1. Bonds and Their Valuation
Chapter 9
Bonds and Their Valuation

2. What is a bond?
A long-term debt instrument in which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond.
Bonds are usually traded in the over-the-counter (OTC) market.
Most bonds are owned by and traded among large financial institutions.

3. Key Features of a Bond (1)
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. (Pure discount bonds (= zero coupon bonds) vs. Coupon bonds)
Maturity date: years until the bond must be repaid.
Issue date: when the bond was issued.
Yield to maturity: rate of return earned on a bond held until maturity (also called the “promised yield”).
YTM = IRR (Internal Rate of Return), the discount rate that makes the present value of the future cash inflows equal to the PV of cash outflows.

4. Key Features of a Bond (2)
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 are not callable until several years after issue. This is known as a deferred call.
A sinking fund provision to pay off a loan over its life rather than all at maturity
It is similar to amortization on a term loan and reduces risk to investor.

5. 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.

6. The Value of Financial Assets1 2 N r%
CF1
CFN
CF2
Value
...

7. Pure Discount Bonds In this equation,
P is the present value or price of the bond
F is the face or future value
n is the investment period
r is the yield-to-maturity

8. Combination of Pure Discount Bonds (1)
Prices of three bonds with different maturities:
Prices of Pure Discount Bonds and Yields
Bonds
Maturity
Price per $1 of Face Vale
Yield (per year) A B C
1 year
2 year
3 year
0.95
0.88
0.80
5.26
6.60
7.72
How much is the value of a security that promises to pay $100 each year for the next three years, i.e. the price of the combination of the three bonds A, B and C?

9. Combination of Pure Discount Bonds (2)
Solution Method:
Compare these results with the following:

10. Present Value of Bonds 1 2 n
CF1
CFn
CF2
Value
...

11. Bond Values over Time
At maturity, the value of any bond must equal its par value.
If the market interest rate 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.

12. 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%?

13. Definitions

14. Example: Current and Capital Gains Yields
Find the current yield and the capital gains yield for a 10-year, 9% annual coupon bond that sells for $887, and has a face value of $1,000.
YTM = Current yield + Capital gains yield
Could also find the expected price one year from now and divide the change in price by the beginning price, which gives the same answer.

15. What is price risk? Does a 1-year or 15-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 15-year Change
5% $1, $1,518.98
10% $1, $1,000.00
15% $ $707.63
The 15-year bond is more sensitive to interest rate changes, and hence has more price risk.
+ 4.8%
– 4.4%
+51.9%
–29.2%

16. What is reinvestment risk?
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.

17. Reinvestment Risk Example
You may invest in either a 15-year bond or a series of fifteen 1-year bonds. Both 15-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 15-year bond strategy:
You can lock in a 10% interest rate, and $50,000 annual income for 15 years, assuming the bond is not callable.

18. Price Risk and Reinvestment Risk
Short -
term
AND/OR
High
coupon
Bonds
Long
Low
Price risk
Reinvestment risk
CONCLUSION: Nothing is riskless!

19. Default Risk
If an issuer defaults, investors receive less than the promised return. Therefore, the expected return on corporate and municipal bonds is less than the promised return.
Bonds with higher default risk have higher market rates: rd = r* + IP + MRP + DRP + LP
Influenced by the issuer’s financial strength and the terms of the bond contract.

20. Types of Bonds Mortgage bonds: bonds backed by fixed assets
Debentures: unsecured bonds
Subordinated debentures: bonds having a claim on assets only after the senior debt has been paid in full in the event of liquidation
Investment-grade bonds: rated triple-B or higher
Junk bonds: double-B or lower bonds

21. 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.

22. Bankruptcy
When a business becomes insolvent, it doesn’t have enough cash to meet its interest and principal payments.
Two main chapters of the Federal Bankruptcy Act:
Chapter 11, Reorganization
Chapter 7, Liquidation
The decision to force a firm to liquidate vs permitting it to reorganize depends on whether the business is worth more or less alive than dead.
The firm’s creditors negotiate with management on the terms of a potential reorganization. The reorganization plan may call for restructuring the debt.

23. 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