1. Bonds, Bond Valuation, and Interest Rates
Chapter 5
Bonds, Bond Valuation, and Interest Rates

2. Topics in Chapter Key features of bonds Bond valuation Measuring yield
Assessing risk

3. 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)∞
For value box in Ch 4 time value FM13.
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

4. Interest Rates & Interest-Bearing Securities
Based on supply & demand for money
Driven by risk factors
Role of Federal Reserve
Basis Point
.01% or

5. 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.

6. 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

7. 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.

8. 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

9. Inflation & Interest Rates
Nominal Interest= %
- Inflation -1%
= Real Int. % =11%
If inflation =
& req’d real return =
Then Nominal rate =? =
12% 8%
=4% 8%
11%
=19%

10. 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

11. 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.

12. 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%.

13. 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.

14. Hypothetical Treasury Yield Curve

15. 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?

16. 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

17. 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.

18. 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 = [ (8)]/10 = 7.5%.
IP20 = [ (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).

19. Step 2: Find MRP based on this equation:
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%.

20. 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% % + 1.9% = 12.65%.

21. 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?

22. 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?

23. 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?

24. 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!!!

25. 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

26. 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…)

27. 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.

28. 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

29. Value of a 10-year, 10% coupon bond if rd = 10%1 2 10
10%
...
V = ?
100
100
,000
$100
$100
$1,000 V = + . . . + + B
(1 + rd)1
(1 + rd)N
(1 + rd)N
= $ $ $385.54
= $1,000.

30. The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10:
N I/YR PV PMT FV
-1,000 $
385.54
$1,000.00
PV annuity
PV maturity value
Value of bond =
INPUTS
OUTPUT

31. What would happen if expected inflation rose by 3%, causing r = 13%?
N I/YR PV PMT FV
INPUTS
OUTPUT
When market interest rate (rd)rises above coupon rate, bond’s value (PV or price) falls below par, so discount.

32. What happens if one year passes but the market i stays at 13%?
N I/YR PV PMT FV
INPUTS
OUTPUT

33. What happens if a second year passes but the market i stays at 13%?
N I/YR PV PMT FV
INPUTS
OUTPUT

34. What happens if 9 years pass but the market i stays at 13%?
N I/YR PV PMT FV
INPUTS
OUTPUT
As a bond approaches maturity, it’s price approaches the face or maturity value of $1000

35. Bond Pricing in Excel

36. What would happen if inflation fell, and rd declined to 7%?
N I/YR PV PMT FV
-1,210.71
INPUTS
OUTPUT
If coupon rate > mrkt i% (rd), price rises above par, and bond sells at a premium.

37. Bond Pricing in Excel PV = ? $1210.71 Years to Mat: 10 Coupon rate:
10%
Annual Pmt:
$100
Par value = FV:
$1,000
Going rate, rd: 7%

38. 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!***

39. 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%?

40. Bond Value ($) vs Years remaining to Maturity
1,372
rd = 7%.
1,211
rd = 10%. M
1,000
837
rd = 13%.
775

41. 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.

42. What’s market value of 10 year 10% coupon bond when market = 7%?
N I/YR PV PMT FV ?
INPUTS
OUTPUT
Bond sells at a premium::
Price today = $1,

43. If you buy a 10%, 10 year bond today for $1,210
If you buy a 10%, 10 year bond today for $1,210.71, and hold it to maturity, what’s your rate of return?
( )
N I/YR PV PMT FV ?
INPUTS
OUTPUT
Solve for i% = 7% = Yield to maturity (YTM)

44. 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 one-year holding period

45. Find i % (rd) that “works”! ...
YTM on a 10-year, 9% annual coupon, $1,000 par value bond selling for $887 90 1 9 10
rd=?
1,000
PV1 .
PV10
PVM
887
Find i % (rd) that “works”!
...

46. Find YTM (i % or rd)             ... ... INT INT M V = + +B     
(1 + rd)1
(1 + rd)N
(1 + rd)N 90
1,000
... 90
887 = + + +      
(1 + rd)1
(1 + rd)N
(1 + rd)N
INPUTS
N I/YR PV PMT FV
10.91
OUTPUT

47. YTM in Excel Years to Mat: 10 Coupon rate: 9% Annual Pmt: $90.00
Current price:
$887.00
Par value = FV:
$1,000.00

48. 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.

49. Find YTM if price were $1,
N I/YR PV PMT FV
7.08
INPUTS
OUTPUT
Sells at a premium. Because coupon = 9% > mrkt i% = 7.08%, bond’s value > par.

50. Definitions Current yield = “Interest Yield”
Capital gains yield =Change in value
= YTM =
Exp total
return
Exp cap
gains yld
Exp
Curr yld

51. Definitions 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

52. 9% coupon, 10-year bond, P = $887, and YTM = 10.91%
Current yield =
= = 10.15%.
$90
$887

53. YTM = Current yield + Capital gains yield.
Cap gains yield = YTM - Current yield
= 10.91% %
= 0.76%.
Could also find values in Years 1 and 2,
get difference, and divide by value in
Year 1. Same answer.

54. 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.
2N rd/ OK INT/2 OK
N I/YR PV PMT FV
INPUTS
OUTPUT

55. Value of 10-year, 10% coupon, semiannual bond if rd = 13%.
2(10) 13/ /2
N I/YR PV PMT FV
INPUTS
OUTPUT

56. Spreadsheet Functions for Bond Valuation
PRICE
YIELD

57. 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

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

59. Nominal Yield to Call (YTC)
N I/YR PV PMT FV
3.765 x 2 = 7.53%
INPUTS
OUTPUT

60. 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%.

61. 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.

62. 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.

63. 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.

64. Bond Ratings % defaulting within: S&P and Fitch Moody’s 1 yr. 5 yrs.
Investment grade bonds:
AAA
Aaa
0.0 AA Aa
0.1 A
0.6
BBB
Baa
0.3
2.9
Junk bonds: BB Ba
1.4
8.2 B
1.8
9.2
CCC
Caa
22.3
36.9
Source: Fitch Ratings

65. Bond Ratings and Bond Spreads (YahooFinance, March 2009)
Long-term Bonds
Yield (%)
Spread (%)
10-Year T-bond
2.68
AAA
5.50
2.82 AA
5.62
2.94 A
5.79
3.11
BBB
7.53
4.85 BB
11.62
8.94 B
13.70
11.02
CCC
26.30
23.62

66. 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…)

67. Bond Ratings Median Ratios (S&P)
Interest coverage
Return on capital
Debt to capital
AAA
23.8
27.6%
12.4% AA
19.5
27.0%
28.3% A
8.0
17.5%
37.5%
BBB
4.7
13.4%
42.5% BB
2.5
11.3%
53.7% B
1.2
8.7%
75.9%
CCC
0.4
3.2%
113.5%

68. 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…)

69. Other factors Earnings stability Regulatory environment
Potential product liability
Accounting policies

70. 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.
i %
10-year
1-year
Change
Change 5%
$1,048
$1,386
38.6%
4.8%
10%
1,000
1,000
25.1%
4.4%
15%
956
749

71. Value
500
1,000
1,500 0% 5%
10%
15%
1-year
10-year rd

72. 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%.

73. 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.

74. 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.

75. Other types of Bonds Zero coupon: Convertible: Income:
Pays no coupon & disct below par
Convertible:
To bondholder’s option
Income:
Pays interest only if interest earned by issuer; won’t bankrupt co.

76. Other types of Bonds Revenue: Floating rate:
Interest paid from revenue generated by project being financed by bonds
Floating rate:
Adjusts coupon rate periodically based on market interest rates

77. Bankruptcy Two main chapters of Federal Bankruptcy Act:
Chapter 11, Reorganization
Chapter 7, Liquidation
Typically, company wants Chapter 11, creditors may prefer Chapter 7.

78. Company has 120 days to file a reorganization plan.
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.

79. Company must demonstrate in its reorganization plan that it is “worth more alive than dead.”
Otherwise, judge will order liquidation under Chapter 7.

80. 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

81. In a liquidation, unsecured creditors generally get zero
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.