© 2003 The McGraw-Hill Companies, Inc. All rights reserved. Interest Rates and Bond Valuation Chapter Seven

© 2003 The McGraw-Hill Companies, Inc. All rights reserved.

Interest Rates and Bond Valuation

Chapter

Seven

7.2

Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.

Chapter Outline

Bonds and Bond Valuation More on Bond Features Bond Ratings Some Different Types of Bonds Bond Markets Inflation and Interest Rates Determinants of Bond Yields

7.3


Bond Definitions 7.1

Bond – a long term debt obligation issued by a corporation Par value (face value) – the amount of money that will be

repaid at the maturity date of the bond Coupon rate – the percentage of the bond’s face value that

will be paid in interest every year Coupon payment – the dollar value of the interest that is paid Maturity date – the point in time when the bond will be

redeemed by the issuer. The investor will receive cash equal to the face value of the bond.

Yield or Yield to maturity – also known as the Internal Rate of Return (IRR) on the bond. It is the return to the investor that is derived from both the coupons received plus any capital gain or loss.

7.4


Present Value of Cash Flows as Rates Change

The market price of a bond is simply the present value of the bond’s future cash flows Bonds have two types of future cash flows

Interest annuity (the stream of coupons) Face value at maturity

When interest rates go up, the market value of the bond will go down

When interest rates go down, the market value of the bond will go up

Therefore, there is an inverse relationship between the interest rate (YTM) and the market value of the bond (price)

7.5


The Bond-Pricing Equation

t

t

r)(1

ValueFace

r

r11- C Bond Value

Where:

C = the periodic interest paid by the bond (payment)

r = the yield-to-maturity for the bond

t = the number of time periods to maturity

7.6


Valuing a Bond with Annual Coupons

Consider a bond with a $1,000 face value, a coupon rate of 10%, paid annually and 5 years to maturity. The yield to maturity is 11%. What is the market value of the bond?

Formula Approach Calculator ApproachFVPMTNI

PV $

7.7


Valuing a Bond with Annual Coupons

Now consider a second bond, also with a $1,000 face value and a 10% coupon, paid annually, but with 20 years to maturity and a yield to maturity of 8%. What is the price of this bond?


PV $

7.8


Graphical Relationship Between Price andYield-to-Maturity

600

700

800

900

1000

1100

1200

1300

1400

1500

0% 2% 4% 6% 8% 10% 12% 14%

The important concept to note is the inverse relationship between

price & YTM

Based on a 10 year, $1,000 bond with an

8% coupon

7.9


Bond Prices: Relationship Between Couponand Yield

If YTM = coupon rate, then face value = market price

If YTM > coupon rate, then face value > market price The bond is selling at a discount, called a discount

bond

If YTM < coupon rate, then face value < market price The bond is selling at a premium, called a

premium bond

7.10


Example – Semiannual Coupons

Most bonds in Canada make coupon payments semi-annually. Suppose you have an 8% semi-annual pay bond with a face value of

$1,000 that matures in 7 years. If the yield is 10%, what is the price of this bond?


PV $

7.11


Interest Rate Risk

Price Risk Change in price due to a change in interest rates Long-term bonds have more price risk than short-

term bonds

Reinvestment Rate Risk Uncertainty concerning the interest rate at which

future cash flows can be reinvested Long-term bonds have more reinvestment rate risk

than short-term bonds

7.12


Figure 7.2 – Interest Rate Risk and Time to Maturity

This graph shows the impact on price as the YTM changes for both a one-year bond and a thirty-year bond.

Both bonds have a $1,000 face value and a 10% coupon. Note how much more sensitive the long bond is to a

change in the YTM.

7.13


Computing Yield-to-Maturity

Yield-to-maturity is the discount rate implied by the current bond price

Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity

If you have a financial calculator, enter N, PV, PMT and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign)

7.14


Example – Finding YTM

For example, assume that a ten year, $1,000 bond with a 6% coupon, paid annually, is currently trading at $950 in the market. What is the bond’s yield-to-maturity (YTM)?

Formula Approach

The YTM is the discount rate that makes the equality true in the bond pricing formula.

Solve for it using the function keys on the calculator or trial & error if using algebra

Calculator ApproachFVPMT

PVN

I %

7.15


Example – Finding the YTM

Consider another bond with a 10% annual coupon rate, 15 years to maturity and a face value of $1000. The current price is $928.09. Will the yield-to-maturity be more or less than 10%?


PVN

I %

7.16


Understanding YTM

The YTM can always be decomposed into its two component parts. These are: Coupon Yield Capital gain or loss

Assume that you buy a 10 year, $1,000 bond with an 8% coupon, priced to yield 6%.

Step #1: First calculate the price of the bond.

Calculator ApproachFVPMTNI

PV $

7.17


Understanding YTM

In Step #2, we calculate the new price after one year has passed, assuming all else remains equal.

Step #3: Calculate the coupon yield by dividing the annual coupon payment by the beginning price


PV $

7.18


Understanding YTM

Step #4: Calculate the capital gain or loss

Step #5: Calculate the Yield to Maturity

7.19


YTM with Semiannual Coupons

Suppose a 20 year, $1,000 bond with a 10% coupon, paid semi-annually, is selling for $1197.93. Find YTM


PVN

I %

7.20


Bond Pricing Theorems

Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate

If you know the price of one bond, you can estimate its YTM and use that to find the price of the second bond

This is a useful concept that can be transferred to valuing assets other than bonds

7.21


Differences Between Debt and Equity 7.2

Debt Not an ownership interest Bondholders do not have

voting rights Interest is considered a cost

of doing business and is tax deductible

Bondholders have legal recourse if interest or principal payments are missed

Excess debt can lead to financial distress and bankruptcy

Equity Ownership interest Common shareholders vote

for the board of directors and other issues

Dividends are not considered a cost of doing business and are not tax deductible

Dividends are not a liability of the firm and shareholders have no legal recourse if dividends are not paid

An all equity firm can not go bankrupt

7.22


The Bond Indenture

Contract between the company (the issuer of the bond) and the bondholders and includes The basic terms of the bonds The total amount of bonds issued A description of property used as security, if applicable Sinking fund provisions Call provisions Details of protective covenants

7.23


Bond Classifications

Registered vs. Bearer Bonds Registered – can only be sold by the registered owner Bearer – similar to cash; possession implies ownership

Security Collateral – secured by financial securities & assets pledged as a

secondary source of repayment Mortgage – secured by real property, normally land or buildings Debentures – unsecured debt with original maturity of 10 years or

more Notes – unsecured debt with original maturity less than 10 years

Seniority Senior versus Junior debt – refers to preference in position with

respect to other lenders (Senior debt is paid first; junior debt paid last) Subordinated debt – indicates that it has a lower priority than other,

more senior debt

7.24


Bond Classifications Continued

Repayment Sinking Fund – Account managed by the bond trustee for early bond

redemption. Reduces default risk & improves marketability.

Call Provision – allows the company to repurchase all or a portion of the issue prior to the original maturity Call premium – amount above the face value the borrower agrees to

pay, should they call the bond before its original maturity Deferred call - Call protected - Canada plus call – Protects the investor against a call by providing

compensation equal to the foregone interest, should a call occur

The issuer usually cannot call the bond during the years immediately after the issue date.

7.25


Covenants

Protective Covenants Negative covenants – things the borrower agrees not to do

Agrees to limit the amount of dividends paid Agree not to pledge assets to other lenders Agree not to merge with, sell to or acquire another firm Agree not to buy new capital assets above $x in value Agree not to issue new debt

Positive covenants – things the borrower agrees to do Maintain a minimum current ratio Provide audited financial statements Maintain collateral in good condition

7.26


Bond Characteristics and Required Returns

The coupon rate depends on the risk characteristics of the bond when issued

7.27


Credit Ratings: Investment Grade

Credit Risk Moody’s Standard & Poors

Fitch Duff & Phelps

Highest quality

Aaa AAA AAA AAA

High quality (very strong)

Aa AA AA AA

Upper Medium (strong)

A A A A

Medium grade

Baa BBB BBB BBB

7.28


Credit Ratings: Speculative or Junk Debt

Credit Risk Moody’s Standard & Poors

Fitch Duff & Phelps

Lower Medium

Ba BB BB BB

Low grade (Speculative)

B B B B

Poor Quality Caa CCC CCC CCC

Most speculative

Ca CC CC CC

7.29


Standard & Poor's Bond Rating Scale AAA - An obligor rated 'AAA' has EXTREMELY STRONG capacity to meet its financial commitments. AA - An obligor rated 'AA' has VERY STRONG capacity to meet its financial commitments. It differs from the highest rated

obligors only in small degree. A - An obligor rated 'A' has STRONG capacity to meet its financial commitments but is somewhat more susceptible to the

adverse effects of changes in circumstances and economic conditions than obligors in higher-rated categories. BBB - An obligor rated 'BBB' has ADEQUATE capacity to meet its financial commitments. However, adverse economic

conditions or changing circumstances are more likely to lead to a weakened capacity of the obligor to meet its financial commitments.

BB - An obligor rated 'BB' is LESS VULNERABLE in the near term than other lower-rated obligors. However, it faces major ongoing uncertainties and exposure to adverse business, financial, or economic conditions which could lead to the obligor's inadequate capacity to meet its financial commitments.

B - An obligor rated 'B' is MORE VULNERABLE than the obligors rated 'BB', but the obligor currently has the capacity to meet its financial commitments. Adverse business, financial, or economic conditions will likely impair the obligor's capacity or willingness to meet its financial commitments.

CCC - An obligor rated 'CCC' is CURRENTLY VULNERABLE, and is dependent upon favorable business, financial, and economic conditions to meet its financial commitments.

CC - An obligor rated 'CC' is CURRENTLY HIGHLY VULNERABLE. R - An obligor rated 'R' is under regulatory supervision owing to its financial condition. During the pendency of the

regulatory supervision the regulators may have the power to favor one class of obligations over others or pay some obligations and not others. Please see Standard & Poor's issue credit ratings for a more detailed description of the effects of regulatory supervision on specific issues or classes of obligations.

SD and D - An obligor rated 'SD' (Selective Default) or 'D' has failed to pay one or more of its financial obligations (rated or unrated) when it came due. A 'D' rating is assigned when Standard & Poor's believes that the default will be a general default and that the obligor will fail to pay all or substantially all of its obligations as they come due. An 'SD' rating is assigned when Standard & Poor's believes that the obligor has selectively defaulted on a specific issue or class of obligations but it will continue to meet its payment obligations on other issues or classes of obligations in a timely manner. Please see Standard & Poor's issue credit ratings for a more detailed description of the effects of a default on specific issues or classes of obligations.

Note: Obligors rated 'BB', 'B', 'CCC', and 'CC' are regarded as having significant speculative characteristics. 'BB' indicates the least degree of speculation and 'CC' the highest. While such obligors will likely have some quality and protective characteristics, these may be outweighed by large uncertainties or major exposures to adverse conditions. Plus (+) or minus (?): Ratings from 'AA' to 'CCC' may be modified by the addition of a plus or minus sign to show relative standing within the major rating categories.

Source: Standard & Poors

7.30


Bond Ratings – Investment Quality

High Grade DBRS’s AAA – capacity to pay is exceptionally

strong DBRS’s AA – capacity to pay is very strong

Medium Grade DBRS’s A – capacity to pay is strong, but more

susceptible to changes in circumstances DBRS’s BBB – capacity to pay is adequate,

adverse conditions will have more impact on the firm’s ability to pay

7.31


Bond Ratings - Speculative

Low Grade DBRS’s BB, B, CCC, CC Considered speculative with respect to capacity to

pay. Very Low Grade

DBRS’s C – bonds are in immediate danger of default

DBRS’s D – in default, with principal and/or interest in arrears

7.32


Stripped or Zero-Coupon Bonds 7.4

Make no periodic interest payments (coupon rate = 0%) All cash flows occur on the maturity date Sometimes called zeroes, or deep discount bonds Bondholder must pay taxes on accrued interest every year,

even though no interest is received (thus are best held in a tax-deferred account, such as an RRSP)

Market price is the PV of the face value at maturity

7.33


Zero Coupon or Stripped Bonds

Assume that you want to purchase a 30 year stripped bond with a $100,000 face value. If the appropriate YTM is 8%, how much will you have to pay today to buy this bond?


PV $

7.34


Floating Rate Bonds

Coupon rate floats depending on some index value There is less price risk with floating rate bonds

The coupon floats, so it is less likely to differ substantially from the yield-to-maturity

Coupons may have a “collar” – the rate cannot go above a specified “ceiling” or below a specified “floor”

7.35


Other Bond Types

Disaster (CAT) bonds – payout to the investor is dependent on the occurrence of some major catastrophic event

Income bonds – coupons are tied to firm profitability Convertible bonds – bonds may be converted into common

stock Real Return bonds – the bond is adjusted for inflation Put bond (retractable bond) – the investor may sell the bond

back to the issuer at a fixed price LYON (Liquid Yield Option Note) - created by Merrill Lynch.

Bond is a callable, puttable, convertible, zero coupon, subordinated note

7.36


Bond Markets 7.5

Primarily over-the-counter transactions with dealers connected electronically

Extremely large number of bond issues, but generally low daily volume in single issues

Makes getting up-to-date prices difficult, particularly on small corporate issues. One alternative for the retail investor is http://www.cbidmarkets.com

Treasury securities are an exception

7.37


Bond Quotations

From the Financial Post, October 20, 2005

Canada 10.000 Jun 01/08 115.94 3.55

The issuer is the Government of Canada The coupon rate is 10% (assumed to be semiannual) The maturity date is June 1, 2008 The quoted price can be interpreted as either the price per $100 of

face value or as a percentage of face value The yield to maturity is 3.55%

Issuer Coupon Maturity Price YTM

7.38


Inflation and Interest Rates 7.6

Nominal rate of interest – quoted rate of interest, includes compensation for deferring consumption and expected inflation

Real rate of interest – compensation for deferring consumption

Expected Inflation – the expected fall in purchasing power of the dollar, due to rising prices

7.39


The Fisher Effect

The Fisher Effect defines the relationship between real rates, nominal rates and inflation

Exact relationship

Where: R = the nominal interest rate r = the real interest rate h = the expected future inflation rate

Approximation of the above relationship is:

h1r1R1

hrR

7.40


Example – Fisher Effect

If we require a 4% real return and we expect inflation to be 6%, what is the nominal rate?

Therefore, the nominal rate is

If both inflation and the real return are low, we can safely use the approximation, which would give us a nominal rate of

7.41


Factors Affecting Required Return

Default risk – the probability that the issuer will not be able to repay the bond as contractually obligated to do (bond rating)

Liquidity premium – liquidity refers to the ability to: Convert to cash At or near face value Short bonds with high coupons that are more frequently traded have

greater liquidity & hence a lower required return Call features – since a call feature allows the bond to be

redeemed early, it increases risk to the bond investor Anything else that affects the risk of the cash flows to the

bondholders, will affect the required returns

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© 2003 The McGraw-Hill Companies, Inc. All rights reserved. Interest Rates and Bond Valuation Chapter Seven