# mbf2273 fund management l2: bonds and bonds valuation

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MBF2273 | Fund ManagementPrepared by Dr Khairul Anuar

L2: Bonds and Bonds Valuation

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Introduction

Bonds are like money market instruments, but they have maturities that exceed one year. These include Treasury bonds, corporate bonds, mortgages, and the like.

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What is Bond Market?

• The bond market is a financial market where participants buy and sell debt securities , usually in the form of bonds.

• The bond market primarily includes: Government-issued securities. Corporate debt securities.

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Types of Bond

Domestic of Bonds

• Bonds issued in the country and currency in which they are traded.

• Unlike international bonds, domestic bonds are not subject to currency risk.

• They usually carry less risk, as the regulatory and taxation requirements are usually known to investors in domestic bonds, or at least to their brokers and accountants.

International Bond• A bond issued in a country or currency other than that of the investor or broker.

• They include :

Eurobonds, which are issued in a foreign currency,

foreign bonds, which are issued by a foreign government or corporation in the domestic market, and

global bonds, which are issued in both domestic and international markets.

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Deutsche Telekom Global Bond

• The largest corporate global bond issue to date is the $14.6 billion Deutsche Telekom multicurrency offering (year 2000).

• The issue includes three U.S. dollar tranches with 5-, 10-, and 30-year maturities

totaling $9.5 billion, two euro tranches with 5- and 10-year maturities totaling €3

billion, two British pound sterling tranches with 5- and 30-year

maturities totaling £950 million, and one 5-year Japanese yen tranche of ¥90 billion

Corporate Bonds: Characteristics of Corporate Bonds

• Registered Bonds– Replaced “bearer” bonds– IRS can track interest income this way

• Restrictive Covenants– Mitigates conflicts with shareholder interests– May limit dividends, new debt, ratios, etc.– Usually includes a cross-default clause

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Corporate Bonds: Characteristics of Corporate Bonds

• Call Provisions – Higher yield– Mechanism to adhere to a sinking fund provision– Interest of the stockholders – Alternative opportunities

• Conversion – Some debt may be converted to equity– Similar to a stock option, but usually more limited

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Application of the Time Value of Money Tool: Bond Pricing

• Bonds - Long-term debt instruments • Provide periodic interest income – annuity series• Return of the principal amount at maturity – future lump sum• Prices can be calculated by using present value techniques i.e.

discounting of future cash flows.• Combination of present value of an annuity and of a lump sum

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Key Components of a Bond

• Par value : Typically $1000• Coupon rate: Annual rate of

interest paid.• Coupon: Regular interest

payment received by holder per year.

• Maturity date: Expiration date of bond when par value is paid back.

• Yield to maturity: Expected rate of return based on price of bond

Figure 1: Merrill Lynch corporate bond.

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Key Components of a Bond

Example 1: Key components of a corporate bond

Let’s say you see the following price quote for a corporate bond:

Issue Price Coupon(%) Maturity YTM% Current Yld. Rating

Hertz Corp. 91.50 6.35 15- Jun-2010 15.438 6.94 B

Price = 91.5% of $1000$915; Annual coupon = 6.35% *1000 $63.50Maturity date = June 15, 2010; If bought and held to maturityYield = 15.438%Current Yield = $ Coupon/Price = $63.5/$915 6.94%

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Pricing a Bond in Steps

Since bonds involve a combination of an annuity (coupons) and a lump sum (par value) its price is best calculated by using the following steps:

Figure 2: How to price a bond.

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Pricing a Bond in Steps (continued)

Example 2: Calculating the price of a corporate bond.Calculate the price of an AA-rated, 20-year, 8% coupon (paid annually) corporate bond (Par value = $1,000) which is expected to earn a yield to maturity of 10%.

Annual coupon = Coupon rate * Par value = .08 * $1,000 = $80 = PMTYTM = r = 10%Maturity = n = 20Price of bond = Present Value of coupons + Present Value of par value

Year 0 1

$80

2

$80

3

$80

20

$80$1,000

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$80 $80…

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Pricing a Bond in Steps (continued)

Example 2: Calculating the price of a corporate bond

Present value of coupons =

=

= $80 x 8.51359 = $681.09

Present Value of Par Value =

Present Value of Par Value =

Present Value of Par Value = $1,000 x 0.14864 = $148.64Price of bond = $681.09 + $148.64 = $829.73

rr1

11

PMTn

0.10

0.101

11

$8020

nr1

1FV

200.101

1$1,000

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Pricing a Bond in Steps (continued)

Method 2. Using a financial calculator Mode: P/Y=1; C/Y = 1 Input: N I/Y PV PMT FVKey: 20 10 ? 80 1000Output -829.73

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• Most corporate and government bonds pay coupons on a semiannual basis.

• Some companies issue zero-coupon bonds by selling them at a deep discount.

• For computing price of these bonds, the values of the inputs have to be adjusted according to the frequency of the coupons (or absence thereof). – For example, for semi-annual bonds, the annual coupon is divided by

2, the number of years is multiplied by 2, and the YTM is divided by 2. – The price of the bond can then be calculated by using the TVM

equation, a financial calculator, or a spreadsheet.

Semiannual Bonds and Zero-Coupon Bonds

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Semiannual Bonds and Zero-Coupon Bonds

Using TVM Equation

Using Financial Calculator

Figure 5: Future cash flow of the Coca-Cola bond.

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Pricing Bonds after Original Issue

The price of a bond is a function of the remaining cash flows (i.e. coupons and par value) that would be paid on it until expiration.

As of August, 2008 the 8.5%, 2022 Coca-Cola bond has only 27 coupons left to be paid on it until it matures on Feb. 1, 2022

Figure 6.6 Remaining cash flow of the Coca-Cola bond.

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Pricing Bonds after Original Issue

Example 3: Pricing a semi-annual coupon bond after original issue: Four years ago, the XYZ Corporation issued an 8% coupon (paid semi-

annually), 20-year, AA-rated bond at its par value of $1000. Currently, the yield to maturity on these bonds is 10%. Calculate the price of the bond today.

Remaining number of semi-annual coupons = (20-4)*2 = 32 coupons = nSemi-annual coupon = (.08*1000)/2 = $40Par value = $1000Annual YTM = 10% YTM/25% = r

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Pricing Bonds after Original Issue

Method 1: Using TVM equations

Bond Price =

rr1

11

Couponr1

1 ValuePar

n

n

Bond Price =

0.050.051

11

$400.051

1$1,000

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Bond Price = $1000 x 0.209866 + $40 x 15.80268 Bond Price = $209.866 + $632.107 Bond Price = $841.97

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Pricing Bonds after Original Issue

Method 2: Using a financial calculator

Mode: P/Y=2; C/Y = 2

Input: N I/Y PV PMT FVKey: 32 10 ? 401000Output -841.97

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Zero-Coupon Bonds

• Known as “pure” discount bonds and sold at a discount from face value

• Do not pay any interest over the life of the bond.

• At maturity, the investor receives the par value, usually $1000.

• Price of a zero-coupon bond is calculated by merely discounting its par value at the prevailing discount rate or yield to maturity.

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Amortization of a Zero-Coupon Bond

• The discount on a zero-coupon bond is amortized over its life.

• Interest earned is calculated for each 6-month period.• for example .04*790.31=$31.62

• Interest is added to price to compute ending price.

• Zero-coupon bond investors have to pay tax on annual price appreciation even though no cash is received.

Table 2: Amortized Interest on a Zero-Coupon Bond

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Amortization of a Zero-Coupon Bond

Example 4: Price of and taxes due on a zero-coupon bond: John wants to buy a 20-year, AAA-rated, $1000 par value,

zero-coupon bond being sold by Diversified Industries Plc. The yield to maturity on similar bonds is estimated to be 9%. a) How much would he have to pay for it? b) How much will he be taxed on the investment after 1 year,

if his marginal tax rate is 30%?

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Amortization of a Zero-Coupon Bond

Example 4 Answer

Method 1: Using TVM equationBond Price = Par Value * [1/(1+r)n] Bond Price = $1000*(1/(1.045)40

Bond Price = $1000 * .1719287 = $171.93

Method 2: Using a financial calculator Mode: P/Y=2; C/Y = 2

Input: N I/Y PV PMT FVKey: 40 9 ? 0 1000Output -171.93

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Amortization of a Zero-Coupon Bond

Example 4 (Answer) (continued)Calculate the price of the bond at the end of 1 year.

Mode:P/Y=2; C/Y = 2Input: N I/Y PV PMT FVKey: 38 9 ? 0 1000Output -187.75

Taxable income = $187.75 - $171.93 = $15.82Taxes due = Tax rate * Taxable income = 0.30*$15.82 = $4.75

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Amortization of a Zero-Coupon Bond

Example 4 (Answer) (continued)Alternately, we can calculate the semi-annual interest earned, for each of the two semi-annual periods during the year.

$171.93 * .045 = $7.736 Price after 6 months $171.93+7.736 = $179.667$179.667 * .045=$8.084 Price at end of year$179.667+8.084 = $187.75Total interest income for 1 year = $7.736+$8.084$15.82 Tax due = 0.30 * $15.82 = $4.75

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Yields and Coupon Rates

• A bond’s coupon rate differs from its yield to maturity (YTM).

• Coupon rate - set by the company at the time of issue and is fixed (except for newer innovations which have variable coupon rates)

• YTM is dependent on market, economic, and company-specific factors and is therefore variable.

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The First Interest Rate: Yield to Maturity

• Expected rate of return on a bond if held to maturity. • The price that willing buyers and sellers settle at

determines a bond’s YTM at any given point. • Changes in economic conditions and risk factors will

cause bond prices and their corresponding YTMs to change.

• YTM can be calculated by entering the coupon amount (PMT), price (PV), remaining number of coupons (n), and par value (FV) into the TVM equation, financial calculator, or spreadsheet.

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The “Other” Interest Rate: Coupon Rate

• The coupon rate on a bond is set by the issuing company at the time of issue

• It represents the annual rate of interest that the firm is committed to pay over the life of the bond.

• If the rate is set at 7%, the firm is committing to pay .07*$1000 = $70 per year on each bond,

• It is paid either in a single check or two checks of $35 paid six months apart.

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Relationship of Yield to Maturity and Coupon Rate

• An issuing firm gets the bond rated by a rating agency such as Standard & Poor’s or Moody’s.

• Then, based on the rating and planned maturity of the bond, it sets the coupon rate to equal the expected yield as indicated in the Yield Book (available in the capital markets at that time) and sells the bond at par value ($1000).

• Once issued, if investors expect a higher yield on the bond, its price will go down and the bond will sell below par or as a discount bond and vice-versa.

• Thus, a bond’s YTM can be equal to (par bond), higher than (discount bond) or lower than (premium bond) its coupon rate.

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Relationship of Yield to Maturity and Coupon Rate

Table 6.3 Premium Bonds, Discount Bonds, and Par Value Bonds

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Relationship of Yield to Maturity and Coupon Rate

Figure 8: Bond prices and interest rates move in opposite directions.

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Bond Ratings

• Ratings are produced by Moody’s, Standard and Poor’s, and Fitch

• Range from AAA (top-rated) to C (lowest-rated) or D (default).

• Help investors gauge likelihood of default by issuer.

• Assist issuing companies establish a yield on newly-issued bonds.

– Junk bonds: is the label given to bonds that are rated below BBB. These bonds are considered to be speculative in nature and carry higher yields than those rated BBB or above (investment grade).

– Fallen angels: is the label given to bonds that have had their ratings lowered

from investment to speculative grade.

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Rating Criteria

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Profitability Capital Structure

Business Model

Management

· Quality of earnings

· EBITDA margins

· Interest coverage indicators

· Volatility of earnings

· Cost Management

· Indebtedness ratios

· Distribution of debt maturities

· Effects of concentrated ownership on funding capabilities

· Barriers to entry

· Competitive environment

· Market position

· Diversification: Clients, Products, Geographic

· Management Structure

· Strategy and Objectives

· Performance Record

U.S. Government Bonds

• Include bills, notes, and bonds sold by the Department of the Treasury

• State bonds, issued by state governments• Municipal bonds issued by county, city, or local government

agencies. • Treasury bills, are zero-coupon, pure discount securities with

maturities ranging from 1-, 3-, and 6-months up to 1 year.• Treasury notes have between two to 10 year maturities. • Treasury bonds have greater than 10-year maturities, when

first issued.

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