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Chapter 5. Bonds, Bond Valuation, and Interest Rates. Topics in Chapter. Key features of bonds Bond valuation Measuring yield Assessing risk. Determinants of Intrinsic Value: The Cost of Debt. Net operating profit after taxes. Required investments in operating capital. −.

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Chapter 5

Chapter 5

Bonds, Bond Valuation, and Interest Rates


Topics in chapter
Topics in Chapter

  • Key features of bonds

  • Bond valuation

  • Measuring yield

  • Assessing risk


Determinants of Intrinsic Value: The Cost of Debt

Net operating

profit after taxes

Required investments

in operating capital

Free cash flow

(FCF)

=

FCF1

FCF2

FCF∞

...

Value = + + +

(1 + WACC)1

(1 + WACC)2

(1 + WACC)∞

Weighted average

cost of capital

(WACC)

Market interest rates

Firm’s debt/equity mix

Cost of debt

Cost of equity

Market risk aversion

Firm’s business risk


Interest rates interest bearing securities
Interest Rates & Interest-Bearing Securities

  • Interest rates:

    • Based on supply & demand for money

    • Driven by risk factors

    • Role of Federal Reserve

    • Basis Point

      • .01% or .0001


Risk term structure of interest rates

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

rd = Required rate of return on a debt security.

r* = Real risk-free rate.

IP = Inflation premium.

DRP = Default risk premium.

LP = Liquidity premium.

MRP = Maturity risk premium.

Risk & Term Structure of Interest Rates


Risk term structure
Risk & Term Structure

  • r = r* + IP + DRP + LP + MRP

  • r = nominal interest rate of a particular security (or required rate of return)

  • r* = real risk-free interest ratetypically 1-4% depending on monetary policyassumes expected inflation = zero

  • IP = Inflation premiumAve. inflation over life of bond

  • DRP = Default risk premiumCompensation for possible defaultFunction of bond ratings


Risk term structure1
Risk & Term Structure

  • r = r* + IP + DRP + LP + MRP

  • LP = Liquidity Premium Compensation for possible difficulty selling bond quickly at fair market value

  • MRP = Maturity Risk PremiumCompensation for possible loss in value due to increase in interest rates over maturity of bond. Affects longer maturities more than shorter.


Premiums added to r real risk free rate for different types of debt
Premiums Added to r* (real risk-free rate) for Different Types of Debt

  • ST Treasury:

    • only IP for ST inflation

  • LT Treasury:

    • IP for LT inflation, MRP

  • ST corporate:

    • ST IP, DRP, LP

  • LT corporate:

    • IP, DRP, MRP, LP


Inflation interest rates
Inflation & Interest Rates Types of Debt

  • Nominal Interest= 12%

    - Inflation -1%

    = Real Int. % =11%

    If inflation =

    & req’d real return =

    Then Nominal rate =? =

12%

  • 8%

    =4%

  • 8%

11%

=19%


Relationship b w nominal real interest rates inflation
Relationship b/w Nominal & Real Interest Rates, & Inflation

  • Nom = Real + Inflation

  • But, inflation not additive, it grows or compounds, so multiply

    • Nom = (Real) x (Infl)

    • And (1+Nom) = (1 + real) x (1 + infl)

    • Is better determinant; known as Fisher effect


Estimating inflation premium ip
Estimating Inflation Premium (IP)

  • Treasury Inflation-Protected Securities (TIPS) are indexed to inflation.

  • IP for a particular length maturity can be approximated as the difference between the yield on a non-indexed Treasury security of that maturity minus the yield on a TIPS of that maturity.


Bond spreads the drp and the lp
Bond Spreads, the DRP, and the LP

  • A “bond spread” is often calculated as the difference between a corporate bond’s yield and a Treasury security’s yield of the same maturity. Therefore:

    • Spread = DRP + LP.

  • Bond’s of large, strong companies often have very small LPs. Bond’s of small companies often have LPs as high as 2%.


Term structure yield curve
Term Structure Yield Curve

  • Term structure of interest rates: the relationship between interest rates (or yields) and maturities.

  • A graph of the term structure is called the yield curve.



What factors can explain shape of this yield curve
What factors can explain shape of this yield curve?

  • Upward slope due to:

    • Increasing expected inflation

    • Increasing maturity risk premium

  • What about liquidity & default risk?


Treasury vs corporate yield curves relationships
Treasury vs. Corporate Yield Curves relationships

  • Corp yield curves are higher than Treasuries, but not necessarily parallel.

  • Spread b/w the two yield curves widens as corporate bond rating decreases due to:

    • DRP & LP


Computing yields
Computing Yields

  • Estimate the inflation premium (IP) for each future year. This is the estimated average inflation over that time period.

  • Step 2: Estimate the maturity risk premium (MRP) for each future year.


Assume investors expect inflation to be 5 next year 6 the following year and 8 per year thereafter
Assume investors expect inflation to be 5% next year, 6% the following year, and 8% per year thereafter.

  • Step 1: Find the average expected inflation rate over years 1 to n:

    IP1 = 5%/1.0 = 5.00%.

    IP10 = [5 + 6 + 8(8)]/10 = 7.5%.

    IP20 = [5 + 6 + 8(18)]/20 = 7.75%.

    Must earn these IPs to break even versus inflation; that is, these IPs would permit you to earn r* (before taxes).


Step 2 find mrp based on this equation
Step 2: Find MRP based on this equation: following year, and 8% per year thereafter.

Assume the MRP is zero for Year 1 and increases by 0.1% each year.

MRPt = 0.1%(t - 1).

MRP1 = 0.1% x 0 = 0.0%.

MRP10 = 0.1% x 9 = 0.9%.

MRP20 = 0.1% x 19 = 1.9%.


Step 3: Add the IPs and MRPs to r*: following year, and 8% per year thereafter.

rRFt = r* + IPt + MRPt .

rRF = Quoted market interest

rate on treasury securities.

Assume r* = 3%:

rRF1 = 3% + 5% + 0.0% = 8.0%.

rRF10 = 3% + 7.5% + 0.9% = 11.4%.

rRF20 = 3% + 7.75% + 1.9% = 12.65%.


Upward vs downward sloping yield curves due to
Upward vs. Downward sloping yield curves due to? following year, and 8% per year thereafter.

  • Real risk-free rate = 3%

  • Expected inflation for

    • Year 1 =7%, Yr 2 = 5%; Yr 3 = 3%

  • What are interest rates for 1, 2, & 3 yr borrowings?


Interest rates mrp problem
Interest Rates & MRP problem following year, and 8% per year thereafter.

  • Assume the real risk-free rate (r*) is 4% and inflation is expected to be 7 percent in Year1; 4% in yr 2; and 3% thereafter. Assume all Treasury Bonds are highly liquid and free of default risk. If 2-yr and 5-yr T-Bonds both yield 11%, what is the difference in the maturity risk premiums (MRPs) on the two bonds; that is, what is MRP5 – MRP2?


Interest rates inflation problem
Interest Rates & Inflation Problem following year, and 8% per year thereafter.

  • Due to the recession, the rate of inflation expected for the coming year is only 3.5%. However, the rate of inflation in Yr 2 and thereafter is expected to be constant at some level above 3.5%. Assume the real risk-free rate (r*) = 2% for all maturities, and there are no maturity premiums. If 3-year T-Bonds yield 3% (0.03) more than the 1-year T-Bonds, what rate of inflation is expected after year 1?


Coupon bonds
Coupon Bonds following year, and 8% per year thereafter.

  • Bond = Debt = Borrowing

  • Fixed Maturity (Maturity Date) = N

  • Par Value=Face Value=Maturity Value=$1000=FV

  • Coupon Rate=Stated Rate (locked in in bond contract)

  • Coupon payment= Coupon rate x face value=PMT

  • Market Rate of interest = Yield to Maturity = rate used to discount bond CF’s = I

  • **PV cash flow of bonds always opposite sign of PMT & FV!!!


Bond perspectives
Bond Perspectives following year, and 8% per year thereafter.

Debt

Asset

Has $

Lender

Buyer or Investor

Bondholder

Creditor

Requires return to invest $ in bonds based on risk

Interest Received (earned) (Revenue) - pay tax on it

Capital Appreciation

  • Needs $

  • Borrower

  • Issuer or seller

  • Debtholder

  • Cost of borrowing

    • Interest Paid (Expense) – generates tax benefit (Svgs)

    • Cost of Debt

      • = Rd or Kd;

      • After-tax cost = Rd (1-t)


Key features of a bond
Key Features of a Bond following year, and 8% per year thereafter.

  • Par value: Face amount; paid at maturity. Assume $1,000.

  • Coupon interest rate: Stated interest rate. Multiply by par value to get dollars of interest. Generally fixed.

(More…)


Key features of a bond1
Key Features of a Bond following year, and 8% per year thereafter.

  • Maturity: Years until bond must be repaid. Declines.

  • Issue date: Date when bond was issued.

  • Default risk: Risk that issuer will not make interest or principal payments.


Value of financial security
Value of Financial Security following year, and 8% per year thereafter.

  • Value of any asset based on the net present value of the expected future cash flows discounted by the interest (discount) rate that reflects risk factors

  • Discount (interest rate) depends on:

    • Riskiness of CFs reflected by DRP, MRP, LP

    • General level of interest rates, which reflects inflation, supply & demand for $, production opportunities, time preferences for consumption


Value of a 10 year 10 coupon bond if r d 10

0 following year, and 8% per year thereafter.

1

2

10

Value of a 10-year, 10% coupon bond if rd = 10%

10%

...

V = ?

100

100

100 + 1,000

$100

$100

$1,000

V

=

.

.

.

+

+

+

B

(1 + rd)1

(1 + rd)N

(1 + rd)N

= $90.91 + . . . + $38.55 + $385.54

= $1,000.


The bond consists of a 10 year 10 annuity of 100 year plus a 1 000 lump sum at t 10

PV annuity following year, and 8% per year thereafter.

PV maturity value

Value of bond

$ 614.46

385.54

$1,000.00

=

=

=

INPUTS

10 10 100 1000

N I/YR PV PMT FV

-1,000

OUTPUT

The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10:


What would happen if expected inflation rose by 3 causing r 13

INPUTS following year, and 8% per year thereafter.

10 13 100 1000

N I/YR PV PMT FV

-837.21

OUTPUT

What would happen if expected inflation rose by 3%, causing r = 13%?

When market interest rate (rd)rises above coupon rate, bond’s value (PV or price) falls below par, so sells @ discount.


What happens if one year passes but the market i stays at 13

INPUTS following year, and 8% per year thereafter.

9 13 100 1000

N I/YR PV PMT FV

-846.05

OUTPUT

What happens if one year passes but the market i stays at 13%?


What happens if a second year passes but the market i stays at 13

INPUTS following year, and 8% per year thereafter.

8 13 100 1000

N I/YR PV PMT FV

-856.04

OUTPUT

What happens if a second year passes but the market i stays at 13%?


What happens if 9 years pass but the market i stays at 13

INPUTS following year, and 8% per year thereafter.

1 13 100 1000

N I/YR PV PMT FV

-973.45

OUTPUT

What happens if 9 years pass but the market i stays at 13%?

As a bond approaches maturity, it’s price approaches the face or maturity value of $1000


Bond pricing in excel
Bond Pricing in Excel following year, and 8% per year thereafter.


What would happen if inflation fell and r d declined to 7

INPUTS following year, and 8% per year thereafter.

10 7 100 1000

N I/YR PV PMT FV

-1,210.71

OUTPUT

What would happen if inflation fell, and rd declined to 7%?

If coupon rate > mrkt i% (rd), price rises above par, and bond sells at a premium.


Bond pricing in excel1
Bond Pricing in Excel following year, and 8% per year thereafter.

  • PV = ? $1210.71


Summary of bond price and interest rate relationships
Summary of Bond price and interest rate relationships following year, and 8% per year thereafter.

  • If market rate of interest increases above the stated (coupon) rate, then bond’s price falls and sells at discount

  • If market rate of interest drops below the stated (coupon) rate, then bond’s price increases and sells at a premium

  • **INVERSE RELATIONSHIP b/w Market i% and Bond’s PRICE!***


Bond prices changing interest rates
Bond prices & changing interest rates following year, and 8% per year thereafter.

  • Suppose the bond was issued 20 years ago and now has 10 years to maturity. What would happen to its value over time if required rate of return remained at 10%, or at 13%, or at 7%?


Bond value vs years remaining to maturity
Bond Value ($) vs Years remaining to Maturity following year, and 8% per year thereafter.

rd = 7%.

1,372

1,211

rd = 10%.

M

1,000

837

rd= 13%.

775

30 25 20 15 10 5 0


Bond price movements over time
Bond Price Movements over time following year, and 8% per year thereafter.

  • At maturity, value of any bond must equal its par value.

  • Value of a premium bond decreases to $1,000.

  • Value of a discount bond increases to $1,000.

  • A par bond stays at $1,000 if mrkt i% (rd)remains constant.


What s market value of 10 year 10 coupon bond when market 7

INPUTS following year, and 8% per year thereafter.

10 7 100 1000

N I/YR PV PMT FV

?

OUTPUT

What’s market value of 10 year 10% coupon bond when market = 7%?

Bond sells at a premium::

Price today = $1,210.71.


If you buy a 10 10 year bond today for 1 210 71 and hold it to maturity what s your rate of return

INPUTS following year, and 8% per year thereafter.

10 (1210.71) 100 1000

N I/YR PV PMT FV

?

OUTPUT

If you buy a 10%, 10 year bond today for $1,210.71, and hold it to maturity, what’s your rate of return?

Solve for i% = 7% = Yield to maturity (YTM)


What s yield to maturity
What’s “yield to maturity”? following year, and 8% per year thereafter.

  • YTM is rate of return earned on a bond held to maturity. Also called “promised yield.”

  • It assumes bond will not default.

  • Includes both interest pmt component & cap gains over bond’s life

  • Interest rate equating bond’s price today to NPV of PMTs & FV. (Think market rate of interest)

  • Vs. Annualized Return which reflects only a one-year holding period


Ytm on a 10 year 9 annual coupon 1 000 par value bond selling for 887

0 following year, and 8% per year thereafter.

1

9

10

rd=?

...

90

90

90

1,000

PV1

.

.

.

PV10

PVM

Find i % (rd) that “works”!

887

YTM on a 10-year, 9% annual coupon, $1,000 par value bond selling for $887


Find ytm i or r d
Find YTM ( following year, and 8% per year thereafter.i % or rd)

INT

INT

M

...

V

=

+

+

+

B

(1 + rd)N

(1 + rd)1

(1 + rd)N

1,000

90

90

...

887

=

+

+

+

(1 + rd)1

(1 + rd)N

(1 + rd)N

INPUTS

10 -887 90 1000

N I/YR PV PMT FV

10.91

OUTPUT


Ytm in excel
YTM in Excel following year, and 8% per year thereafter.


Bond prices int rates
Bond Prices & Int. Rates following year, and 8% per year thereafter.

  • If coupon rate < mrkt i % (rd), bond sells at a discount.

  • If coupon rate = i %, bond sells at its par value.

  • If coupon rate > i%, bond sells at a premium.

  • If market i% rises, price falls.

  • Price = par at maturity.


Find ytm if price were 1 134 20

INPUTS following year, and 8% per year thereafter.

10 -1134.2 90 1000

N I/YR PV PMT FV

7.08

OUTPUT

Find YTM if price were $1,134.20.

Sells at a premium. Because coupon = 9% > mrkt i% = 7.08%, bond’s value > par.


Definitions
Definitions following year, and 8% per year thereafter.

Current yield = “Interest Yield”

Capital gains yield =Change in value

= YTM = +

Exp total

return

Exp cap

gains yld

Exp

Curr yld


Definitions1
Definitions following year, and 8% per year thereafter.

Annual coupon pmt

Current price

Current yield =

Capital gains yield =

= YTM = +

Change in price

Beginning price

Exp total

return

Exp

Curr yld

Exp cap

gains yld


9 coupon 10 year bond p 887 and ytm 10 91

$90 following year, and 8% per year thereafter.

$887

Current yield =

= 0.1015 = 10.15%.

9% coupon, 10-year bond, P = $887, and YTM = 10.91%


Ytm current yield capital gains yield
YTM = Current yield + Capital gains yield. following year, and 8% per year thereafter.

Cap gains yield = YTM - Current yield

= 10.91% - 10.15%

= 0.76%.

Could also find values in Years 1 and 2,

get difference, and divide by value in

Year 1. Same answer.


Semiannual bonds

INPUTS following year, and 8% per year thereafter.

2N rd/2 OK INT/2 OK

N I/YR PV PMT FV

OUTPUT

Semiannual Bonds

1. Multiply years by 2 to get periods = 2N.

2. Divide nominal rate by 2 to get periodic rate = rd/2.

3. Divide annual INT by 2 to get PMT = INT/2.


Value of 10 year 10 coupon semiannual bond if rd 13

2(10) 13/2 100/2 following year, and 8% per year thereafter.

20 6.5 50 1000

N I/YR PV PMT FV

-834.72

INPUTS

OUTPUT

Value of 10-year, 10% coupon, semiannual bond if rd = 13%.


Spreadsheet functions for bond valuation
Spreadsheet Functions following year, and 8% per year thereafter.for Bond Valuation

  • PRICE

  • YIELD


Call provision
Call Provision following year, and 8% per year thereafter.

  • Issuer can refund if rates decline. That helps the issuer but hurts the investor.

  • Therefore, borrowers are willing to pay more, and lenders require more, on callable bonds.

  • Most bonds have a deferred call and a declining call premium

  • Yield to call: yearly rate of return earned on a bond until it’s called


Callable bonds and yield to call
Callable Bonds and Yield to Call following year, and 8% per year thereafter.

  • A 10-year, 10% semiannual coupon,$1,000 par value bond is selling for$1,135.90 with an 8% yield to maturity.It can be called after 5 years at $1,050.


Nominal yield to call ytc

INPUTS following year, and 8% per year thereafter.

10 -1135.9 50 1050

N I/YR PV PMT FV

3.765 x 2 = 7.53%

OUTPUT

Nominal Yield to Call (YTC)


If you bought bonds would you be more likely to earn ytm or ytc
If you bought bonds, would you be more likely to earn YTM or YTC?

  • Coupon rate = 10% vs. YTC = rd = 7.53%. Could raise money by selling new bonds which pay 7.53%.

  • Could thus replace bonds which pay $100/year with bonds that pay only $75.30/year.

  • Investors should expect a call, hence YTC = 7.53%, not YTM = 8%.


Investor returns on callable bonds
Investor returns on callable bonds YTC?

  • In general, if a bond sells at a premium, then coupon > market rate, so a call is likely.

  • So, investors expect to earn:

    • YTC on premium bonds.

    • YTM on par & discount bonds.


What s a sinking fund
What’s a sinking fund? YTC?

  • Provision to pay off a loan over its life rather than all at maturity.

  • Similar to amortization on a term loan.

  • Reduces risk to investor, shortens average maturity.

  • But not good for investors if rates decline after issuance.


Sinking funds are generally handled in 2 ways
Sinking funds are generally handled in 2 ways YTC?

  • Call x% at par per year for sinking fund purposes.

    • Call if rd is below the coupon rate and bond sells at a premium.

  • Buy bonds on open market.

    • Use open market purchase if rd is above coupon rate and bond sells at a discount.



Bond ratings and bond spreads yahoofinance march 2009
Bond Ratings and Bond Spreads YTC?(YahooFinance, March 2009)


What factors affect default risk and bond ratings
What factors affect default risk and bond ratings? YTC?

  • Financial ratios

    • Debt ratio

    • Coverage ratios, such as interest coverage ratio or EBITDA coverage ratio

    • Profitability ratios

    • Current ratios

(More…)



Other factors that affect bond ratings
Other Factors that Affect Bond Ratings YTC?

  • Provisions in the bond contract

    • Secured versus unsecured debt

    • Senior versus subordinated debt

    • Guarantee provisions

    • Sinking fund provisions

    • Debt maturity

(More…)


  • Other factors YTC?

    • Earnings stability

    • Regulatory environment

    • Potential product liability

    • Accounting policies


Interest rate or price risk for 1 year and 10 year 10 bonds
Interest rate (or price) risk for 1-year and 10-year 10% bonds

Interest rate risk: Rising mrkt i % (rd) causes bond’s price to fall.

10-year

i %

Change

Change

1-year

5%

$1,048

$1,386

38.6%

4.8%

10%

1,000

1,000

25.1%

4.4%

15%

956

749


Value

1,500 bonds

10-year

1-year

1,000

500

rd

0

0%

5%

10%

15%

Value


What is reinvestment rate risk
What is reinvestment rate risk? bonds

  • The risk that CFs will have to be reinvested at future lower rates, reducing income.

  • Illustration: Suppose you just won $500,000 playing the lottery. You’ll invest the money and live off interest. You buy a 1-year bond with a YTM of 10%.



The maturity risk premium
The Maturity Risk Premium reinvest.

  • Long-term bonds: High interest rate risk, low reinvestment rate risk.

  • Short-term bonds: Low interest rate risk, high reinvestment rate risk.

  • Nothing is riskless!

  • Yields on longer term bonds usually are greater than on shorter term bonds, so the MRP is more affected by interest rate risk than by reinvestment rate risk.


Other types of bonds
Other types of Bonds reinvest.

  • Zero coupon:

    • Pays no coupon & sells @ disct below par

  • Convertible:

    • To stock @fixed price @ bondholder’s option

  • Income:

    • Pays interest only if interest earned by issuer; won’t bankrupt co.


Other types of bonds1
Other types of Bonds reinvest.

  • Revenue:

    • Interest paid from revenue generated by project being financed by bonds

  • Floating rate:

    • Adjusts coupon rate periodically based on market interest rates


Bankruptcy
Bankruptcy reinvest.

  • Two main chapters of Federal Bankruptcy Act:

    • Chapter 11, Reorganization

    • Chapter 7, Liquidation

  • Typically, company wants Chapter 11, creditors may prefer Chapter 7.


  • If company can’t meet its obligations, it files under Chapter 11. That stops creditors from foreclosing, taking assets, and shutting down the business.

  • Company has 120 days to file a reorganization plan.

    • Court appoints a “trustee” to supervise reorganization.

    • Management usually stays in control.



If the company is liquidated here s the payment priority
If the company is liquidated, here’s the payment priority: is “worth more alive than dead.”

  • Past due property taxes

  • Secured creditors from sales of secured assets.

  • Trustee’s costs

  • Expenses incurred after bankruptcy filing

  • Wages and unpaid benefit contributions, subject to limits

  • Unsecured customer deposits, subject to limits

  • Taxes

  • Unfunded pension liabilities

  • Unsecured creditors

  • Preferred stock

  • Common stock


  • In a liquidation, unsecured creditors generally get zero. This makes them more willing to participate in reorganization even though their claims are greatly scaled back.

  • Various groups of creditors vote on the reorganization plan. If both the majority of the creditors and the judge approve, company “emerges” from bankruptcy with lower debts, reduced interest charges, and a chance for success.


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