bond valuation

1

Learning Module

Definitions

Par or Face Value - The amount of money that is paid to the bondholders at

maturity. For most bonds this amount is $1,000. It also generally represents the amount of money borrowed by the bond issuer.

Coupon Rate - The coupon rate, which is generally fixed, determines the

periodic coupon or interest payments. It is expressed as a percentage of the bond's face value. It also represents the interest cost of the bond to the issuer.

2

Definitions

Coupon Payments - The coupon payments represent the periodic interest

payments from the bond issuer to the bondholder. The annual coupon payment is calculated by multiplying the coupon rate by the bond's face value. Since most bonds pay interest semiannually, generally one half of the annual coupon is paid to the bondholders every six months.

Maturity Date - The maturity date represents the date on which the bond

matures, i.e., the date on which the face value is repaid. The last coupon payment is also paid on the maturity date.

3

Definitions

Original Maturity - The time from when the bond was issued until its maturity

date.

Remaining Maturity - The time currently remaining until the maturity date.

Call Date - For bonds which are callable, i.e., bonds which can be

redeemed by the issuer prior to maturity, the call date represents the earliest date at which the bond can be called.

4

Definitions

Call Price - The amount of money the issuer has to pay to call a

callable bond (there is a premium for calling the bond early). When a bond first becomes callable, i.e., on the call date, the call price is often set to equal the face value plus one year's interest.

Required Return - The rate of return that investors currently require on a

bond.

5

Definitions

Yield to Maturity - The rate of return that an investor would earn if he bought

the bond at its current market price and held it until maturity. Alternatively, it represents the discount rate which equates the discounted value of a bond's future cash flows to its current market price.

Yield to Call - The rate of return that an investor would earn if he bought

a callable bond at its current market price and held it until the call date given that the bond was called on the call date.

6

Bond Valuation

Bonds are valued using time value of money concepts.

Their coupon, or interest, payments are treated like an equal cash flow stream (annuity).

Their face value is treated like a lump sum.

7

Example

Assume Hunter buys a 10-year bond from the KLM corporation on January 1, 2003. The bond has a face value of $1000 and pays an annual 10% coupon. The current market rate of return is 12%. Calculate the price of this bond today.

1. Draw a timeline

8

$100 $100$100

$100$100

$100$100

$100$100$100

$1000+

??

Example

2. First, find the value of the coupon stream Remember to follow the same approach

you use in time value of money calculations.

You can find the PV of a cash flow stream PV = $100/(1+.12)1 + $100/(1+.12)2 +

$100/(1+.12)3 + $100/(1+.12)4 + $100/(1+.12)5 + $100/(1+.12)6 + $100/(1+.12)7 + $100/(1+.12)8 + $100/(1+.12)9+ $100/(1+.12)10

Or, you can find the PV of an annuity PVA = $100 * {[1-(1+.12)-10]/.12}

PV = $565.02

9

Example

3. Find the PV of the face value PV = CFt / (1+r)t

PV = $1000/ (1+.12)10

PV = $321.974. Add the two values together to get the total PV

$565.02 + $321.97 = $886.99 Alternatively, on your calculator

PMT = 100FV = 1000n = 10i = 12PV = ?

Note that if the payments had been semiannual, PMT=50, FV=1000, n=20, i=6, PV=?=$885.30.

10

Realized Return

Sometimes you will be asked to find the realized rate of return for a bond.

This is the return that the investor actually realized from holding a bond.

Using time value of money concepts, you are solving for the required rate of return instead of the value of the bond.

11

Example

Doug purchased a bond for $800 5-years ago and he sold the bond today for $1200. The bond paid an annual 10% coupon. What is his realized rate of return? n

PV = [CFt / (1+r)t] t=0

$800 = [$100/(1+r) + $100/(1+r)2 + $100/(1+r)3 + $100/(1+r)4 + $100/(1+r)5] + [$1200/(1+r)5]

To solve, you need use a “trail and error” approach. You plug in numbers until you find the rate of return that solves the equation.

The realized rate of return on this bond is 19.31%.

12

Example

This is much easier to find using a financial calculator:

n = 5PV = -800FV = 1200PMT = 100i = ?, this is the realized rate of return on this bond

Note that if the payments had been semiannual, n=10, PV=-800, FV=1200, PMT=50, i=?=9.47%. Thus, the realized return would have been 2 * 9.47% = 18.94%.

13

Market Analysis

Fundamental Analysis Technical Analysis

14

Fundamental Analysis A method of evaluating a security that

entails attempting to measure its intrinsic value by examining related economic, financial and other qualitative and quantitative factors.

Fundamental analysts attempt to study everything that can affect the security's value, including macroeconomic factors (like the overall economy and industry conditions) and company-specific factors (like financial condition and management). 

15

Fundamental Analysis

Top to bottom Approach Macroeconomic Analysis Industry Analysis Company Analysis

Bottom Up Approach Company Analysis Industry Analysis Macroeconomic Analysis

16

Macroeconomic factors

Inflation Interest Rate Industrial Production Savings Exchange rate FDI

17

Macroeconomic factors

FPI Money Supply Oil Prices Consumption Index Per Capita Income Taxes

18

Technical Analysis

It involves examination of prices or volume to explore the trends so that these can be used for investment decision making.

19

Technical Analysis

A method of evaluating securities by analyzing statistics generated by market activity, such as past prices and volume. Technical analysts do not attempt to measure a security's intrinsic value, but instead use charts and other tools to identify patterns that can suggest future activity.

20

Technical Analysis (Assumptions)

Prices are determined on basis of supply and demand.

Prices are affected by rational and irrational factors.

Prices move in trends. Trends changes due to shift in supply

and demand.

21

Criticism

EMH Trading rule instability

22

Types of T.Analyst

Contrary opinion rule Follow the smart money Other environmental factors Price and volume based measures

23

Contrary opinion rule

Cash position of mutual fund Investment Advisory opinion Credit balances in brokerage account Put/Call ratio Future Trade bullish on stock index

future

24

Follow the smart money

Confidence Index Avg return of Top10 rated bonds Avg return of 40DJIA bond Index Investment Advisory opinion Credit balances in brokerage account Put/Call ratio Future Trade bullish on stock index

future

25

Other environmental factors Breadth of Market Advances Declines Stock Price above 200 days moving

Average Short Interest Ratio

26