4 bond and stock valuation

Cash Flows for Bondholders If you buy a share of coupon bond, you can receive cash in 2 ways: Price of the bond is the present value of above future cash flows... Present Value of Cash

Topic Bonds and

Chapter Outline

Valuation of Stocks: three models

stocks

Bond Definitions

Par value (face value)

Coupon rate (interest rate of bond)

Maturity date (expiration date)

Yield or Yield to maturity (YTM)

(or Annual Effective Rate of Bond)

Cash Flows for Bondholders

If you buy a share of coupon bond, you can receive cash in 2 ways:

Price of the bond is the present value of

above future cash flows

Present Value of Cash Flows as

Rates Change

Remember, as interest rates increase

present values decrease

So, as interest rates increase, bond prices

decrease and vice versa

The Bond-Pricing Equation

t

t

r) (1

F r

r) (1

1 -

1 C Value

Valuing a Discount Bond with

Annual Coupons

annual coupons The par value is $1000 and the

bond has 5 years to maturity The yield to maturity is 11% What is the value of the bond?

Using the formula:

Using the calculator:

Valuing a Premium Bond with

Annual Coupons

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?

B = 100[1 – 1/(1.08) 20 ] / 08 + 1000 / (1.08) 20

Graphical Relationship Between Price and Yield-to-maturity

Bond Prices: Relationship

Between Coupon and Yield

Why?

Selling at a discount, called a discount bond

Why?

Selling at a premium, called a premium bond

Maturity = 7 years; Par value = $1000

How many coupon payments are there?

What is the semiannual coupon payment?

What is the semiannual yield?

B = 70[1 – 1/(1.08) 14 ] / 08 + 1000 / (1.08) 14 = 917.56

Or PMT = 70; N = 14; I/Y = 8; FV = 1000; CPT PV =

-917.56

Computing Yield-to-maturity

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

YTM with Annual Coupons

rate, 15 years to maturity and a par value of

$1000 The current price is $928.09

YTM with Semiannual

Coupons

semiannual coupons, has a face value of

$1000, 20 years to maturity and is selling for

$1197.93

CPT I/Y = 4% (Is this the YTM?)

Table 7.1

Zero-Coupon Bonds

0%)

difference between the purchase price and the par value

original issue discount bonds (OIDs)

good examples of zeroes

Floating Rate Bonds

inflation-linked Treasuries

The coupon floats, so it is less likely to differ

substantially from the yield-to-maturity

above a specified “ceiling” or below a specified

“floor”

Corporate Bonds Quotations

for the trading date Jan 19, 2006

4.500 June 15,2010 97.984 5.016 71 5 116,790

What is the coupon rate on the bond?

When does the bond mature?

What is the bid price? What does this mean?

What is the ask price? What does this mean?

How much did the price change from the previous day?

What is the yield based on the ask price?

Bond Ratings – Investment

more susceptible to changes in circumstances

adequate, adverse conditions will have more impact on the firm’s ability to pay

Bond Ratings - Speculative

The “B” ratings are the lowest degree of speculation.

being paid

interest in arrears

Interest Rate Risk

Change in price due to changes in interest rates

Long-term bonds have more price risk than short-term

bonds

Low coupon rate bonds have more price risk than high

coupon rate bonds

Figure 7.2

Inflation and Interest Rates

Real rate of interest – change in purchasing power

Nominal rate of interest – quoted rate of

interest, change in purchasing power and

The Fisher Effect

The Fisher Effect defines the relationship

between real rates, nominal rates and

Because the real return and expected

inflation are relatively high, there is significant difference between the actual Fisher Effect

and the approximation

Term Structure of Interest

Rates

yields, all else equal

different coupons, etc (securities-specific risks)

real rate, inflation rate and interest rate risk.

Normal – upward-sloping, long-term yields are higher than term yields

short-
Inverted – downward-sloping, long-term yields are lower than term yields

short-Upward-Sloping Yield Curve

Downward-Sloping Yield Curve

Figure 7.7

Factors Affecting Required

Return

ratings

frequent trading will generally have lower

required returns

Anything else that affects the risk of the cash flows to the bondholders will affect the

required returns

Quick summary

bond prices change?

important?

bonds?

Cash Flows for Stockholders

If you buy a share of stock, you can receive cash in two ways

the market or back to the company

As with bonds, the price of the stock is the

present value of these expected cash flows

One Period Example

Suppose you are thinking of purchasing the stock of Moore Oil, Inc and you expect it to pay a $2 dividend in one year and you

believe that you can sell the stock for $14 at that time If you require a return of 20% on

investments of this risk, what is the maximum you would be willing to pay?

Two Period Example

Now what if you decide to hold the stock for two years? In addition to the dividend in one year, you expect a dividend of $2.10 in two years and a stock price of $14.70 at the end

of year 2 Now how much would you be

willing to pay?

Three Period Example

years? In addition to the dividends at the end of

years 1 and 2, you expect to receive a dividend of

$2.205 at the end of year 3 and the stock price is

expected to be $15.435 Now how much would you

be willing to pay?

PV = 2 / 1.2 + 2.10 / (1.2) 2 + (2.205 + 15.435) / (1.2) 3 = 13.33

Developing The Model

would sell the stock

You would find that the price of the stock is

really just the present value of all expected

future dividends

So, how can we estimate all future dividend payments?

Estimating Dividends:

Special Cases

percent every period

1 Zero Growth

then this is a perpetuity and the present value of

expected future dividends can be found using the

perpetuity formula

P0 = D / R

every quarter and the required return is 10% with

quarterly compounding What is the price?

P0 = 50 / (.1 / 4) = $20

2 Constant Growth Model

Dividends are expected to grow at a constant percent per period

With a little algebra and some series work,

this reduces to:

D g)

1 ( D

DGM – Example 1

Suppose Big D, Inc just paid a dividend of

$.50 It is expected to increase its dividend by 2% per year If the market requires a return of 15% on assets of this risk, how much should the stock be selling for?

P0 = 50(1+.02) / (.15 - 02) = $3.92

DGM – Example 2

Suppose TB Pirates, Inc is expected to pay a

$2 dividend in one year If the dividend is

expected to grow at 5% per year and the

required return is 20%, what is the price?

(1.05) in this example?

Stock Price Sensitivity to Dividend Growth, g

0 50

Stock Price Sensitivity to Required Return, R

0 50

Example - Gordon Growth

Company - I

a dividend of $4 next period and dividends

are expected to grow at 6% per year The

required return is 16%

What is the current price?

expected next year, so we don’t multiply the

dividend by 1+g

Example – Gordon Growth

Company - II

What is the price expected to be in year 4?

What is the implied return given the change

in price during the four year period?

The price grows at the same rate as the

dividends

3 Nonconstant

Growth-Example

Suppose a firm is expected to increase

dividends by 20% in one year and by 15% in two years After that dividends will increase at

a rate of 5% per year indefinitely If the last

dividend was $1 and the required return is

20%, what is the price of the stock?

Remember that we have to find the PV of all

expected future dividends

Quick Quiz – Part I

What is the value of a stock that is expected

to pay a constant dividend of $2 per year if

the required return is 15%?

What if the company starts increasing

dividends by 3% per year, beginning with the next dividend? The required return stays at 15%

Using the DGM to Find R

Start with the DGM:

g P

D g

P

g) 1

(

D R

R for solve

and rearrange

g - R

D g

R

-g) 1

(

D P

0

1 0

0

1 0

0

+

= +

+

=

= +

=

Finding the Required Return

Table 8.1 - Summary of Stock

Valuation

Features of Common Stock

Voting Rights

liquidation

maintain proportional ownership if desired

Dividend Characteristics

dividend has been declared by the Board

declaring dividends

expense; therefore, they are not tax deductible

depends on the holding period

Features of Preferred Stock

dividends can be paid to common stockholders

preferred dividends can be deferred indefinitely

missed preferred dividends have to be paid

before common dividends can be paid

Preferred stock generally does not carry

voting rights

Reading Stock Quotes

Sample Quote

4.5 57.50 38.60 HarrahEntn HET 1.20 2.3 20 10943 52.03 0.35

What information is provided in the stock quote?

This quote is the Harrahs Entertainment quote from Figure 8.2 in the text.

Reading Stock quotes in VN

90 BMC

559 0.1

15.4 BHS

2184 FL-0.2

5.5 BBT

5167 FL-0.9

17.1 BBC

3368 0.3

11.8 ASP

6551 -0.2

31 ANV

160 FL-1.4

27.9 ALT

3896 -0.4

11.3 ALP

5525 FL-1

20.9 AGF

1200 -1.4

33.1 ACL

777 0

30.4 ABT

Khối lượng GD Thay đổi (+/-)

Giá khớp

Mã CK

Quick Quiz – Part II

You observe a stock price of $18.75 You

expect a dividend growth rate of 5% and the most recent dividend was $1.50 What is the required return?

What are some of the major characteristics of common stock?

What are some of the major characteristics of preferred stock?

Basics of Chapter

Valuation of Stocks: three models

stocks