# gbus502 vicentiu covrig 1 bonds and their valuation (chapter 7)

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Bonds and their valuationBonds and their valuation(chapter 7)(chapter 7)

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Bond marketsBond markets

Bond: A long-term debt instrument in which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond

Primarily traded in the over-the-counter (OTC) market. Most bonds are owned by and traded among large financial

institutions. Full information on bond trades in the OTC market is not published,

but a representative group of bonds is listed and traded on the bond division of the NYSE.

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Key Features of a BondKey Features of a Bond Par value – face amount of the bond, which

is paid at maturity (assume $1,000). Coupon interest rate – stated interest rate (generally fixed) paid

by the issuer. Multiply by par to get dollar payment of interest. Maturity date – years until the bond must be repaid. Issue date – when the bond was issued. Yield to maturity - rate of return earned on

a bond held until maturity (also called the “promised yield”) Some bonds are callable Call provision: Allows issuer to refund the bond issue if rates

decline (helps the issuer, but hurts the investor)

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What is the value of a 10-year, 10% annual coupon What is the value of a 10-year, 10% annual coupon bond, if rbond, if rdd (discount rate)= 10%? (discount rate)= 10%?

$1,000 V$385.54 $38.55 ... $90.91 V

(1.10)$1,000

(1.10)$100

... (1.10)$100

V

B

B

10101B

0 1 2 nkd

100 100 + 1,000100VB = ?

...

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What is the opportunity cost of debt What is the opportunity cost of debt capital?capital?

The discount rate (rd ) is the opportunity cost of capital, and is the rate that could be earned on alternative investments of equal risk.

rd = r* + IP + MRP + DRP + LP

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We have a bond with a coupon rate of 10%, paid annually, that matures in 10 years, with a face/par value of $1,000, and rd is 13%. Calculate the bond’s value. When rd is above the coupon rate, the bond’s value falls below par, and sells at a discount.

INPUTS

OUTPUT

N I/YR PMTPV FV

10 13 100 1000

-837.21

Using a financial calculator to value Using a financial calculator to value a bonda bond

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What is the value of a 10-year, 10% What is the value of a 10-year, 10% semiannual coupon bond, if rsemiannual coupon bond, if rdd = 13%? = 13%?

1. Multiply years by 2 : N = 2 * 10 = 20.

2. Divide nominal rate by 2 : I/YR = 13 / 2 = 6.5.

3. Divide annual coupon by 2 : PMT = 100 / 2 = 50.

INPUTS

OUTPUT

N I/YR PMTPV FV

20 6.5 50 1000

- 834.72

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Exam type questionExam type questionYou intend to purchase a 10-year, $1,000 face value bond that pays interest of

$60 every 6 months. If your nominal annual required rate of return is 10 percent

with semiannual compounding, how much should you be willing to pay for this

bond?a. $ 826.31b. $1,086.15c. $ 957.50d. $1,124.62 *Financial calculator solution:Inputs: N = 20; I = 5; PMT = 60; FV = 1000.Output: PV = -$1,124.62; VB = $1,124.62.

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What is the YTM on a 10-year, 9% annual What is the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for coupon, $1,000 par value bond, selling for

$887?$887?

Must find the rd that solves this model.

10d

10d

1d

Nd

Nd

1d

B

)r(1

1,000

)r(1

90 ...

)r(1

90 $887

)r(1

M

)r(1

INT ...

)r(1

INT V

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Using a financial calculator to find Using a financial calculator to find YTMYTM

Solving for I/YR, the YTM of this bond is 10.91%. This bond sells at a discount, because YTM > coupon rate.

INPUTS

OUTPUT

N I/YR PMTPV FV

10

10.91

90 1000- 887

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DefinitionsDefinitions

maturity toheld isit if bond

aon earnedreturn of rate maturityto-yieldYTM

CGY

Expected

CY

Expected YTM return totalExpected

price Beginning

pricein Change (CGY) yield gains Capital

priceCurrent

paymentcoupon Annual (CY) yieldCurrent

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A 10-year, 10% semiannual coupon bond selling A 10-year, 10% semiannual coupon bond selling for $1,135.90 can be called in 4 years for $1,050, for $1,135.90 can be called in 4 years for $1,050,

what is its yield to call (YTC)?what is its yield to call (YTC)?

The bond’s yield to maturity can be determined to be 8%. Solving for the YTC is identical to solving for YTM, except the time to call is used for N and the call premium is FV.

INPUTS

OUTPUT

N I/YR PMTPV FV

8

3.568

50 1050- 1135.90

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Exam type questionExam type question

Consider a $1,000 par value bond with a 7 percent annual coupon. The bond pays interest annually. There are 9 years remaining until maturity. What is the current yield on the bond assuming that the required return on the bond is 10 percent?a. 10.00%b. 8.46% *c. 7.00%d. 8.52%Current yield = Annual coupon payment/Current price.Step 1: Find the price of the bond:

N = 9; I/YR = 10; PMT = 70; FV = 1000; and then solve for PV = -$827.23. VB = $827.23.Step 2: Calculate the current yield: CY = $70/$827.23 = 8.46%.

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When is a call more likely to occur?When is a call more likely to occur?

In general, if a bond sells at a premium, then (1) coupon > rd, so (2) a call is more likely.

So, expect to earn:- YTC on premium bonds.

- YTM on par & discount bonds.

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Bond values over timeBond values over time At maturity, the value of any bond must equal its

par value. If kd remains constant:

- The value of a premium bond would decrease over time, until it reached $1,000.

- The value of a discount bond would increase over time, until it reached $1,000.

- A value of a par bond stays at $1,000.

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What is interest rate (or price) risk?What is interest rate (or price) risk?

Interest rate risk is the concern that rising kd will cause the value of a bond to fall.

% change 1 yr rd 10yr % change+4.8% $1,048 5% $1,386 +38.6%

$1,000 10% $1,000-4.4% $956 15% $749 -25.1%

The 10-year bond is more sensitive to interest rate changes, and hence has more interest rate risk.

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What is reinvestment rate risk?What is reinvestment rate risk? Reinvestment rate risk is the concern that kd will fall, and future CFs will have

to be reinvested at lower rates, hence reducing income.

EXAMPLE: Suppose you just won $1,000,000 playing the lottery. You

intend to invest the money and live off the interest.

If you choose to invest in series of 1-year bonds, that pay a 8% coupon you receive $80,000 in income and have $1,000,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to $30,000.

If you choose a 30-year bond that pay a 10 % coupon you receive $100,000 in income; you can lock in a 10% interest rate, and $100,000 annual income for 30 years

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Conclusions about interest rate and Conclusions about interest rate and reinvestment rate riskreinvestment rate risk

CONCLUSION: Nothing is riskless!

Short-term AND/OR High coupon bonds

Long-term AND/OR Low coupon bonds

Interest

rate riskLow High

Reinvestment rate risk

High Low

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Evaluating default risk:Evaluating default risk:Bond ratingsBond ratings

Bond ratings are designed to reflect the probability of a bond issue going into default

Mortgage bonds: a bond backed by fixed assets Debentures: unsecured bond Investment-grade bonds Junk bonds

Investment Grade Junk Bonds

Moody’s Aaa Aa A Baa Ba B Caa C

S & P AAA AA A BBB BB B CCC D

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Factors affecting default risk and bond Factors affecting default risk and bond ratingsratings

Financial performance

- Debt ratio

- TIE ratio

- Current ratio Bond contract provisions

- Secured vs. Unsecured debt

- Senior vs. subordinated debt

- Debt maturity

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Other factors affecting default riskOther factors affecting default risk Earnings stability

Regulatory environment

Potential antitrust or product liabilities

Pension liabilities

Potential labor problems

Accounting policies

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Exam type questionExam type question

Which of the following Treasury bonds will have the largest amount of interest rate risk (price risk)?a. A 7 percent coupon bond that matures in 12 years. *b. A 9 percent coupon bond that matures in 10 years.c. A 12 percent coupon bond that matures in 7 years.d. A 7 percent coupon bond that matures in 9 years.Statement a is correct. The longer the maturity and the lower the coupon of a

bond, the more sensitive it is to interest rate (price) risk. The bond in answer a has a maturity greater than or equal to and a coupon less than or equal to all the other

bonds.

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Exam type questionExam type questionWhich of the following statements is most correct?a. Junk bonds typically have a lower yield to maturity relative to investment

grade bonds.b. A debenture is a secured bond that is backed by some or all of the firm’s

fixed assets.c. Subordinated debt has less default risk than senior debt.d. None of the statements above is correct. *Statement d is correct; the others are false. Junk bonds have a higher yield to maturity relative to investment grade bonds. A debenture is an unsecured bond, while subordinated debt has greater default risk than senior debt.