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Bond Valuation

- FIL 404
- Keldon Bauer, PhD

Introduction

- The valuation of all financial securities is

based on the expected PV of future cash flows.

Introduction

- ECFt Expected cash flow at time t.
- r The required return (based on economic

conditions riskiness). - Value increases as cash flow increases or r

decreases.

Capital Market Instruments

- There are two forms of capital
- Debt The right to an agreed cash flow.
- Equity The ownership interest in the business

(therefore the residual cash flow). - A bond is a long-term promissory note by business

or government.

Bond Terminology

- Principal Amount Face Value Maturity Value

Par Value The amount borrowed and the principal

that will be returned at maturity. - Coupon (Interest) Payment Payment of promised

interest (typically at six month intervals).

Payment/Face value is the coupon interest rate.

Bond Terminology

- Maturity Date Date when the principal and any

outstanding interest payments are remitted. - Issue date Date when bond was issued.
- Default risk Risk that issuer will not make

interest or principal payments.

Bond Terminology

- Call Provision Clause in the indenture giving

the issuer the right to early redemption (or

recall). - New Issue versus Outstanding Bonds Bonds in the

primary or secondary markets

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.

Whats 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.

Sinking Funds Two Ways

- 1. Call x at par per year for sinking fund

purposes. - 2. Buy bonds on open market.
- Company would call if rd is below the coupon rate

and bond sells at a premium. Use open market

purchase if rd is above coupon rate and bond

sells at a discount.

Bond Valuation

- Two major components
- Interest payments (an annuity).
- Principal (future lump-sum).

Bond Valuation Interest Review

- The discount rate (rBond) is the opportunity cost

of capital, i.e., the rate that could be earned

on alternative investments of equal risk. - For debt securities
- rBond r IP LP MRP DRP

Bond Valuation - Example 1

- The value of a 15 year 10,000 bond, paying

semi-annual payments of 500, when market rate is

10.

Bond Valuation - Example 2

- The value of a 7 year 10,000 bond, paying

semi-annual payments of 500, when market rate is

10.

Bond Valuation - Example 3

- The value of a 7 year 10,000 bond, paying

semi-annual payments of 500, when market rate is

8.

Bond Valuation - Example 4

- The value of a 7 year 10,000 bond, paying

semi-annual payments of 500, when market rate is

12.

Some Conclusions

- Return or loss on bonds comes from two

components. - Interest Payment (Current Yield) (Interest

Payment)/VB - Change in Face Value (Capital Gain) (VEnding -

VBeginning)/VBeginning

Current Yield - Example

- The value of a 7 year 10,000 bond, paying

semi-annual payments of 500, when market rate is

8.

Capital Gains Yield - Example

- The value of a 7 year 10,000 bond, paying

semi-annual payments of 500, when market rate is

8.

Total Yield - Example

- The value of a 7 year 10,000 bond, paying

semi-annual payments of 500, when market rate is

8.

Some Conclusions

- When market rate rB the bond sells at par or

face value. - When market rate lt rB the bond sells at a

premium. - When interest rates go down, bond prices go up.
- When market rate gt rB the bond sells at a

discount.

Some Conclusions

- As time to maturity approaches zero, market value

approaches face value. - If a 15 year, 10 coupon bond at 5 10 and 15

market rates were sold on the market, the values

of the bond would be as shown in the following

graph.

Value of a 10 Coupon Bond

Some Conclusions

- As time to maturity approaches zero, market value

approaches the face value of the bond.

Yield to Maturity (YTM)

- Yield to Maturity (YTM) The effective interest

rate earned on the bond. - The text has a formula to estimate the YTM, but

your calculator can calculate it directly. - Input the n, PV (Market Value), PMT (semi-annual

payments), FV (Par Value), and have it compute i

(then adjust).

YTM - Example

- What is the yield-to-maturity of a bond with

current market value of 950.51, a par value of

1,000 (which is returned in seven years), making

a coupon payment of 45 every six months?

Answer 10.00

Bond Values - Example

- What is the market value of a bond with current

market rate of 10, a par value of 1,000 (which

is returned in seven years), making a coupon

payment of 54 every six months?

Answer 1,039.59

Interest Rate Risk

- Two types of interest rate risk associated with

bond value. - Price Risk
- Reinvestment Risk
- Price Risk The risk of change in price give

change in interest. - As interest increases, value decreases.

Price Risk - Effect of Maturity

Price Risk - Effect of Payment

Interest Rate Risk

- Reinvestment Risk The risk of worse

reinvestment opportunities when repaid. - When interest rates increase reinvestment

opportunities improve. - Note Price and Reinvestment Risks go in

opposite directions.

Bond Market

- 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!

Bond Market

- True or False All 10-year bonds have the same

price and reinvestment rate risk. - False! Low coupon bonds have less reinvestment

rate risk but more price risk than high coupon

bonds.

Default Risk

- Bond indenture
- Trustee
- Restrictive covenants
- Mortgage bonds
- Debentures
- Subordinated debentures
- Development bonds
- Municipal bond insurance

Default Risk

- Bond Ratings
- Standard and Poors (SP)
- Moodys
- Investment Grade vs Speculative Grade
- Rating Criteria

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