1. Bonds and Their Valuation
Chapter 7
Bonds and Their Valuation
Key Features of Bonds Bond Valuation Measuring Yield Assessing Risk

2. What is a bond?
A long-term debt instrument in which a borrower agrees to make payments of principal & interest, on specific dates, to the holders of the bond.
Treasury bonds
Corporate bonds
Foreign bonds
Treasury bonds are issued by the government. Have no or low default risk

3. Bond Markets Primarily traded in the over-the-counter (OTC) market
Most bonds are owned by and traded among large financial institutions.
Default risk is often referred to as “credit risk”
Changes and affect the bond price

4. Key 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 value 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 (YTM): rate of return earned on a bond held until maturity
also called the “promised yield”
Fixed-rate bonds
Floating-rate bonds (interest rate I adjusted every 6 months)
Zero-coupon bonds: pay no interest-sold at discount

5. Why are they called coupons?

6. Effect of a Call Provision
Allows issuer to refund the bond issue if rates decline
Helps the issuer, but hurts the investor
Borrowers are willing to pay more, and lenders require more, for callable bonds.
Most bonds have a deferred call & a declining call premium.

7. What is 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

8. How are sinking funds executed?
Call x% of the issue at par, for sinking fund purposes
Likely to be used if rd is below the coupon rate and the bond sells at a premium.
Buy bonds in the open market.
Likely to be used if rd is above the coupon rate and the bond sells at a discount.

9. The Value of Financial Assets1 2 N r%
CF1
CFN
CF2
Value
...
The value of any financial assets is the present value if the cash flow expected from the asset
A bond is valued as the present value of the stream of interest payment plus the present value of the par value that is received on the bond maturity date
What is the value of any asset?
What are the CFs? R% is a function of risk? INT

10. Other Types (Features) of Bonds
Convertible bond – may be exchanged for common stock of the firm, at the holder’s option.
Warrant – long-term option to buy a stated number of shares of common stock at a specified price.
Putable bond – allows holder to sell the bond back to the company prior to maturity.
Income bond – pays interest only when interest is earned by the firm.
Indexed bond – interest rate paid is based upon the rate of inflation.

11. What is the opportunity cost of debt capital?
The discount rate (rd) is the Opportunity Cost of capital
The rate that could be earned on alternative investments of equal risk
Market rate of interest in the bond
rd = r* + IP + MRP + DRP + LP
When equal to coupon rate, the bond sells as par

12. What is the value of a 10-year, 10% annual coupon bond, if rd = 10%?1 2 N
10%
100
,000
VB = ?
...

13. Calculating the Value of a Bond
This bond has a $1,000 lump sum (the par value) due at maturity (t = 10), and annual $100 coupon payments beginning at t = 1 and continuing through t = 10, the price of the bond can be found by solving for the PV of these cash flows.
Excel: =PV(.10,10,100,1000)
INPUTS
OUTPUT N
I/YR
PMT PV FV 10
100
-1000
1000
When Price (PV) = Par value we say the bond is selling at par. This happens when I% or r% = Coupon I%
When a bond is issued its coupon interest rate is set equal to the market rate which makes its price equal to par

14. Premium bond
What’s the value of its 10-year bonds outstanding with the same risk but a 13% annual coupon rate?
The annual coupon payment is $130
The same YTM as the previous bond (10%)
This bond sells at a premium because:
the coupon rate > the yield to maturity.
Excel: =PV(.10,10,130,1000)
INPUTS
OUTPUT N
I/YR
PMT PV FV 10
130
1000

15. Discount bond
What’s the value of its 10-year bonds outstanding with the same risk but a 7% annual coupon rate?
The annual coupon payment is $70.
The same YTM as the previous bond (10%)
This bond sells at a discount because:
the coupon rate < the yield to maturity
Excel: =PV(.10,10,70,1000)
INPUTS
OUTPUT N
I/YR
PMT PV FV 10 70
1000

16. Changes in Bond Value over Time
What would happen to the value of these three bonds if the required rate of return remained at 10%?
Years
to Maturity
1,184
1,000
816 10
13% coupon rate
7% coupon rate
10% coupon rate VB 5
Why is the value of the bond affected by the r%?
Why does it sell at a premium or a discount based on its coupon rate?

17. Bond Values over Time
At maturity, the value of any bond must equal its par value.
If rd 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.
The value of a par bond stays at $1,000.

18. Example

19. What is the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $887?
Must find the rd that solves this model.
Again what is YTM?

20. Solving for the YTM Solving for I/YR, the YTM of this bond is 10.91%.
This bond sells at a discount,
because YTM > coupon rate
Excel: =RATE(10,90,-887,1000)
INPUTS
OUTPUT N
I/YR
PMT PV FV 10
-887 90
10.91
1000

21. Find YTM If the Bond Price is $1,134.20
Solving for I/YR, the YTM of this bond is 7.08%.
This bond sells at a premium,
because YTM < coupon rate
Excel: =RATE(10,90, ,1000)
INPUTS
OUTPUT N
I/YR
PMT PV FV 10 90
7.08
1000

22. Yield to Maturity (YTM)
Bond promised rate of return: The return investor will receive if all the promised payments are made
YTM changes as the interest rates change
If you buy a bond on its issuance date & hold it till maturity you will receive the YTM calculated on the purchase date
If you buy a bond later on, the YTM will depend on your purchase price
YTM equals to expected rate of return only when:
Probability of default is zero & the bond is not callable

23. In the absence of default risk & assuming market equilibrium
Definitions
Why is it expected? Because a company could default on its payments?
In the absence of default risk & assuming market equilibrium

24. An Example: Current & Capital Gains Yields
Find the current yield and the capital gains yield for a 10-year, 9% annual coupon bond that sells for $887 & has a face value of $1,000.

25. Calculating Capital Gains Yield
YTM = Current yield + Capital gains yield Could also find the expected price one year from now & divide the change in price by the beginning price, which gives the same answer.

26. Example

27. What is price risk? Does a 1-year or 10-year bond have more price risk?
Price risk is the concern that rising rd will cause the value of a bond to fall.
rd 1-year Change 10-year Change
5% $1,048 $1,386
10% 1, ,000
15%
The 10-year bond is more sensitive to interest rate changes, and hence has more price risk.
+ 4.8%
– 4.4%
+38.6%
–25.1%
Why does the value of the bond decrease if interest rates go up

28. Why does the value of the bond decrease if interest rates go up?

29. Why does a longer-term bond have more sensitivity to interest rate movements (higher interest rate risk) than shorter-term bonds?
Because given higher interest rates the paid principal at the end is discounted over many years so its worth less given the higher interest rates
Alternatively, it is worth less because I can take the money and invest instead in a higher interest rate bond

30. Illustrating Price Risk
Value ($)
10-Year Bond
1-Year Bond
YTM(%)

31. Illustrating Price Risk

32. Example

33. What is Price risk?
The risk if decline in price in a bond’s price due to increase in interest rate “Called interest rate risk “
Relates to the current market value of bond portfolio
Rising in interest rate cause losses to bondholders
Higher in bonds that have longer maturities
For bond with similar coupons, the longer bond maturities the more its price changes in response to a given change in interest rate

34. What is reinvestment risk?
The risk of income decline due to drop in interest rate
Relates to the income of portfolio
Reinvestment risk is the concern that rd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income.
EXAMPLE:
Suppose you just won $500,000 playing the lottery. You intend to invest the money and live off the interest.

35. Reinvestment Risk Example
You may invest in either a 10-year bond or a series of ten 1-year bonds.
Both 10-year and 1-year bonds currently yield 10%.
If you choose the 1-year bond strategy:
After Year 1, you receive $50,000 in income and have $500,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to $15,000.
If you choose the 10-year bond strategy:
You can lock in a 10% interest rate, and $50,000 annual income for 10 years, assuming the bond is not callable.

36. Conclusions about Price Risk & Reinvestment Risk
Short -
term
AND/OR
High
coupon
Bonds
Long
Low
Price risk
Reinvestment risk
If you are a retiree living off your interest income, you want to minimize your reinvestment risk
Someone who needs the money one year from now is not concerned with reinvestment risk, but the value of his bond when he wants to sell it
CONCLUSION: Nothing is riskless!
Risk depend on investment horizon

37. Semiannual Bonds Multiply years by 2: Number of periods = 2N
Divide nominal rate by 2: Periodic rate (I/YR) = rd/2
Divide annual coupon by 2: PMT = Annual coupon/2
INPUTS
OUTPUT N
I/YR
PMT PV FV 2N OK
cpn/2
rd/2
If we have bonds that make semi-annual payments, what should we do to the number of periods and the interest rate?

38. What is the value of a 10-year, 10% semiannual coupon bond, if rd = 13%?
Multiply years by 2: N = 2 x 10 = 20
Divide nominal rate by 2: I/YR = 13/2 = 6.5
Divide annual coupon by 2: PMT = 100/2 = 50
Excel: =PV(.065,20,50,1000)
INPUTS
OUTPUT N
I/YR
PMT PV FV 20 50
6.5
1000

39. Annual Coupon Vs. Semiannual Coupon
Would you prefer to buy a 10-year, 10% annual coupon bond or a 10-year, 10% semiannual coupon bond, all else equal?
The semiannual bond’s effective rate is:
Excel: =EFFECT(.10,2) = 10.25%
10.25% > 10% (the annual bond’s effective rate), so you would prefer the semiannual bond.

40. Example
If the proper price for this semiannual bond is $1,000, what would be the proper price for the annual coupon bond?
The semiannual bond has a 10.25% effective rate, so the annual bond should earn the same EAR. At these prices, the annual and semiannual bonds are in equilibrium.
Excel: =PV(.1025,10,100,1000)
INPUTS
OUTPUT N
I/YR
PMT PV FV 10
100
10.25
1000

41. Example

42. Yield to Call (YTC)
If a company calls its bonds, investors will not earn YTM. Instead, they will earn Yield to Call (YTC).
This will happen if interest rates are below the coupon rate.
rd is YTC

43. Example
A 10-year, 10% semiannual coupon bond selling for $1, can be called in 4 years for $1,050, what is its yield to call (YTC)?
The bond’s yield to maturity is 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.
Excel: =RATE(8,50, ,1050)
INPUTS
OUTPUT N
I/YR
PMT PV FV 8 50
3.568
1050

44. Yield to Call 3.568% represents the periodic semiannual yield to call
YTCNOM = rNOM = 3.568% x 2 = 7.137% is the rate that a broker would quote
The effective yield to call can be calculated.
YTCEFF = ( )2 – 1 = 7.26%
Excel: =EFFECT(.07137,2)
= 7.26%

45. If you bought these callable bonds, would you be more likely to earn the YTM or YTC?
The coupon rate = 10% compared to YTC = 7.137%. The firm could raise money by selling new bonds which pay 7.137%.
Could replace bonds paying $100 per year with bonds paying only $71.37 per year.
Investors should expect a call, and to earn the YTC of 7.137%, rather than the YTM of 8%.

46. When is a call more likely to occur?
In general, if a bond sells at a premium, then:
coupon > rd,
so a call is more likely.
So, expect to earn:
YTC on premium bonds.
YTM on par and discount bonds.

47. If you buy a callable bond & interest rates decline, will the value of your bond rise as much as it would have risen if the bond was not callable?

48. Example

49. Example

50. Default Risk
If an issuer defaults, investors receive less than the promised return
Therefore, the expected return on corporate bonds is less than the promised return
Influenced by the issuer’s financial strength and the terms of the bond contract.

51. Types of Bonds Mortgage bonds Debentures Subordinated debentures
Investment-grade bonds
Junk bonds

52. Evaluating Default Risk: Bond Ratings
Investment Grade
Junk Bonds
Moody’s
Aaa Aa A Baa
Ba B Caa C
S & P
AAA AA A BBB
BB B CCC C
Bond ratings are designed to reflect the probability of a bond issue going into default
Influence bond’s interest rate and firm cost of debt
Ratings are important both to firm & to investors
Do not have the incentive to measure the risk
Paid by the issuing firms
Do not adjust immediately to changes in credit quality
Enron bonds

53. Default Risk & Bond Ratings

54. Factors Affecting Default Risk & Bond Ratings
Financial performance & Ratios (Debt, TIE & Current ratios)
Qualitative factors: Bond contract terms
Secured vs. unsecured debt
Senior vs. subordinated debt
Guarantee and sinking fund provisions
Debt maturity
Miscellaneous qualitative factors
Earnings stability & senstivity to economical change
Regulatory environment
Potential antitrust or product liabilities
Pension liabilities
Potential labor problems

55. Bankruptcy When a company is insolvent (can’t pay its obligations):
Two main chapters of the Federal Bankruptcy Act:
Reorganization (Chapter 11)
Liquidation (Chapter 7)
For large organizations, reorganization occurs more frequently than liquidation
Stockholders generally receive little in reorganization & nothing in liquidations
Typically, a company wants Reorganization, while creditors may prefer Liquidation
Bondholders’ treatment depends on the term of the bond

56. Reorganization
Company must demonstrate in its reorganization plan that it is “worth more alive than dead”
If company can’t meet its obligations …
It files under Chapter 11 to stop creditors from foreclosing, taking assets & closing the business & it has 120 days to file a reorganization plan. Management usually stays in control.
Court appoints a “trustee” to supervise reorganization.
The debt could be restructured
Reduce interest rate
Postpone the maturity date
Debt is exchanged for equity
Restructuring is done to reduce the firm’s debt level (leverage) to a reasonable level that can be met with its projected cash flows

57. Priority of Claims in Liquidation
Secured creditors from sales of secured assets
Trustee’s costs
Wages, subject to limits
Taxes
Unfunded pension liabilities
Unsecured creditors
Preferred stock
Common stock

58. Reorganization
In a liquidation, unsecured creditors generally receive nothing.
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 & the judge approve, the company “emerges” from bankruptcy with lower debts, reduced interest charges, and a chance for success.