1. Valuation of Bonds Bond Key Features
Bond - a term promissory note - loan agreement - a contract- specifying loan amount, methods of payment and interest if any.
Most common Bond features:
Par value: Face amount; paid at maturity. Assume $1,000.
Coupon interest rate: Stated interest rate. Multiply by par to get $ of interest. Generally fixed.
Maturity: Years until bond
is repaid.
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Fin 301- Bond Valuation | Dr. Menahem Rosenberg

2. Fin 301- Bond Valuation | Dr. Menahem Rosenberg
Special Features
Call feature:
Issuer can refund if rates decline (will pay a call premium). That helps the issuer but hurts the investor.
Most bonds have a deferred call and a declining call premium.
Conversion feature:
Lender (bond holder) can exchange the bond with a pre-specified number of stocks.
Since it provide an equity option, the interest rate on such a bond might be lower, reducing the Cash Flow drain.
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Fin 301- Bond Valuation | Dr. Menahem Rosenberg

3. Fin 301- Bond Valuation | Dr. Menahem Rosenberg
Asset Valuation
Asset Value as Present Value of the Cash Flows it will produce:
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Fin 301- Bond Valuation | Dr. Menahem Rosenberg

4. Fin 301- Bond Valuation | Dr. Menahem Rosenberg
Pure Discount Bonds
A pure discount bond (also called Zero Coupon or Zeroes) is a security that promises to pay a specified single cash payment (face value or par value) at a specified date called its maturity date
Note
There is no cash flow associated with interest
Pure discount bonds are purchased at a discount from their face or par value
4/17/2019
Fin 301- Bond Valuation | Dr. Menahem Rosenberg

5. Fin 301- Bond Valuation | Dr. Menahem Rosenberg
Pure Discount Bond
The pure discount bond is an example of the present value of a lump sum equation we analyzed previously.
Let i be the appropriate discount rate, n number of periods to maturity.
When we observe a price, we can compute the discount rate used to set that price:
The yield-to-maturity is the discount rate that makes the present value of the cash flows from the bond equal to the current price of the bond.
4/17/2019
Fin 301- Bond Valuation | Dr. Menahem Rosenberg

6. Determinants of Rates of Return
“Real” vs “Nominal” rates
r* - real risk free rate, T-bill rate when there is no inflation
rf - risk free rate, free of any risk including inflation risks
r - Nominal rate, as rate required by assets holders
IP – Inflation premium
Short Term T-Bill rate of return
(3) r = rf = r* + IP
4/17/2019
Fin 301- Bond Valuation | Dr. Menahem Rosenberg

7. Determinants of Rates of Return
For other assets (long term government, foreign government, municipal, corporate) add all or some of the following:
DRP - Default Risk Premium
LP Liquidity Premium
MRP – Maturity Risk Premium
So that:
(4) r = r* + IP +DRP + LP + MRP
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Fin 301- Bond Valuation | Dr. Menahem Rosenberg

8. Fin 301- Bond Valuation | Dr. Menahem Rosenberg
Yield Curve
Term Structure: the relationship between interest rates (or yields) and maturities.
A graph of the term structure is called the Yield Curve.
We use pure discount bonds yield to maturity as the different period rates, called also pure discount rate
June data.
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Fin 301- Bond Valuation | Dr. Menahem Rosenberg

9. Fin 301- Bond Valuation | Dr. Menahem Rosenberg
Coupon Bonds
A coupon bond obligates the issuer to
make periodic payments of interest (called coupon payments) to the bond holder until the bond matures
at maturity the face value of the bond is also paid to the bond holder
and the contract is satisfied
The coupon rate is the interest rate applied to the face value to compute the coupon payment
A bond with a face value of $1,000 and a coupon rate of 10% pays an annual coupon of $100
At maturity, the payment is $1,000+$100
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Fin 301- Bond Valuation | Dr. Menahem Rosenberg

10. Fin 301- Bond Valuation | Dr. Menahem Rosenberg
Coupon Bond Price
We can always analyze any fixed income contract into a sum of pure discount bonds
Let i0,t be the t years pure discount rate.
Such that i0,1 is a one year pure rate and i0,10 is the 10 years pure discount rate
A bond with F par value and that pays $C coupon every period and is maturing in T periods.
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Fin 301- Bond Valuation | Dr. Menahem Rosenberg

11. Fin 301- Bond Valuation | Dr. Menahem Rosenberg
The YTM of a Coupon Bond
We have the price of the coupon bond, and the timing and magnitude of its future cash flows, so we can determine its YTM
The yield-to-maturity is the (one equal) discount rate that makes the present value of the cash flows from the bond equal to the current price of the bond.
i that solves for the price is the YTM
If we are provided a bond YTM, we can use it to price the bond.
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Fin 301- Bond Valuation | Dr. Menahem Rosenberg

12. Par, premium, and Discount Bonds
A coupon bond with its current price equal to its par value is a par bond
If it is trading below par it is a discount bond
If it is trading above par it is a premium bond
At maturity, the value of any bond must equal its par value.
If a bond is currently valued at a premium (discount), as it approached maturity its value will decline (appreciate) towards par value.
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Fin 301- Bond Valuation | Dr. Menahem Rosenberg

13. Fin 301- Bond Valuation | Dr. Menahem Rosenberg
Bond Yields
YTM is the rate of return earned on a bond held to maturity. Also called “promised yield.”
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Fin 301- Bond Valuation | Dr. Menahem Rosenberg

14. Fin 301- Bond Valuation | Dr. Menahem Rosenberg
Bond Risks
Reinvestment Risk: The risk that Cash Flows will have to be reinvested in the future at lower rates, reducing income.
Interest rate risk: Rising discount rates cause bond’s price to fall.
Long-term bonds: High interest rate risk, low reinvestment rate risk.
Short-term bonds: Low interest rate risk, high reinvestment rate risk.
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Fin 301- Bond Valuation | Dr. Menahem Rosenberg

15. Fin 301- Bond Valuation | Dr. Menahem Rosenberg
Bond Default Risk
If issuer defaults, investors receive less than the promised return.
Bond Ratings Services Provide One Measure of Default Risk
Investment Grade
Junk Bonds
Moody’s
Aaa Aa A Baa
Ba B Caa C
S&P
AAA AA A BBB
BB B CCC D
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Fin 301- Bond Valuation | Dr. Menahem Rosenberg

16. Fin 301- Bond Valuation | Dr. Menahem Rosenberg
Bond Default Risk
Financial performance
Debt ratio
TIE ratio
Current ratios
Provisions in the bond contract
Secured vs. unsecured debt
Senior vs. subordinated debt
Guarantee provisions
Sinking fund provisions
Debt maturity
Other factors
Earnings stability
Regulatory environment
Potential product liability
Accounting policies
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Fin 301- Bond Valuation | Dr. Menahem Rosenberg