bond valuation

Week 7

Bond Valuation

FACULTY OF BUSINESS AND ACCOUNTANCY

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Interest Rates and Required Returns

Corporate Bonds

Valuation Fundamentals

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Learning Objectives1. Describe interest rate fundamentals, the term structure of

interest rates, and risk premiums.

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

3. Discuss the general features, quotations, ratings, popular types, and international issues of corporate bonds.

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

5. Apply the basic valuation model to bonds and describe the impact of required return and time to maturity on bond values.

6. Explain the yield to maturity (YTM), its calculation, and the procedure used to value bonds that pay interest semiannually.

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Interest Rates & Required Returns

The Real Rates of Interest

Nominal or Actual Rate of Interest (Return)

Inflation and the Cost of Money

The Fundamentals

Term Structure of Interest Rates

Theories of Term StructureYield Curves

Risk Premiums: Issuer and Issue Characteristics

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• The interest rate or required return represents the price of money.

• Interest rates act as a regulating device. • Interest rates represent the compensation that a

demander of funds must pay a supplier.

Interest Rates & Required Returns

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• The real interest rate is the rate that creates an equilibrium between the supply of savings and the demand for investment funds in a perfect world.

• In this context, a perfect world is one in which there is no inflation, where suppliers and demanders have no liquidity preference, and where all outcomes are certain.

• The supply-demand relationship that determines the real rate is shown in Figure 6.1 on the following slide.

The Real Rates of Interest

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• Ignoring risk factors, the cost of funds is closely tied to inflationary expectations.

• The risk-free rate of interest, RF, which is typically measured by a 3-month Treasury bill (T-bill) compensates investors only for the real rate of return and for the expected rate of inflation.

Inflation and the Cost of Money

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• 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 differs from the real rate of interest, k* as a result of two factors:

Inflationary expectations reflected in an inflation premium (IP), and Issuer and issue characteristics such as default risks and contractual provisions as reflected in a risk premium

(RP).

Nominal or Actual Rate of Interest (Return)

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The term structure of interest rates relates the interest rate to the time to maturity for securities with a common default risk profile.

Typically, treasury securities are used to construct yield curves since all have zero risk of default.

However, yield curves could also be constructed with AAA or BBB corporate bonds or other types of similar risk securities.

Term Structure of Interest Rates

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Yield Curves

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1. Expectations Theory2. Liquidity Preference Theory3. Market Segmentation Theory

Theories of Term Structure

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Risk Premiums: Issue an Issuer Characteristics

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Corporate Bonds

Bond Indenture

Nominal or Actual Rate of Interest (Return)

Inflation and the Cost of Money

Legal Aspects of Corporate Bonds

Term Structure of Interest Rates

Theories of Term StructureYield Curves

Risk Premiums: Issuer and Issue Characteristics

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A bond is a long-term debt instrument that pays the bondholder a specified amount of periodic interest rate over a specified period of time.

0 1 2 3 4

Principal

RM1,000-RM1,000

Bond

Amount borrowed by the company and the amount owed to the bond holder on the maturity date

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0 1 2 3 4

RM1,000 -RM1,000

Bond

Maturity date

The time at which a bond becomes due and the principal must be repaid.

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0 1 2 3 4

RM1,000-RM1,000

Bond

8%

RM80 RM80 RM 80 RM80

Coupon rate or payment

Specified interest rate (or RM amount) that must be periodically paid.

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0 1 2 3 4

-RM1,000

Bond

8%

RM 80 RM80

Coupon rate or payment

Buy here at RM980

9.14%

Yield to maturity

the yield (expressed as a compound rate of return) earned on a bond from the time it is acquired until the maturity date of the bond

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Corporate Bonds

Trustee

Standard debt provision

Restricted debt provision

Bond Indenture

Types of Bonds

Costs of Bonds

General FeaturesBond

Quotation

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Corporate Bond

Legal document that specifies both the rights of the bondholders and the duties of the issuing corporation.

Trustee

Amount and timing of all interest and principal

payments

Sinking –fund requirements

Security interest provisions

Standard and Restrictive Provisions

Bond Indenture

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Standard debt provisions in the indenture specify certain record keeping and general business procedures that the issuer must follow.

Maintain satisfactory accounting records Audited financial statements Pay taxes and liabilities when due Maintain all facilities in good working order.

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Restrictive debt provisions are contractual clauses in a bond indenture that place operating and financial constraints on the borrower.

Common restrictive covenants include provisions that specify:

- Minimum equity levels - Prohibition against factoring receivables - Fixed asset restrictions - Constraints on subsequent borrowing - Limitations on cash dividends.

In general, violations of restrictive covenants give bondholders the right to demand immediate repayment.

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Sinking fund requirements are restrictive provisions often included in bond indentures that provide for the systematic retirement of bonds prior to their maturity.

The bond indenture identifies any collateral (security) pledged against the bond and specifies how it is to be maintained.

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• The longer the bond’s maturity, the higher the interest rate (or cost) to the firm.

• The larger the size of the offering, the lower will be the cost (in % terms) of the bond.

• Also, the greater the risk of the issuing firm, the higher the cost of the issue.

• Finally, the cost of money in the capital market is the basis form determining a bond’s coupon interest rate.

Costs of Bonds to the Issuer

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Allows bondholders to exchange their bonds for a specified number of shares of common stock.

Bondholders will exercise this option only when the market price of the stock is greater than the conversion price.

1. Conversion feature of convertible bonds

General Features

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2. Call feature

Gives the issuer the opportunity to repurchase the bond prior to maturity at the call price.

In general, the call premium is equal to one year of coupon interest and compensates the holder for having it called prior to maturity.

Furthermore, issuers will exercise the call feature when interest rates fall and the issuer can refund the issue at a lower cost.

Issuers typically must pay a higher rate to investors for the call feature compared to issues without the feature.

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3. Stock purchase warrants

Bonds also are occasionally issued with stock purchase warrants attached to them to make them more attractive to investors.

Warrants give the bondholder the right to purchase a certain number of shares of the same firm’s common stock at a specified price during a specified period of time.

Including warrants typically allows the firm to raise debt capital at a lower cost than would be possible in their absence.

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Valuation Fundamentals

• The (market) value of any investment asset is simply the present value of expected cash flows.

• The interest rate that these cash flows are discounted at is called the asset’s required return.

• The required return is a function of the expected rate of inflation and the perceived risk of the asset.

• Higher perceived risk results in a higher required return and lower asset market values.

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Basic Valuation Model

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Basic Bond Valuation

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Bond Valuation: Bond FundamentalsFirm AB on 1 January 2011, issued a 10% coupon interest rate, 10-year bond with a $1,000 par value that pays interest annually.

$614.45

$385.54$1,000.0

0

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Required Returns and Bond Values

Whenever the required return on a bond differs from the bond’s coupon interest rate, the bond’s value

will differ from its par.

Bond Values for Various Required Returns

Firm AB’s 10% Coupon Interest Rate, 10-Year Maturity, $1,000 Par, 1 Jan. 2011 Issue, Paying Annual Interest.

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Firm AB’s 10% Coupon Interest Rate, 10-Year Maturity, $1,000 Par, 1 Jan. 2011 Issue, Paying

Annual Interest.

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It is also important to note that a bond’s price will approach par value as it approaches the maturity date,

regardless of the interest rate and regardless of the coupon rate.

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• The yield to maturity measures the compound annual return that an investor earn if he buy the bond at a specific price and hold it to maturity.

• It considers all bond cash flows. It is essentially the bond’s IRR (rd) based on the current price.

• Note that the yield to maturity will only be equal to the bond’s coupon rate if the bond is selling for its face value (RM1,000).

Yield to Maturity

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Firm AB’s bond, which currently sells for $1,080, has a 10% coupon interest rate and $1,000 par value, pays interest annually, and has 10 years to maturity. What is the bond’s YTM?

$1,080 = $100 x (PVIFArd,10yrs) + $1,000 x (PVIFrd,10yrs)

Solve

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Semiannual Interest and Bond Values

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Relationship Between Bond Prices and Yields• Bond prices are inversely related to bond yields

(move in opposite directions)

• As interest rates in the economy change, the price or value of a bond changes:– if the required rate of return increases, the price

of the bond will decrease– if the required rate of return decreases, the price

of the bond will increase

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When the coupon rate matches the discount rate, thebond always sellsfor its par value.

Bonds with Maturity Dates Annual Compoundin

g For example, find the price of a 10% coupon bond

with three years to maturity if market interest rates are currently 10%.

Set:EndP/YR 1

Maturity (periods) N 3I/YR 10

Market Price PV -1,000Coupon Interest PMT 100

FV 1,000

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What would happen to the bond’s price if interest rates increased from 10% to 15%?

When the interestrate goes up, the

bond price will always go down.

Bonds with Maturity Dates Annual Compounding

Set:EndP/YR 1

N 3I/YR 15PV -885.84

PMT 100 FV 1’000

Set:EndP/YR 1

N 3I/YR 10PV -1,000

PMT 100 FV 1,000

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What would happen to the bond’s price it had a 15 year maturity rather than a 3 year maturity?

And the longer the maturity, the greater

the price decline.

Bonds with Maturity Dates Annual Compoundin

g

Set:EndP/YR 1

N 15I/YR 15PV -707.63

PMT 100 FV 1’000

Set:EndP/YR 1

N 3I/YR 15PV -885.84

PMT 100 FV 1’000

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What would happen to the original 3 year bond’s price if interest rates dropped from 10% to 5%?

Bonds with Maturity Dates Annual Compoundi

ng

Set:EndP/YR 1N 3I/YR 5PV -1,136.16PMT 100 FV 1’000

Set:EndP/YR 1N 3I/YR 10PV -1,000PMT 100 FV 1’000

When interest rates

go down, bond prices will

alwaysgo up.

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Annual Compoundin

g

What if we considered a similar bond, but with a 15 year maturity rather than a 3 year maturity?

Bonds with Maturity Dates

And the longer the maturity,

the greater the price increase will be.

Set:EndP/YR 1N 3I/YR 5PV -1,136PMT 100 FV 1’000

Set:EndP/YR 1N 15I/YR 5

PV-

1,1518.98

PMT 100 FV 1’000

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Bonds with Maturity Dates Semi-Annual Compoundin

g If we had the same bond, but with semi-annual coupon payments, we would have to divide the 10% coupon rate by two, divided the discount rate by two, and multiply n by two.

Set:EndP/YR 2N 3x2 = 6I/YR 10/2 = 5PV -1,137.70

PMT 100/2 = 50

FV 1’000

Thus, the value is slightly larger than the price of the annual coupon bond (1,136.16) because the investor receives payments sooner.

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Coupon Effects on Price Volatility

• The amount of bond price volatility depends on three basic factors:– length of time to maturity– risk – amount of coupon interest paid by the bond

• First, we already have seen that the longer the term to maturity, the greater is a bond’s volatility

• Second, the riskier a bond, the more variable the required return will be, resulting in greater price volatility.

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Coupon Effects on Price Volatility (cont.)

• Finally, the amount of coupon interest also impacts a bond’s price volatility.

• Specifically, the lower the coupon, the greater will be the bond’s volatility, because it will be longer before the investor receives a significant portion of the cash flow from his or her investment.

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Current = Annual Coupon Interest Yield Current Market Price

For example, a 10% coupon bond which is currently selling at RM1,150 would have a current yield of:

Current = RM100 = 8.7% Yield RM1,150

Current Yield• The Current Yield measures the annual return to

an investor based on the current price.

For premium bonds, the current yield > YTM.For discount bonds, the current yield < YTM.

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Bonds in Malaysia

• http://bondinfo.bnm.gov.my• www.sc.com.my