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Principles of Managerial Finance

Sixteenth Edition, Global Edition

Interest Rates and Bond Valuation

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Learning Goals

LG 1 Describe interest rate fundamentals, the term structure of interest rates, and risk premiums.

LG 2 Review the legal aspects of bond financing and bond cost.

LG 3 Discuss the general features, yields, prices and international issues of corporate bonds.

LG 4 Understand the key inputs and basic model used in the bond valuation process.

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Interest Rates and Required Returns

Interest Rate Fundamentals

Interest Rate

Usually applied to debt instruments such as bank loans or bonds
the compensation paid by the borrower of funds to the lender
from the borrower’s point of view, the cost of borrowing funds
The interaction of supply and demand determines interest rates

Required Return

The return that the supplier of funds requires the demander to pay
Applies to almost any kind of investment

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Supply-Demand Relationship

Long Description:

The vertical axis represents the equilibrium interest rate and the horizontal axis represents funds supplied or demanded.

The details of the graph are as follows:

A supply line S naught slopes upward from the lower left corner to the upper right corner. Another supply line S1, also an upward sloping line, is parallel to S naught and is drawn below it.
A demand line D slopes downward from the upper left corner to the lower right corner intersects both the supply lines.
It intersects the line S naught at S naught equals D on the horizontal axis and r naught on the vertical axis. The demand line intersects line S1 at S1 equals D on the horizontal axis and r1 on the vertical axis.
Dashed straight lines are drawn to the axes from the points of intersection.
A downward arrow from r naught to r1 and a rightward arrow from S naught to S1 is visible between the dashed lines.

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Interest Rates and Required Returns

Interest Rate Fundamentals

Inflation

A rising trend in the prices of most goods and services

Liquidity Preference

A general tendency for investors to prefer short-term (i.e., more liquid) securities

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Interest Rates and Required Returns

Interest Rate Fundamentals

Negative Interest Rates

When a loan carries an interest rate below zero, the lender essentially pays interest to the borrower rather than the other way around
A natural question is, why would anyone buy an investment if it paid an interest rate below zero?

The answer is that there is no good, safe alternative offering a better return

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Interest Rates and Required Returns

Interest Rate Fundamentals

Nominal and Real Interest Rates

Nominal Rate of Interest

The actual rate of interest charged by the supplier of funds and paid by the demander

Real Rate of Interest

The rate of return on an investment measured not in dollars but in the increase in purchasing power that the investment provides
The real rate of interest measures the rate of increase in purchasing power

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Interest Rates and Required Returns

Term Structure of Interest Rates

Yield Curves

Term Structure of Interest Rates

The relationship between the maturity and rate of return for bonds with similar levels of risk

Yield Curve

A graphic depiction of the term structure of interest rates

Yield to Maturity (YTM)

Compound annual rate of return earned on a debt security purchased on a given day and held to maturity
An estimate of the market’s required return on a particular bond

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Interest Rates and Required Returns

Risk Premiums: Issuer and Issue Characteristics

Several factors influence a bond’s risk premium

Default risk or credit risk

The likelihood that a corporation will fail to make interest payments or principle repayments on its bonds

Bond characteristics

e.g., Time to maturity

Interest rate risk

When interest rates in the economy change, bond prices move in the opposite direction
Some bonds are more sensitive to interest rate risk and therefore pay higher risk premiums to compensate investors

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Government and Corporate Bonds

Municipal Bond

A bond issued by a state or local government body

Corporate Bond

A long-term debt instrument indicating that a corporation has borrowed a certain amount of money and promises to repay it in the future under clearly defined terms

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Government and Corporate Bonds

Par Value, Face Value, Principal

The amount of money the borrower must repay at maturity, and the value on which periodic interest payments are based

Coupon Rate

The percentage of a bond’s par value that will be paid annually, typically in two equal semiannual payments, as interest

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Government and Corporate Bonds

Legal Aspects of Corporate Bonds

Bond Indenture

A legal document that specifies both the rights of the bondholders and the duties of the issuing corporation

Standard Debt Provisions

Provisions in a bond indenture specifying certain record-keeping and general business practices that the bond issuer must follow; normally, they do not place a burden on a financially sound business

Restrictive Covenants

Provisions in a bond indenture that place operating and financial constraints on the borrower

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Government and Corporate Bonds

Legal Aspects of Corporate Bonds

Subordination

In a bond indenture, the stipulation that subsequent creditors agree to wait until all claims of the senior debt are satisfied

Sinking-Fund Requirement

A restrictive provision often included in a bond indenture, providing for the systematic retirement of bonds prior to their maturity

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Government and Corporate Bonds

Legal Aspects of Corporate Bonds

Collateral

A specific asset against which bondholders have a claim in the event that a borrower defaults on a bond

Secured Bond

A bond backed by some form of collateral

Unsecured Bond

A bond backed only by the borrower’s ability to repay the debt

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Government and Corporate Bonds

Legal Aspects of Corporate Bonds

Trustee

A paid individual, corporation, or commercial bank trust department that acts as the third party to a bond indenture and can take specified actions on behalf of the bondholders if the terms of the indenture are violated

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Government and Corporate Bonds

General Features of a Bond Issue

Conversion Feature

A feature of convertible bonds that allows bondholders to change each bond into a stated number of shares of common stock

Call Feature

A feature included in nearly all corporate bond issues that gives the issuer the opportunity to repurchase bonds at a stated call price prior to maturity

Call Price

The stated price at which a bond may be repurchased, by use of a call feature, prior to maturity

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Data on Selected Bonds

Bond data from http://finra-markets.morningstar.com/BondCenter/ActiveUSCorpBond.jsp, accessed on April 23, 2020.

Company	Coupon	Maturity	Price	Yield (YTM)
Verizon	5.050%	Mar. 15, 2034	123.88	2.915%
Apple	3.850	Aug. 4, 2046	124.36	2.554
Tesla	5.300	Aug. 15, 2025	94.50	6.542
Safeway	7.450	Sep. 15, 2027	105.10	6.566
Amazon	4.250	Aug. 22, 2057	99.98	4.251

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Government and Corporate Bonds

International Bond Issues

Eurobond

A bond issued by an international borrower and sold to investors in countries with currencies other than the currency in which the bond is denominated

Foreign Bond

A bond that is issued by a foreign corporation or government and is denominated in the investor’s home currency and sold in the investor’s home market

Bulldog Bond

Foreign bond issued in Britain

Samurai Bond

Foreign bond issued in Japan

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Bond Valuation

Bond Fundamentals

Bonds are long-term debt instruments used by business and government to raise large sums of money, typically from a diverse group of lenders
Most corporate bonds

pay interest semiannually (every six months) at a stated coupon rate
have an initial maturity of 10 to 30 years
and have a par value, principal, or face value, of $1,000 that the borrower must repay at maturity

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Example

MTN just issued a 6% coupon rate, 10-year bond with a GHs1,000 par value that pays interest annually. Investors who buy this bond receive the contractual right to two types of cash flows: (1) $60 annual interest (6% coupon rate × $1,000 par value) distributed at the end of each year and (2) the $1,000 par value at the end of the tenth year.

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Bond Valuation

Bond Values for Annual Coupons

B₀ = value (or price) of the bond at time zero
C = annual coupon interest payment in dollars
n = number of years to maturity
M = par value in dollars
r = annual required return on the bond

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Bond Valuation

Bond Values for Annual Coupons

B₀ = value (or price) of the bond at time zero
C = annual coupon interest payment in dollars
n = number of years to maturity
M = par value in dollars
r = annual required return on the bond

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Bond Valuation

Yield to Maturity (YTM)

The compound annual rate of return earned on a bond purchased assuming that all payments arrive on time and that the investor holds the bond to maturity
Mathematically, a bond’s YTM is the discount rate that equates the bond’s market price to the present value of its cash flows

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Example

Mr. Amin wishes to determine the current value of the MTN bond. If the bond pays interest annually and the required annual return on the bond is 6% (equal to its coupon rate), what is the bond’s value.

We can calculate the bond’s value using Equation 6.5a:

The timeline on the next slide depicts the computations involved in finding the bond value.

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Example

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Bond Valuation

Bond Values for Semiannual Coupons

As a practical matter, most bonds make semiannual rather than annual interest payments
Calculating the value for a bond paying semiannual interest requires three changes to the approach we’ve used so far:

Convert the annual coupon payment, C, to a semiannual payment by dividing C by 2
Recognize that if the bond has n years to maturity it will make 2n coupon payments (i.e., in n years there are 2n semiannual periods)
Discount each payment by using the semiannual required return calculated by dividing the annual required return, r, by 2

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Bond Valuation

Bond Values for Semiannual Coupons

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Bond Valuation

Bond Values for Semiannual Coupons

B₀ = value (or price) of the bond at time zero
C = annual coupon interest payment in dollars
n = number of years to maturity
M = par value in dollars
r = annual required return on the bond

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Example

Assuming that the Mills Company bond pays interest semiannually and that the required annual return, r, is 6%, Equation 6.6a indicates that the bond’s value is

As before, because the required return equals the coupon rate, the bond sells at par value. We will soon see that when the required return does not equal the coupon rate, the bond may sell above or below par value.

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Bond Valuation

Changes in Bond Prices

When the required return rises, the bond price falls, and when the required return falls, the bond price rises
Required Returns and Bond Prices

Discount

The amount by which a bond sells below its par value

When the required return is greater than the coupon rate, the bond’s value will be less than its par value

Premium

The amount by which a bond sells above its par value

When the required return falls below the coupon rate, the bond’s value will be greater than par

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Example

Let’s reconsider the MTN bond paying a 6% coupon rate and maturing in 10 years (assume annual interest payments). Initially, we assumed that the required return on this bond was 6%, so the bond’s value was equal to par value, $1,000. Let’s see what happens to the bond’s value if the required return is higher or lower than the coupon rate. Table 6.5 shows that at an 8% required return, the bond sells at a discount with a value of $865.80, but if the required return is 4%, the bond sells at a premium with a value of $1,162.22.

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Bond Values for Various Required Returns (Mills Company’s 6% Annual Coupon Bond with a 10-Year Maturity and $1,000 Par Value)

Required return, r	Bond value, B₀	Status
8%	$ 865.80	Discount
6	1,000.00	Par value
4	1,162.22	Premium

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Bond Values and Required Returns

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Bond Valuation

Changes in Bond Prices

Interest Rate Risk

The chance that a bond’s required return will change and thereby cause a change in the bond’s price
Other things being equal, Long-term bond prices move more when rates change whereas short-term bond prices are less sensitive to rate changes

Long-term bonds are associated with more interest rate risk