Chapter 5
Bonds, Bond Valuation, and
Interest Rates
1
Topics in Chapter




Key features of bonds
Bond valuation
Measuring yield
Assessing risk
2
Determinants of Intrinsic Value: The Cost of Debt
Net operating
profit after taxes
Free cash flow
(FCF)
Value =
Required investments
in operating capital
−
=
FCF1
FCF2
FCF∞
... +
+
+
(1 + WACC)1
(1 + WACC)2
(1 + WACC)∞
Weighted average
cost of capital
(WACC)
Market interest rates
Cost of debt
Firm’s debt/equity mix
Market risk aversion
Cost of equity
Firm’s business risk
3
Interest Rates & InterestBearing Securities

Interest rates:

Based on supply & demand for money

Driven by risk factors

Role of Federal Reserve

Basis Point

.01% or .0001
4
Risk & Term Structure of
Interest Rates
rd = r* + IP + DRP + LP + MRP
rd
r*
IP
DRP
LP
MRP
= Required rate of return on a debt security.
=
=
=
=
=
Real risk-free rate.
Inflation premium.
Default risk premium.
Liquidity premium.
Maturity risk premium.
5
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 rate
typically 1-4% depending on monetary policy
assumes expected inflation = zero
IP = Inflation premium
Ave. inflation over life of bond
DRP = Default risk premium
Compensation for possible default
Function of bond ratings
6
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 Premium
Compensation for possible loss in value due
to increase in interest rates over maturity of
bond.
Affects longer maturities more than shorter.
7
Premiums Added to r* (real risk-free
rate) for Different Types of Debt

ST Treasury:


LT Treasury:


IP for LT inflation, MRP
ST corporate:


only IP for ST inflation
ST IP, DRP, LP
LT corporate:

IP, DRP, MRP, LP
8
Inflation & Interest Rates

Nominal Interest=
12%
- Inflation
-1%
= Real Int. %
=11%
If inflation =
& req’d real return =
Then Nominal rate =? =
12%
- 8%
=4%
8%
11%
=19%
9
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
10
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.
11
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%.
12
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.
13
Hypothetical Treasury Yield
Curve
14%
10%
MRP
IP
r*
8%
6%
4%
2%
19
17
15
13
11
9
7
5
3
0%
1
Interest Rate
12%
Years to Maturity
14
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?
15
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
16
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.
17
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).
18
Assume the MRP is zero for Year 1 and
increases by 0.1% each year.
Step 2: Find MRP based on
this
equation:
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*:
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?


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?
21
Interest Rates & MRP problem
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?

22
Interest Rates & Inflation Problem

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?
23
Coupon Bonds







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!!!
24
Bond Perspectives
Debt
Asset

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)




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
25
Key Features of a Bond


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…)
26
Key Features of a Bond



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.
27
Value of Financial Security


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
28
Value of a 10-year, 10%
coupon bond if rd = 10%
0
1
2
10%
V=?
VB =
10
...
100
$100
100
$100
100 + 1,000
$1,000
.
.
.
+
+
+
1
N
(1 + rd)
(1 + rd)
(1 + rd)N
= $90.91 +
= $1,000.
. . . + $38.55 + $385.54
29
The bond consists of a 10-year, 10%
annuity of $100/year plus a $1,000 lump
sum at t = 10:
PV annuity
PV maturity value
Value of bond
INPUTS
OUTPUT
10
N
10
I/YR
= $ 614.46
=
385.54
= $1,000.00
PV
-1,000
100
PMT
1000
FV
30
What would happen if expected inflation
rose by 3%, causing r = 13%?
INPUTS
OUTPUT
10
N
13
I/YR
PV
-837.21
100
PMT
1000
FV
When market interest rate (rd)rises above
coupon rate, bond’s value (PV or price)
falls below par, so sells @ discount.
31
What happens if one year passes but the
market i stays at 13%?
INPUTS
OUTPUT
9
N
13
I/YR
PV
-846.05
100
PMT
1000
FV
32
What happens if a second year passes but
the market i stays at 13%?
INPUTS
OUTPUT
8
N
13
I/YR
PV
-856.04
100
PMT
1000
FV
33
What happens if 9 years pass but the
market i stays at 13%?
INPUTS
OUTPUT
1
N
13
I/YR
PV
-973.45
100
PMT
1000
FV
As a bond approaches maturity, it’s price
approaches the face or maturity value of $1000
34
Bond Pricing in Excel
Years to Mat:
Coupon rate:
Annual Pmt:
Par value = FV:
Going rate, rd:
10
10%
$100
$1,000
10%
35
What would happen if inflation
fell, and rd declined to 7%?
INPUTS
OUTPUT
10
N
7
I/YR
PV
-1,210.71
100
PMT
1000
FV
If coupon rate > mrkt i% (rd), price rises
above par, and bond sells at a premium.
36
Bond Pricing in Excel

Years to Mat:
10
Coupon rate:
10%
Annual Pmt:
$100
Par value = FV:
Going rate, rd:
PV = ? $1210.71
$1,000
7%
37
Summary of Bond price and
interest rate relationships



If market rate of interest increases
above the stated (coupon) rate, then
bond’s price falls and sells at discount
If market rate of interest drops below
the stated (coupon) rate, then bond’s
price increases and sells at a premium
**INVERSE RELATIONSHIP b/w Market
i% and Bond’s PRICE!***
38
Bond prices & changing
interest rates

Suppose the bond was issued 20 years
ago and now has 10 years to maturity.
What would happen to its value over
time if required rate of return remained
at 10%, or at 13%, or at 7%?
39
Bond Value ($) vs Years
remaining to Maturity
1,372
1,211
rd = 7%.
rd = 10%.
1,000
M
837
rd = 13%.
775
30
25
20
15
10
5
0
40
Bond Price Movements over time




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.
41
What’s market value of 10 year 10%
coupon bond when market = 7%?
INPUTS
OUTPUT
10
N
7
I/YR
PV
?
100
PMT
1000
FV
Bond sells at a premium::
Price today = $1,210.71.
42
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
OUTPUT
10
N
(1210.71) 100 1000
I/YR
PV
PMT
FV
?
Solve for i% = 7% = Yield to maturity
(YTM)
43
What’s “yield to maturity”?





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 oneyear holding period
44
YTM on a 10-year, 9% annual coupon,
$1,000 par value bond selling for $887
0
rd=?
1
887
10
...
90
PV1
.
.
.
PV10
PVM
9
90
90
1,000
Find i % (rd) that “works”!
45
Find YTM (i % or rd)
VB =
INT
INT
M
... +
+
+
N
1
(1 + rd)
(1 + rd)
(1 + rd)N
1,000
90
90
...
887 =
+
+
+
1
N
(1 + rd)
(1 + rd) (1 + rd)N
INPUTS
OUTPUT
10
N
I/YR
10.91
-887
PV
90
PMT
1000
FV
46
YTM in Excel
Years to Mat:
10
Coupon rate:
9%
Annual Pmt:
$90.00
Current price:
Par value = FV:
$887.00
$1,000.00
47
Bond Prices & Int. Rates





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.
48
Find YTM if price were
$1,134.20.
INPUTS 10
N
OUTPUT
I/YR
7.08
-1134.2 90
PV
PMT
1000
FV
Sells at a premium. Because
coupon = 9% > mrkt i% =
7.08%, bond’s value > par.
49
Definitions
Current yield = “Interest Yield”
Capital gains yield =Change in value
Exp total = YTM = Exp
+ Exp cap
return
gains yld
Curr yld
50
Definitions
Current yield =
Annual coupon pmt
Current price
Capital gains yield =
Exp total
return
Change in price
Beginning price
Exp
Exp cap
= YTM =
+
Curr yld
gains yld
51
9% coupon, 10-year bond, P =
$887, and YTM = 10.91%
Current yield
$90
= $887
= 0.1015 = 10.15%.
52
YTM = Current yield + Capital
gains yield.
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.
53
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.
INPUTS
2N
N
rd/2
I/YR
OK
PV
INT/2
PMT
OK
FV
OUTPUT
54
Value of 10-year, 10% coupon,
semiannual bond if rd = 13%.
2(10)
INPUTS
20
N
OUTPUT
13/2
6.5
I/YR
PV
-834.72
100/2
50
PMT
1000
FV
55
Spreadsheet Functions
for Bond Valuation


PRICE
YIELD
56
Call Provision




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
57
Callable Bonds and Yield to
Call

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.
58
Nominal Yield to Call (YTC)
INPUTS 10
N
OUTPUT
-1135.9 50
I/YR
PV
PMT
3.765 x 2 = 7.53%
1050
FV
59
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%.
60
Investor returns on callable
bonds


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.
61
What’s a sinking fund?




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.
62
Sinking funds are generally
handled in 2 ways

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.
63
Bond Ratings
S&P and Fitch Moody’s
% defaulting within:
1 yr.
5 yrs.
Investment grade bonds:
AAA
Aaa
0.0
0.0
AA
Aa
0.0
0.1
A
A
0.1
0.6
BBB
Baa
0.3
2.9
BB
Ba
1.4
8.2
B
B
1.8
9.2
CCC
Caa
22.3
36.9
Junk bonds:
Source: Fitch Ratings
64
Bond Ratings and Bond
Spreads (YahooFinance, March 2009)
Long-term Bonds
10-Year T-bond
AAA
AA
A
BBB
BB
B
CCC
Yield (%)
Spread (%)
2.68
5.50
5.62
5.79
7.53
11.62
13.70
26.30
2.82
2.94
3.11
4.85
8.94
11.02
23.62
65
What factors affect default risk
and bond ratings?

Financial ratios




Debt ratio
Coverage ratios, such as interest coverage
ratio or EBITDA coverage ratio
Profitability ratios
Current ratios
(More…)
66
Bond Ratings Median Ratios
(S&P)
AAA
AA
A
BBB
BB
B
CCC
Interest
coverage
23.8
19.5
8.0
4.7
2.5
1.2
0.4
Return on
capital
27.6%
27.0%
17.5%
13.4%
11.3%
8.7%
3.2%
Debt to
capital
12.4%
28.3%
37.5%
42.5%
53.7%
75.9%
113.5%
67
Other Factors that Affect Bond
Ratings

Provisions in the bond contract





Secured versus unsecured debt
Senior versus subordinated debt
Guarantee provisions
Sinking fund provisions
Debt maturity
(More…)
68

Other factors




Earnings stability
Regulatory environment
Potential product liability
Accounting policies
69
Interest rate (or price) risk for 1year and 10-year 10% bonds
Interest rate risk: Rising mrkt i %
(rd) causes bond’s price to fall.
i % 1-year Change 10-year Change
5% $1,048
10%
1,000
15%
956
4.8%
4.4%
$1,386
1,000
749
38.6%
25.1%
70
Value
1,500
10-year
1-year
1,000
500
rd
0
0%
5%
10%
15%
71
What is reinvestment rate
risk?


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%.
72


Year 1 income = $50,000. At year-end
get back $500,000 to reinvest.
If rates fall to 3%, income will drop
from $50,000 to $15,000. Had you
bought 30-year bonds, income would
have remained constant.
73
The Maturity Risk Premium




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.
74
Other types of Bonds

Zero coupon:


Convertible:


Pays no coupon & sells @ disct below par
To stock @fixed price @ bondholder’s option
Income:

Pays interest only if interest earned by issuer;
won’t bankrupt co.
75
Other types of Bonds

Revenue:


Interest paid from revenue generated by project
being financed by bonds
Floating rate:

Adjusts coupon rate periodically based on
market interest rates
76
Bankruptcy

Two main chapters of Federal
Bankruptcy Act:



Chapter 11, Reorganization
Chapter 7, Liquidation
Typically, company wants Chapter 11,
creditors may prefer Chapter 7.
77


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.
78


Company must demonstrate in its
reorganization plan that it is “worth
more alive than dead.”
Otherwise, judge will order liquidation
under Chapter 7.
79
If the company is liquidated,
here’s the payment priority:











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
80


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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