory

Risk

A risk premium is attached to the risk-free rate to cover such things as default risk, maturity risk, liquidity risk, contractual provisions, and tax risk. In general, securities with the highest risk premiums are considered to have a high rate of default, have a long maturity, contain unfavorable contractual provisions, or not be tax exempt.

There is a risk-return trade-off, in that investors must be compensated for accepting greater risk with the expectation of greater returns. The higher the risk, the higher the expected return.

Valuation Fundamentals

Valuation is the process that incorporates the time value of money with the concept of risk and return to determine the worth of an asset.

The value of any asset depends on the cash flows it is expected to provide over time.

In addition to making cash flow estimates, the timing of the cash flows must be known. In combination with one another, the cash flow and its timing fully define the return expected from the asset.

The level of risk associated with a cash flow can affect its value. In general, the greater the risk ofthe cash flows, the lower its value. Therefore, in the valuation process the higher the risk, the greater the required return (discount rate).

The Basic Valuation Model

The value of any asset is the present value of all future cash flows it is expected to provide over the relevant time period.

Bond Valuation

Bonds are long-term debt instruments used by businesses and governments to raise large sums of money. The value of a bond is the present value of the contractual payments its issuers are obligated to make from the current time until it matures. The

interest rate the holder of the bond will receive is called the coupon rate. It does not change while the bond is outstanding. Most corporate bonds have a maturity, or par value, of R1,000. This is the amount the firm pays to the holder when the bond matures. The discount rate used to value bonds is rate of interest bonds with similar risk are yielding in the market at the time the bond is being valued. This rate will change over time.

Bond Value Behavior

There are certain external forces that constantly change the value of a bond in the marketplace. Since these forces are not controlled by bond issuers or investors, it is important to understand the impact required return and time to maturity have on bond value.

When the required return on a bond differs from the bond’s coupon interes t rate, the bond’s value will differ from its par value. Increases in the basic cost of long-term funds or in risk will raise the required return.

Alternatively, decreases in the basic cost of long-term funds or in risk will lower the required return. When the required return is greater than the coupon interest rate, the bond value will be less than its par value.

In this case, the bond will be selling at a discount. When the required return is less than the coupon, the bond value will be greater than par value. In this case, the bond will be selling at a premium. In the following graph, the bond has a coupon interest rate of 10%. Notice that when the market rate is 10%, the bond sells at par (R1,000). When rates fall, the market price increases and when rates rise, the market price decreases.

Whenever the required return of a bond is different from its coupon interest rate, the amount of time to maturity affects bond value. Constant required returns allow the bond’s value to approach par as the bond moves closer to maturity.

The change in the value of a bond due to changing required returns is affected by time.

A change in a bond’s required return that has 10 years to maturity will have a greater impact on the bond’s value than a change in required return on a bond with only 1 year left to maturity.

Yield to Maturity (YTM)

The yield to maturity (YTM) is the rate that investors earn if they buy a bond at a specific price and hold it until maturity. There are many ways to calculate the YTM of a bond.

Semiannual interest and Bond Values

The valuation of a bond paying semi-annual interest can be found by performing a simple modification to the equation used to find the value of a bond with annual interest payments.

1. Convert the annual interest, I, to semiannual by dividing by two.

2. Multiply the years to maturity, n, by two.

3. Convert the required rate return from an annual rate, rd, to a semiannual rate by dividing it by two.

STUDYGUIDELINE

When the par value is not given it is always assumed to be at a R1000 unless stated otherwise (see prescribed book page 234)

Input a negative sign when calculating the number of years, yield to maturity and coupon interest rate on either PV OR FV

*NB! If the negative sign is not inserted the financial calculator will display no solution

How to value a bond

?There is the normal value (par value) of the bond, which is usually to the value of R1000 unless specified otherwise

?The coupon rate, which is a fixed percentage and indicates the fixed amount that the investor will receive (an interest payment)

?There is the YTM or current rate in the markets (not a fixed interest rate)

?The present value of the bond that we will be paying for the investment

Using a financial calculator to work out bond value

FV Nominal value (Par value) or (Face value)

PMT Coupon

I/YR Yield to maturity

N Time to maturity

PV Bond value

It is important to note that we work with five variables when calculating the value of a bond.

Time to maturity

When the required return is greater than coupon interest rate

The bond value is less than par value (nominal value) the bond is said to sell at a discount

When the required return falls below the coupon interest rate

The bond value will be greater than par value (nominal value) the bond is said to sell at a premium

Yield to maturity

?The yield to maturity (YTM) measures the compound annual return to an investor and considers all bond cash flows.

?YTM is essentially the bond’s IRR based on the current price.

?The YTM will only be equal to the current yield if the bond is selling for its par value (R1,000).

?And that rate will be the same as the bond’s coupon rate.

?For premium bonds, the current yield > YTM.

?For discount bonds, the current yield < YTM

ASSESSMENT FORMAT

This study unit is assessed by way of both multiple-choice questions and long questions (short answer questions) in the examination [Remember to show your workings!].

We require you to be able to compute any of the present value, YTM, interest or coupon of either a bond that pays semi-annual or annual interest.

You should also be able to compute the nominal and real interest rates and distinguish between the two. You will also be required to describe the term structure of interest rates theory.

Prescribed book reference: chapter 6: Principal of Managerial Finance, 2nd edition REVIEW QUESTIONS: MCQ

Question 1

Bond value: semi compounded

The Hills bond has an 8% coupon rate (with interest paid semi-annually), a maturity value of R1 000, and matures in 5 years. If the bond is priced to yield 6%, what is the bond's current price?

Question 2

Yield to maturity: semi-compounded

The Jerry Company bond has an 8% coupon rate (semi-annual interest), a maturity value of R1 000, matures in 5 years, and a current price of R1 200. What is the Jerry’s Company yield-to-maturity?

The interest is compounded quarterly and therefore the yield to maturity will be 1,80% × 2 = 3,6%

Question 3

Coupon interest rate: semi compounded

The INJ bond has a current price of R800, a maturity value of R1 000, and matures in 5 years. If interest is paid semi-annually and the bond is priced to yield 8%, what is the bond's annual coupon rate?

R 15,34 is a semi-annual coupon, so the annual coupon is R 113,24, which gives a

coupon rate of 3,07% =(15,34 × 2

1 000)

Question 4

Number of years: semi compounded

Network Communications has a 7%, semiannual coupon bond outstanding with a current market price of R1 023,46. The bond has a par value of R1 000 and a yield to maturity of 6.72%. How many years is it until this bond matures?

Semi-annual compounding interest involves two compounding periods per year and therefore the number of years will be 25,05 ÷ 2 = 12,53

REVIEW QUESTIONS: SHORT QUESTIONS

Question 1

French Fry Inc has two bond issues outstanding, and both sell for R701,22. The first issue has a coupon rate of 8% and 20 years to maturity. The second has an identical yield to maturity as the first bond, but only five years until maturity. Both issues pay interest annually. What is the annual interest payment on the second issue?

** When the par value is not given it is always assumed to be R1000

Firstly solve for the missing variable in this case is the yield to maturity

The first issue bond

From the computed yield to maturity it can be used to solve the coupon payment for the second issue.

The second issue bond

Question 2

You are contemplating the purchase of a 20-year bond that pays R50 in interest each six months. You plan to hold this bond for only 10 years, at which time you will sell it in the marketplace. You require a 12 percent annual return, but you believe the market will require only an 8 percent return when you sell the bond 10 years hence. Assuming you are a rational investor, how much should you be willing to pay for the bond today? Calculate value of bound at year 10

Calculate value of bond at year 0 using the value of the bond at year 10 as the future value

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