chapter 3: debt financing - albert...

Direcció Financera IIDirecció Financera II

Chapter 3: Debt financingp g

Albert Banal-Estanol

Debt issuing as part of a leverage buyout (LBO)g p g

What is an LBO? How to decide among these options?Albert Banal-Estanol Direcció Financera II - Chapter 3

What is an LBO? How to decide among these options?

In this chapter we should talk about…p

Public debt (bonds):Th t t l t t f b d i The contractual content of a bond issue

Bond types and characteristics

Private debt: Private debt: Term loans Revolving credit Private placements

Valuing corporate (and government) bonds Relationship between yield and price of zero and non-zero coupon bonds

Price dynamics sensitivity to changes in interest rates and the duration Price dynamics, sensitivity to changes in interest rates and the duration Valuation using arbitrage for safe and risky bonds

Provisions and covenants Provisions and covenants

Government bonds

Albert Banal-Estanol Direcció Financera II - Chapter 3

The prospectus of a bond issuep p Indenture or trust deed: bond agreement between borrower and a trust company

Trust company: a company that represents the bondholders and makes sure Trust company: a company that represents the bondholders and makes sure that the terms of the indenture are enforced

Main elements: Principal or face value and coupon rates (interests), and their dates Principal: nominal amount for calculating interest, typically repaid on due date Coupon: for a given coupon rate (0 for zero-coupon or pure discount bonds): Coupon: for a given coupon rate (0 for zero coupon or pure discount bonds):

Example: $1000 bond with a 10% coupon rate with semi annual paymentsyearper coupons ofnumber

principal x ratecupon CPN

Example: $1000 bond with a 10% coupon rate with semi-annual payments, pay coupons: $1000 x 0.10 / 2 = $50 every 6 months

Types of bonds:yp Registered bond - a bond in which the Company's records show ownership

and interest and principal are paid directly to each owner Bearer bonds - the bond holder must send in coupons to claim interest and


must send a certificate to claim the final payment of principal

Types of corporate debtyp p Secured debt

S ifi l d d ll l h b dh ld h di l i i h Specific assets are pledged as collateral that bondholders have a direct claim to in the event of bankruptcy

Example1: mortgage bonds (property as collateral)

E ample 2 Asset backed bonds (an kind of asset) Example 2: Asset-backed bonds (any kind of asset) Unsecured debt:

In the event of bankruptcy, bondholders have a claim to only the assets that are not already pledged as collateral on other debtpledged as collateral on other debt

Examples: Notes (maturities<10 years) and debentures (longer)

Tranches: Different classes of securities that comprise a single bond issue All classes of securities are paid from the same cash flow source

SeniorityA b dh ld ’ i it i l i i t t l d i th d bt A bondholder’s priority in claiming assets not already securing other debt

Most debenture issues contain clauses restricting the company from issuing new debt with equal or higher priority than existing debt


International bonds

Domestic Bonds Domestic Bonds Issued by local entity and traded in local market, but purchased by foreigners

Foreign Bonds Issued by a foreign company in a local market and intended for local investors They are denominated in the local currency. They are denominated in the local currency. Yankee bond - a bond sold publicly by a foreign company in the US Samurai - a bond sold by a foreign firm in Japan Bulldogs- foreign bonds in the United Kingdomg g g

EurobondsNot denominated in the local currency of the country in which they are issued Not denominated in the local currency of the country in which they are issued

Global Bonds


Bonds that are offered for sale in several different markets simultaneously

Private Debt (not publicly traded)( p y )

T L Term Loans: A bank loan that lasts for a specific term

Syndicated: funded by a group of banks rather than just one Syndicated: funded by a group of banks rather than just one

Revolving Line of Credit: credit commitment for specific period (2,3 years) that can be used as needed

Private Placements: Bond issue sold to small group of investors rather than the general public Bond issue sold to small group of investors rather than the general public

Private as compared to public debt: Private as compared to public debt: Less costly to issue (lower registration costs)

But also less liquid (but might be traded within financial institutions)


q ( g )

Other types of debt: Sovereign Debtyp g

D bt i d b ti l t Debt issued by national governments The U.S. treasury issues:

Treasury bills: pure discount bonds with maturities up to 26 weeks

Treasury Notes : semi-annual coupon bonds with maturities of 2 to y p10 years

Treasure bonds: semi-annual coupon bonds with maturities > 10 years

Long Bonds: those with longest outstanding maturities (currently 30 years)30 years)

TIPS (Treasury-Inflation-Protected Securities): inflation-indexed bond (the outstanding principal is adjusted for inflation)


V l i C ( d G ) B dValuing Corporate (and Government) Bonds

Yield to maturity (cost of debt!)y ( )

Definition: Definition: unique implicit discount rate r that makes the bond cash flows have

the value at its current price. Example: for a safe bond…

NN

rC

rC

rCP

)1(FV...

)1()1( 22

11

The IRR of investing in the bond, given its current price

Example:Safe bond without coupon with $ 100 000 of principal has a price of Safe bond without coupon with $ 100,000 of principal has a price of $ 96,618.36. The cash flows and the YTM is:

100 000

%

1

100,00096,618.36 (1 )

YTM


The YTM that solves the equation is 3.5%

Zero-coupon bondsp

Special type of bonds: They don’t pay coupons and therefore are always sold at a discount (lower

price than the principal), and are also called pure discount bond Treasury Bills: U.S. government bonds with maturities of less than one year Treasury Bills: U.S. government bonds with maturities of less than one year

The YTM of a zero-coupon bond maturing in n years, can be written as:1

1

n

nFVYTMP

Since a safe bond without coupon maturing in n years gives an interest without risk in that period YTM must be equal to the risk-free interest rate

P

without risk in that period, YTM must be equal to the risk-free interest rate What if not?


Coupon bondsp

These bonds: Pay, in addition to the principal, coupons Treasury notes: U.S. government bonds with maturities of one to ten years

T b d U S t b d ith t iti f t Treasury bonds: U.S. government bonds with maturities of over ten years

YTM of a bond with CPN annual coupons maturing in n years, is y s.t.

1 1 1 (1 ) (1 )

N N

FVP CPNy y y

Similarly, if we know YTM, we can calculate P (We specify P or YTM)Th d t f i YTM i th t it d t d d th i i l (t

(1 ) (1 ) N Ny y y

The advantage of using YTM is that it does not depend on the principal (to solve this prices are often given in percentage of the principal)


What is the YTM of the following bond?

A t b d A treasury bond… of $ 1,000 due in 5 years paying a nominal coupon of 10 5% paying a nominal coupon of 10.5% The market price is 1078.80

“Cash flows”:

C0 C1 C2 C3 C4 C5

-1078.80 105 105 105 105 1105

IRR f th CF 8 5%Albert Banal-Estanol Direcció Financera II - Chapter 3

IRR of these CF = 8.5%

Relationship between price and YTM

Questions: Questions: Why bonds traded at a discount have CPN < YTM? Can zero-coupon bonds trade at a premium? Can zero-coupon bonds trade at a premium?

Coupon rate often chosen so that trading initially at par but Coupon rate often chosen so that trading initially at par, but The price changes later because time to maturity changes And interest rates affect the YTM and the price


p

Dynamicsy

If the rest does not change, as time passes ...If the rest does not change, as time passes ... The YTM will not change

The price (discount or premium) approaches the parp ( p ) pp p

Example:p Zero coupon bond with a YTM of 5% and FV 100. Value:

14.23$)05.01(

100maturity) toyears 30( 30 P

5 years after, the value is)05.01(

53.29$)0501(

100maturity) toyears 25( 25 P

Notice that buying for $ 23.14 and selling to 29.53 after five years, IRR is: )05.01(

%51142353.29 5/1


14.23

Bond prices for a constant YTMp

f ?Albert Banal-Estanol Direcció Financera II - Chapter 3

Why the changes of non-zero coupon bonds are not smooth?

What happens if the YTM changes?pp g

If interest rates change in the economy If interest rates change in the economy ... Rates that investors demand for investing in bonds also change The price of the asset in the market also changes

Example: Zero coupon bond with a YTM of 5% and FV 100. Value:

If, suddenly, investors demand a 6%

14.23$)05.01(

100YTM)%5( 30 P

, sudde y, esto s de a d a 6%

In general41.17$

)06.01(100)%6( 30

YTMP

In general, ... A higher YTM reduces the present value of remaining cash flows If rates rise, the YTM rise and bond prices fall


p What types of bonds are more subject to fluctuations in the price?

YTM and price of a 30 year zero-30 year zero-coupon bond


Sensitivity to changes in interest rates 1600

1200

1400

800

1000

rice

400

600Pr

0

200

0 2 4 6 8 10 12 14

5 Year 9% Bond 1 Year 9% Bond


Interest rates

Sensitivity and its measurementy• We have that ...

• Long-term bonds are more sensitive to changes in interest rates than short-term bonds

• Similarly, bonds with higher coupon rates are less sensitive to changes in interest rates because they pay more upfront

• Duration of a bond:

• measures the price sensitivity to changes in interest rates

• ponders the years for their contribution to total present valueponders the years for their contribution to total present value

• average number of years of the discounted cash flows


Computing the “duration” of a bondp g

...PVTotal

)(3PVTotal

)(2PVTotal

)(1Duration 321

CPVCPVCPV

P i f h l P i f h l

PVTotalPVTotalPVTotal

Year Ct PV(Ct) al 2.75%Proportion of the total PV [PV(Ct)/Total PV]

Proportion of the total PV multiplied by year

1 55 53.53 0.049 0.0492 55 52.1 0.047 0.0943 55 50.7 0.046 0.1384 1055 946.51 0.858 3.433

Total PV = 1102.83 1 Duration= 3.714 years


Valuing safe bonds using arbitrageg g g

So far we focused on the relationship between price and YTM So far, we focused on the relationship between price and YTM Here, we should look at the price and YTM using similar bonds of known price

Price and yield of any safe bond with coupon? Price and yield of any safe bond with coupon? By arbitrage, (government) spot interest rates should give same return on cash flows Replicate cash flows of a coupon bond using zero coupon-spot interest rates

For example ... $ 1,000 bond paying 10% per year is equivalent to a portfolio of 3 zero-coupon bonds


Where do we get the spot interest rates from?

The yield curve (US): January 2005/05/06


What does it explain the different shapes of the three curves?

What would happen if the value was not $1153?pp $

At the starting point of the project (say 2012) the yields and price ofAt the starting point of the project (say, 2012), the yields and price of bonds without coupons (per each $100 of principal are)


The actual value depends on the year the project is started. Why?

Instead of prices, we can use YTMsp ,

The price should be equal to:

NN

N

YTMC

YTMC

YTMCP

)1(FV...

)1()1( 22

21

1

1

where YTMn is the YTM of a zero-coupon bond maturing on the same date

In the example

N )()()( 21

11531100100100P

Match the term of the cash flow and the term of the discount rate

1153)045.01()04.01()35.01( 321

P

An increase in interest rates decreases NPVs

Notice that the YTM of the bond is a (complexly) weighted average of the YTM of the zero-coupon bond with equal and shorter maturitiesp q

44.0 toequal is 1153)1(

1100)1(

100)1(

100321

y

yyy


Risky bond valuationRisky bond valuation

S f h l d i k f b d ( T bill ) So far we have valued risk-free bonds (e.g. Treasury bills)

Other bonds, like corporate bonds, issuer can default (credit risk):

The risk of insolvency changes price of a bond and YTM. How?

We should see that…

Investors pay less for bonds with credit risk than they would for an otherwise identical default-free bond

The yield of bonds with credit risk will be higher than that of otherwise identical default-free bonds


Example: two extremesp

No Default: 1-year zero coupon with a YTM of 4%: No Default: 1 year, zero coupon with a YTM of 4%:

1

1000 1000 $961.541 1.04

PYTM

Certain Default: issuer will pay 90% of obligation900 900 $865.38

1 1 04

P

YTM The yield to maturity in the second case is

11 1.04 YTM

10001 1 15 56%FVYTM

(we should use promised rather the actual cash flow) YTM higher than the expected return:

1 1 15.56%865.38

YTMP

YTM higher than the expected return:

%4138865

900

38.865Albert Banal-Estanol Direcció Financera II - Chapter 3

In reality: risk of defaulty One-year, $1000, zero-coupon bond 50%: repay face value in full /50%: default and receive $900 Because of uncertainty, the discount rate is 5.1% (1.1%

premium because default more likely if economy is weak)950 $903 90 P 10001 1 1063

FVYTM

Investors receive 10.63% at most. In the bad scenario:

$903.901.051

P 1 1 .1063903.90

YTMP

900

The average return is:%43.01

90.903900

g

Notice that lower YTM does not imply lower expected return%1.5%)43.0(5.0%)63.10(5.0

Notice that lower YTM does not imply lower expected return


Valuing corporate bonds using arbitrage

A bond of IBM: pays $ 115 every December for 5 years

S th t i J 2009 Suppose that we are in January 2009 In December 2013 it pays an additional $ 1,000 and bond is canceled. The bond rating is AAA (YTM in the WSJ for AAA bonds is 7 5%) The bond rating is AAA (YTM in the WSJ for AAA bonds is 7.5%)

Price Price

84.161,1$

0751115,1

0751115

0751115

0751115

0751115

5432 P 075.1075.1075.1075.1075.1 5432


D f l b bili i d V l Ri k (V R)Default probabilities and Value-at-Risk (VaR)

Ratings and financial ratiosg

Median of the ratings during three yearsMedian of the ratings during three years

(1998 – 2000).

Ratio AAA AA A BBB BB B CCCEBITDA / interests 21.4 10.1 6.1 3.7 2.1 0.8 0.1Return on capital % 34.9 21.7 19.4 13.6 11.6 6.6 1Gross margin % 27 22 1 18 6 15 4 15 9 11 9 11 9Gross margin % 27 22.1 18.6 15.4 15.9 11.9 11.9Total debt / capital % 22.9 37.7 42.5 48.2 62.6 74.8 87.7

Gross margin %= (revenue-cost of goods sold)/revenueg % ( g )

Return on capital= net operating profit divided by invested capital (value)


Credit scoring modelsg Companies more likely to go bankrupt, if they have…

Low return on assets and low interest coverage (EBIT/Interest exp) Low return on assets and low interest coverage (EBIT/Interest exp) How can we create a measure (score)?

M th d 1 S l i d Method 1: Solvency index: Draw straight line separating those who failed and those who do

not, so that there are few who default above and many below, y The solvency ratio (Z) is:

Z = return on assets + 5 x coverage of interestZ = return on assets + 5 x coverage of interest

Companies with Z> 5 considered "no problem“


Method 1: Solvency indexy8

6

7

%4

5

n as

sets

,Quebraron

No quebraron

2

3

Ret

urn

onZ=5D

0

1

2R

0-0.3 0.2 0.7 1.2

Interest coverage ratio


Method 2: Multiple discriminant analysisp y

N d t b t i t d t l t i bl No need to be restricted to only two variables This technique calculates how much weight should be placed on

each variable to separate the two groups “Altman” weights predict 95% of the bankruptcies:

+earningsRetained85capitalgNet workin72Z

T lSales1.0+

T lEquity.42+

T lEBIT3.1

+assets Total

g85.assets Total

pg.72=Z

PredictionIf Z 1 2 lik l t b k t

assetsTotalassetsTotalassetsTotal

If Z <1.2 likely to go bankrupt, If 1.2 <Z <2.9 not clear If Z> 2.9 likely to have no problems


y p

Market-based risk models

E ti t b bilit f t i b k t i Estimate probability of entering bankruptcy in a certain period using: Expected growth in the market value of its assets Variability of future asset values Face value and maturity of the debt

Applied to companies, countries, etc. …


Example: Worldcomp

The actual market value of the assets of WorldCom t it h d i l

90,000

assets, as it approached insolvency

60,000

70,000

80,000Market value of the assets

ns ·$

40,000

50,000

60,000

lue

mill

ion

Date of insolvency

10,000

20,000

30,000

Solvency level

Val

0

,

/09/20

01/01

/2001

/07/20

01/01

/2002

/02/20

02/03

/2002

/03/20

02/10

/2002

/07/20

02


27/09

11/01

12/07

15/01

21/02

28/03

05/03

06/10

19/07

Estimation of the probability of default in next year

Moody’s estimation of the probability of insolvency of

25

t WorldCom (index between 0.02 and 0.20)

20

of d

efau

ltne

xt y

ear

10

15

roba

bilit

y ur

ing

the

n

Date of

5

Pr du Date of insolvency

0

/09/20

01/01

/2001

/07/20

01/01

/2002

/02/20

02/03

/2002

/03/20

02/10

/2002

/07/20

02


27/09

11/01

12/07

15/01

21/02

28/03

05/03

06/10

19/07

Value at Risk (VaR)( )How much can I lose with a given probability and timeframe? Relatively new technique Relatively new technique Attempts to be a measure of risk Defines risk as "potential loss“

A li d t i t t ( t k b d ) Applied to any investment (stock, bonds,…) Now required by official standards e.g. for banks

Factors Value of assets Daily volatilityy y Days of prediction (k) Distribution of returns Likelihood of potential loss Likelihood of potential loss


Value at Risk (VaR)

B d d l f l ti f t & l tilit Based on a model of evolution of returns & volatility Predicts the evolution of future returns (cumulative k periods)

and calculates the expected loss with a given probabilityand calculates the expected loss with a given probability

VaR of a portfolio/asset on a horizon k for a probability p is:VaR of a portfolio/asset on a horizon k for a probability p is:

p = Pr [∆V (k) ≤ VaR]p [ ( ) ]

where ∆V (k) is the change in the value of the portfolio / asset


Value at Risk (VaR) of an asset( )

Specify a statistical process for the daily return of the asset Specify a statistical process for the daily return of the asset Calculate the distribution of future (cumulative) returns: rtN(μt, σ²t) Depending on μt and σ²

t , calculate the (conditional) distribution [k]r[k] = rt+1 + rt +2 + ... + rt+k

From this, calculate possible losses and their probabilities

Example 1: RISKMETRICS (JP Morgan)rtN(0, σ²t) and σ²t= ασ²t-1+(1-α)r²t-1

thenr[k] N(0,kσ²t+1)

Example 2: rtN(μ σ²)rtN(μ, σ )

then r[k] N(kμ,kσ²)


Examplep

You own a portfolio of $ 10 m in IBM stock IBM has a dailyYou own a portfolio of $ 10 m. in IBM stock. IBM has a daily volatility of 2%. Calculate the VaR for a period of 10 days at 99% (maximum loss at 1% probability)(expressed typically positive even if it is a loss)(expressed, typically, positive, even if it is a loss)

%32610020%74.140632.033.2intervals Confidence

%32.61002.010

621,473,1$000,000,101474.0 VaR


Value at Risk (VaR) of a portfolioWhat if you also have $ 5 billion of stock of AT & T, with daily

volatility of 1%. AT&T and IBM have a correlation of .7.Wh t i th V R f AT&T d f th bi d tf li ?What is the VaR of AT&T and of the combined portfolio?What is the benefit of diversification? (lower expected loss)

%01.50158.010

%58.131322+31+32

10

&2

&2222

portfolioTATIBMTATIBMportfolio

379,751,1$000,000,15$1168.0%1_%68.1105.033.2intervals Conficence

10

VaR

3797511$026,842,1$ e therefor405,368$y 621,473,1$ & TATIBM

V RSumVaRVaR

647,90$Var-Sumgainsation Diversific

379,751,1$

Portfolio

PortfolioVaR


C d i iCovenants and Repayment Provisions

Covenants and provisionsp Restrictive covenants

Limitations set by bondholders on the actions of the Corporation Limitations set by bondholders on the actions of the Corporation For example, covenants may: restrict the ability of management to

pay dividends, the level of further indebtedness or specify that the issuer must maintain a minimum amount of working capitalissuer must maintain a minimum amount of working capital

Repayment provisions:

Issuer can repurchase a fraction of the outstanding bonds in the Issuer can repurchase a fraction of the outstanding bonds in the market or make a tender offer for the entire issue

For callable bonds, exercise the call provision

Callable bonds:

Issuers have the right (but not the obligation) to retire all outstanding g ( g ) gbonds on (or after) a specific date (the call date), for the call price

Call a bond issue if interest rates lower -> lower price than in market!


Prices of callable (at par) and non-callable bonds on call date

f % fAlbert Banal-Estanol Direcció Financera II - Chapter 3

If callable and yield<5%, call and refinance at lower rate!

Prices of callable (at par) and non-callable bonds prior to call date


More bond terminologygy Sinking fund: company makes regular payments into a fund

d i i t d b t t th lif f th b dadministered by a trustee over the life of the bond These payments are then used to repurchase bonds.

Negative Pledge Clause: the processing of giving unsecured debentures equal protection and when assets are mortgaged

Poison Put: a clause that obliges the borrower to repay the bond if a large quantity of stock is bought by single investor, which

th fi b d t b t d t dcauses the firms bonds to beat down rated

Pay in kind (PIK): a bond that makes regular interest payments, ay d ( ) a bo d t at a es egu a te est pay e ts,but in the early years of the bonds life the issuer can choose to pay interest in cash or more bonds with an equivalent face value


Convertible Provisions

Convertible Bond Corporate bond with a provision that gives the bondholder an

ti t t it i t fi d b f h f t koption to convert it into a fixed number of shares of common stock

Conversion Ratio The number of shares received upon conversion of a convertible

bond, usually stated per $1000 of face value Conversion Price

The face value of a convertible bond divided by the number of The face value of a convertible bond divided by the number of shares received if the bond is converted


Examplep

You have a convertible bond with a $1000 face value and a conversion ratio of 15

If you convert bond into stock, you will receive 15 shares

If you do not convert, you will receive $1000 By converting you essentially “pay” $1000 for 15 shares, y g y y p y

implying a conversion price per share of $66.67. If the price of the stock exceeds $66.67, you will choose to

h i ill k h hconvert; otherwise, you will take the cash.


Convertible Bond Value


G b dGovernment bonds

Nominal and real interest rates

Nominal interest rate: the one that ...Nominal interest rate: the one that ... .. you pay when you borrow money ... specified in the contract is used to discount cash flows ... is used to discount cash flows

Real interest rate: the type ... of growth of your purchasing power after adjusting for inflation ... of growth of your purchasing power, after adjusting for inflation ... you are actually paying or obtaining, determined by funds’ supply/demand It is related to the actual productivity of the economy

The relationship between them:

irririirr

irr rrr

, thereforeand, 1

is that , 111


The nominal interest rate and the inflationReturn of the US Treasury Bills and the rate of inflation (1953-2003)

14

16

Treasury Bills

10

12 Inflation

6

8

%

2

4

-2

0

1953

1958

1963

1968

1973

1978

1983

1988

1993

1998

2003


Why do they appear to move together?

Determining real interest rates (Fisher 1930)SUPPLY OF FUNDS DEMAND FOR FUNDS

g ( )

Household savingsFamilies investments

(e.g. housing)

Companies savings(e.g. retained earnings)

Companies’ investment(e.g. equipment, facilities,

inventories)

Public surplus

inventories)

Public deficitIntermediari

es and financialp

Foreign savings Foreign credit= current account surplus

financial markets

= current account deficitp


Impact of an increase in public deficit? And of an increase in return on investments?

Term structure of interest rates (US): January 2005/05/06


What does it explain the different shapes of the three curves?

What determines the shape of the yield curve?

Basically the interest rates expectations: Basically the interest rates expectations: Suppose short-term are equal to long-term rates (curve is flat) If (all) interest rates are expected to rise in the future: invest short-term and reinvest later! Nobody would want to invest long term, so long-term rates should rise (curve increasing) And if they are expected to fall ... that would happen?

Decreasing (“inverted”) yield curve: It is expected that interest rates fall in future

As rates fall as the economy worsens is a negative projection As rates fall as the economy worsens is a negative projection

Increasing (“steep”) yield curve:g ( p ) y It is expected that interest rates will rise in future It can be interpreted as a positive economic projection


Graphical analyis

Assets with the same liquidity, risk and tax treatment, b t diff t t iti h diff t i ldbut different maturities have different yields

Interest rate

1 month 3 months 1 year 10 yersTerm to maturity


Level Change: Increase in expected inflation or level of activity

Higher interest rates!


Change of slope: tighter monetary policy g p g y p y

Monetary policy affects short-term rates!short-term rates!


Curve becomes negative: recession coming?g g

Change in interest expectations!expectations!


Short, long-term interest rates and spread (US)


Euro zone


The liquidity preference theoryq y p y

The expectations theory leaves out any type of riskp y y yp

Bond prices have some volatility, and this causes some risk, higher for longer-term bonds (creates a liquidity premium!)

Uncertainty about inflation is one of those risks (affecting nominal interest rate expectations). Therefore, if there is more uncertainty about inflation (or in ti f l til i fl ti ) li idit i ill b hi h d ill b ttimes of volatile inflation) liquidity premium will be higher and will be steeper

Investors incur extra risk (interest rate, not insolvency) to maintain long-term bonds so they demand a premium for liquidity Curve will normally be upwardbonds, so they demand a premium for liquidity. Curve will normally be upward sloping

Yield curve & capital budgetsYield curve & capital budgetsCash flows should be discounted using information from yield curveIf you trust in other theories ... use arbitration to your advantage


Value at Risk (VaR)Value at Risk (VaR)Diversification gains

700000

800000

500000

600000

300000

400000

100000

200000

-100000

0-1.5 -1 -0.5 0 0.5 1 1.5


Correlation between the two bonds

chapter 3: debt financing - albert...

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