1. Interest Rates and Bond Valuation Chapter 6
Objectives:
Know the important bond features and bond types
Understand bond values and why they fluctuate
Understand bond ratings and what they mean
And next week we finish Chapter 6 on:
Understand the impact of inflation on interest rates
Understand the term structure of interest rates and the determinants of bond yields

2. Bond Definitions Bond = borrowing on long term basis
Bills and Notes are shorter term versions
Par value (or face value) = principal paid at maturity
Coupon rate = annual coupon / face value
Coupon payment = stated interest on bond, though there have been whiskey bonds and other emoluments and indentures
Maturity date = specific date when principal is repaid
Yield or Yield to Maturity = the rate required in the market (YTM)
Current Yield = Annual Coupon/Price

3. State of NY Controller’s Revenue Bond $1,000 Redeemable July 17, 1888
$100 US Savings Bond
US Steel $100,000 bond
With coupons on the edge

4. A Whiskey Certificate like a Whiskey Bond
Old R.B. Grainger Whiskey - Louisville, Kentucky 1906

5. Bonds as a Stream of Cash Flows
The value of bond often has two parts:
Bond Value = PV of coupons + PV of par value
Bond Value = PV of annuity + PV of lump sum
As interest rates increase  the present values decreases 
So, as interest rates increase, bond prices decrease and vice versa

6. The Bond Pricing Equation
This formalizes the calculations we have been doing.
The first term is just a perpetuity C/r of coupon payments, but that the stream ends t periods.
The second term is just the present value of the face value received in t years.

7. .
NY Central and Hudson River Railroad Company Bond, in 1898 for $1,000.
When firms default on bond payments, bondholders may become equity holders, they may have collateral value of assets of the company, or as in this case, their value dwindles until their use is a mere historic document selling for $49.95

8. Discount Bond with Annual Coupons
Consider a bond with a coupon rate of 10% and annual coupons. The par value is $1,000 and the bond has 5 years to maturity. The yield to maturity is 11%. What is the value of the bond?
Using the formula:
B = PV of annuity + PV of lump sum
B = 100[1 – 1/(1.11)5] / ,000 / (1.11)5
B = = $ Less than $1,000?
The bond is selling at a discount. Why?
Using the calculator:
N = 5; I/Y = 11; PMT = 100; FV = 1,000
CPT PV =

9. Premium Bond with Annual Coupons
Suppose you are looking at a bond that has a 10% annual coupon and a face value of $1000. There are 20 years to maturity and the yield to maturity is 8%. What is the price of this bond?
Using the formula:
B = PV of annuity + PV of lump sum
B = 100[1 – 1/(1.08)20] / / (1.08)20
B = = $1,196.36
The bond is selling at a premium. Why?
Using the calculator:
N = 20; I/Y = 8; PMT = 100; FV = 1000
CPT PV = -1, sign convention

10. Price and Yield-to-maturity (YTM)
PREMIUM BONDS
Bond Price
DISCOUNT
BONDS
Yield-to-maturity (YTM)
Coupon rate = 8% with annual coupons; Par value = $1,000; Maturity = 10 years

11. Relationship Between Coupon and Yield
If YTM = coupon rate, then par value = bond price
If YTM > coupon rate, then par value > bond price
Reasons Why?
The discount increase the yield above coupon rate
The high YTM reduced the value of the coupon annuity and the face value
Also, other newly issued debt will be paying a coupon equivalent to the YTM, so why buy this bond unless sold at a discount
Price below par value, called a discount bond
If YTM < coupon rate, then par value < bond price
Why? Higher coupon rate causes value above par
A price above par value, called a premium bond

12. Example
Let the Coupon rate = 14% with semiannual coupons; YTM = 16%; Maturity = 7 years; Par value = $1,000
What is the bond worth now?
How many coupon payments are there?
What is the semiannual coupon payment?
What is the semiannual yield?
B = 70[1 – 1/(1.08)14] / ,000 / (1.08)14 =
Or PMT = 70; N = 14; I/Y = 8; FV = 1,000; CPT PV =

13. Two Forms of Interest Rate Risk
Price Risk
Change in price due to changes in interest rates
Long-term bonds have more price risk than short-term bonds, hence are more volatile
Low coupon rate bonds have more price risk than high coupon rate bonds, since most of its value is in the par value
Reinvestment Rate Risk
Uncertainty concerning rates at which cash flows can be reinvested
Short-term bonds have more reinvestment rate risk than long-term bonds
High coupon rate bonds have more reinvestment rate risk than low coupon rate bonds

14. Figure 6.2
Figure 6.2

15. Computing yield-to-maturity (YTM)
Yield-to-maturity is the rate implied by the current bond price
Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity
If you have a financial calculator, enter N, PV, PMT, and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign)
CPT I/Y, the missing piece of information.

16. YTM with Annual Coupons
Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1,000. The current price is $
Will the yield be more or less than 10%?
N = 15; PV = ; FV = 1,000; PMT = 100
CPT I/Y = 11%

17. YTM with Semiannual Coupons
Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1,000, 20 years to maturity and is selling for $1,
Is the YTM more or less than 10%?
What is the semiannual coupon payment?
How many periods are there?
N = 40; PV = -1,197.93; PMT = 50; FV = 1,000; CPT I/Y = 4% (Is this the YTM?)
YTM = 4%*2 = 8%

18. YTM with Semiannual Coupons
Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1,000, instead had 19 years to maturity, also at 4% for 6 months.
Don’t change anything except N = 38 and CPT PV.
N = 38; PMT = 50; FV = 1,000; I/Y = 4%
CPT PV = -1,193.68
Note that the price slowly declines toward $1,000 over time for Premium Bonds.

19. Current Yield vs. YTM Current Yield = annual coupon / price
Yield to maturity = current yield + capital gains yield
Example: 10% coupon bond, with semiannual coupons, face value of 1,000, 20 years to maturity, $1, price
Current yield = 100 / 1, = = 8.35%
Price in one year, assuming no change in YTM = 1,193.68
Capital gain yield = (1, – 1,197.93) / 1, = = -.35%
YTM = = 8%, which the same YTM computed earlier

20. Bond Pricing Theorems
Law of One Price: Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate
If you know the price of one bond, you can estimate its YTM and use that to find the price of the second bond
This is a useful concept that can be transferred to valuing assets other than bonds - Imputed or Matrix Pricing.

21. Differences Between Debt and Equity
Not an ownership interest
Creditors do not have voting rights
Interest is considered a cost of doing business and is tax deductible
Creditors have legal recourse if interest or principal payments are missed
Excess debt can lead to financial distress and bankruptcy
Equity
Ownership interest
Common stockholders vote for the board of directors and other issues
Dividends are not considered a cost of doing business and are not tax deductible
Dividends are not a liability of the firm and stockholders have no legal recourse if dividends are not paid
An all equity firm is unlikely to go bankrupt since it has no debt (only supplier debt)

22. The Bond Indenture
Contract between the company and the bondholders that includes
The basic terms of the bonds
The total amount of bonds issued
A description of property used as security, if applicable
Sinking fund provisions
Call provisions
Details of protective covenants

23. Bond Classifications Registered vs. Bearer Forms Security
Collateral – secured by financial securities
Mortgage – secured by real property, normally land or buildings
Debentures – unsecured, at least in the US, in England, debentures are secured debt
Notes – unsecured debt with original maturity less than 10 years
Seniority – who gets paid first

24. Bond Characteristics and Required Returns
The coupon rate depends on the risk characteristics of the bond when issued
Which bonds will have the higher coupon, all else equal? Circle Higher Interest Rate
Subordinated debenture versus senior debt?
A bond with a sinking fund versus a bond without a sinking fund?
A callable bond versus a non-callable bond?
Short term note versus a long term bond?

25. Bond Ratings – Investment Quality
High Grade
Moody’s Aaa and S&P AAA – capacity to pay is extremely strong
Moody’s Aa and S&P AA – capacity to pay is very strong
Medium Grade
Moody’s A and S&P A – capacity to pay is strong, but more susceptible to changes in circumstances
Moody’s Baa and S&P BBB – capacity to pay is adequate, adverse conditions will have more impact on the firm’s ability to pay

26. Bond Ratings – Speculative or Junk
Low Grade
Moody’s Ba, B, Caa and Ca
S&P BB, B, CCC, CC
Considered speculative with respect to capacity to pay. The “B” ratings are the lowest degree of speculation.
Very Low Grade
Moody’s C and S&P C – income bonds with no interest being paid
Moody’s D and S&P D – in default with principal and interest in arrears