6-1

Valuing Shares and Bonds

Chapter Six

6-2

Chapter Objectives

• Outline the features of bonds.• Calculate the value (price) of a bond assuming

annual and semi-annual coupons.• Understand the implications of interest rate risk for

the value of a bond.• Calculate the value of an ordinary share under

different dividend growth scenarios.• Explain the components of required return.

6-3

Debt Securities

• Debt securities are issued when an organisation wishes to borrow money from the public on a long-term basis.

• Bonds are issued by the government.

• Debentures are secured and issued by a corporation.

• Notes are unsecured debt securities issued by a corporation.

• More recently, these are all known as bonds.

6-4

Types of Bond

The 4 Primary Types of Bonds

•Government Bonds (Treasuries)

•Agency Bonds (Agencies)

•Municipal Bonds (Munis)

•Corporate Bonds (Corporates)

6-5

Types of BondGovernment Bonds (Treasuries)

It is the debt securities that issued and backed by the center government.

The safest investments in the world. 

4 distinct categories such as treasury bills (maturing in less than one year) , treasury notes (maturing in one to 10 years), Treasury Bonds (maturing in 10 to 30 years), Treasury Inflation Protected Securities (maturities of 5, 10, and 30 years).

6-6

Types of Bond

Agency Bonds (Agencies)

Debt securities that issued by institutions that were originally created by the Government.

Pay regular fixed-interest payments until maturity and have terms of two or more years.

Discount notes have maturities of less than one year. 

6-7

Types of Bond

Municipal Bonds (Munis)Local governments often borrow money by issuing bonds, similar to the center Government, but on a smaller scale.

Free from center, state and local government income taxes.

Two main types of municipal bonds, general obligation bonds and revenue bonds.

Most municipal bonds mature from 1 to 30 years.

6-8

Types of Bond

Corporate Bonds (Corporates)

Debt securities that issued by the corporations to raise money for investment.

A short-term corporate bond is less than 5 years; intermediate is 5 to 12 years, and long term is over 12 years. 

6-9

Bond Features

• Coupon payments are the stated interest payments. Payment is constant and payable every year or half-year.

• Face value (par value) is the principal amount repayable at the end of the term.

• Coupon rate is the annual coupon divided by the face value of a bond.

• Maturity is the specified date at which the principal amount is payable.

6-10

Bond Yields• When interest rates rise, the present value of the

bond’s remaining cash flows declines, and the bond is worth less. When interest rates fall, the bond is worth more.

• An inverse relationship exists between market interest rates and bond price.

• The inverse relationship between interest rates and values is one of the fundamental concepts of finance theory. It is applicable to any cash flow that is being valued today.

6-11

Bond Yields

• Yield to maturity (YTM) is the market interest rate that equates a bond’s present value of interest payments and principal repayment with its price.

• Given the yield to maturity or ‘yield’, we can calculate the present value of the cash flows as an estimate of the bond’s current market value.

• There is an inverse relationship between market interest rates and bond price.

6-12

Bond Price Sensitivity to Interest Rates (YTM)

4% 6% 8% 10% 12% 14% 16%

$1 800

$1 600

$1 400

$1 200

$1 000

$ 800

$ 600

Bond price

Yield to maturity, YTM

Coupon = $10020 years to maturity$1000 face value

Key Insight: Bond prices and YTMs are inversely related.

6-13

Bond Value

tr

F

r

tr / C

1

111

valueface ofPVpaymentscoupon of PVV

6-14

Example 1—Bond Value• A bond with a face value of $1000 and a coupon rate

of 6 per cent has 10 years to maturity. What is the market price of this bond if the market interest rate is 12 per cent?

$660.99 3.1058

$1000 5.6502 $60

1.12

$1000

0.12

1.121/ 1 $60 V 10

10

6-15

Example 2—Bond Value• Assume now that the bond’s coupons are paid

half-yearly.

$655.90 3.2071

$1000 11.4699 $30

1.06

$1000

0.06

1.061/ 1 $30 V 20

20

6-16

Bond Values• If the market interest rate is the same as the coupon

rate, the bond’s value is the same as the face value.

• If the market interest rate rises above the coupon rate, the bond’s value falls below the face value. The bond is then said to be a discount bond.

• If the market interest rate falls below the coupon rate, the bond’s value rises above the face value. The bond is then said to be a premium bond.

6-17

Interest Rate Risk• Interest rate risk is the risk that arises for bond

holders from changes in interest rates.

• How much interest rate risk a bond has depends on how sensitive its price is to interest rate changes. This depends on two things:

– All other things being equal, the longer the time to maturity, the greater the interest rate risk.

– All other things being equal, the lower the coupon rate, the greater the interest rate risk.

6-18

Interest Rate Risk and Time to Maturity

Interest rate 1 year 30 years

5% $1 047.62$1 768.62

10 1 000.001 000.00

15 956.52 671.70

20 916.67 502.11

Time to Maturity

6-19

Calculating Yield to Maturity (YTM)• Yield to maturity (YTM) 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.

• If you have a financial calculator, enter N, PV, PMT and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign).

6-20

Example―Calculating YTM• Consider a bond with a 8 per cent annual coupon

rate, 10 years to maturity and a par value of $1000. The current price is $935.82.– Will the yield be more or less than 8 per cent?

Enter:

10 -935.82 1 000 80

N I/Y PV FV PMT

Solve for → 9.00

YTM = 9%

6-21

Bond Price Reporting• Each working day an estimated $7–8 billion of

securities is traded in Australian money and fixed interest markets.

• Information on notes, bonds, and debentures issued by large companies and government bodies are reported in newspapers (e.g. Australian Financial Review) and by financial agencies (e.g. Bloomberg).

• A typical reporting system lists the issuer, the coupon, maturity date, quantity in millions, the YTM bid and offer, and the last traded yield.

6-22

Ordinary Share Valuation• Share valuation is more difficult than debenture

valuation for a number of reasons:– uncertainty of promised cash flows– shares have no maturity– observing the market rate of return is not easy.

• However, there are cases in which the present value of future cash flows for a share can be derived and thus the share’s value determined.

6-23

Ordinary Share Valuation

• The market value of a share is the present value of all expected net cash flows to be received from the share, discounted at a rate of return that reflects the riskiness of those cash flows.

• The expected net cash flows to be received from a share are all future dividends.

• Dividend growth is an important aspect of share valuation.

6-24

Zero Growth Dividend• Shares have a constant dividend into perpetuity, with

no growth in dividends.

• A share in a company with a constant dividend is much like a preference share.

• The value of a share is then the same as the value of an ordinary perpetuity.

r

D P 0

Example:• If ARAMCO is expected to pay cash dividends of $8

per share and ARAMCO has a 10% required rate of return, what is the value of the stock?

P0 = D/r = 8/0.10 = $80

Here D = $8 and r = 10% = 0.10

6-25Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan

6-26

g)(r

D

g)(r

g1 D P

g 1 D D

100

t0t

Constant Growth Dividend• Dividends grow at a constant rate each time period.

Therefore we have a growing perpetuity. • The constant dividend growth model determines the

current price of a share as its dividend next period divided by the discount rate less the dividend growth rate.

6-27

Example—Constant Growth DividendCompany ABC has just paid a dividend of 30 cents per share, which is expected to grow at 3 per cent per annum. What price should you pay for the share if the required rate of return on the investment is 12 per cent?

43.3$0.09

0.309

0.09

1.030.30

0.03 0.12

.0310.30 P0

6-28

Non-constant Growth Dividend• The growth rate cannot exceed the required rate of

return indefinitely but can do so for a number of years.

• Allows for ‘super normal’ or ‘erratic’ growth rates over some finite length of time.

• The dividends have to grow at a constant rate at some point in the future.

6-29

Example—Non-constant Growth Dividend• A company has just paid a dividend of 30 cents per

share and that dividend is expected to grow at a rate of 10 per cent per annum for the next three years, and at a rate of 3 per cent per annum forever after that.

• Assuming a required rate of return of 14 per cent, calculate the current market price of the share.

6-30

Solution—Non-constant Growth Dividend

6-31

Solution—Non-constant Growth Dividend (continued)

$3.74

0.03 0.14

$0.411

g r

D P 4

3

6-32

$3.36

$2.524 $0.269 $0.279 $0.289

1.14

$3.74

1.14

$0.399

1.14

$0.363

1.14

$0.330

r 1

P

r 1

D

r 1

D

r 1

D P

332

33

33

22

11

0

Solution—Non-constant Growth Dividend (continued)

6-33

Share Price Sensitivity to Dividend Growth, g

0 2% 4% 6% 8% 10%

50

45

40

35

30

25

20

Share price ($)

Dividend growth rate, g

D1 = $1Required return, R, = 12%

15

10

5

6-34

Share Price Sensitivity to Required Return, r

6% 8% 10% 12% 14%

100

90

80

70

60

50

40

Share price ($)

Required return, R

D1 = $1Dividend growth rate, g, = 5%

30

20

10

6-35

Components of the Required Return• The total return, r, has two components:

– Dividend yield– Capital gains yield

• The dividend yield is a share’s cash dividend divided by its current price (D1/P0).

• The growth rate (g) can be interpreted as the capital gains yield, and is the rate at which the value of the investment grows.

6-36

Components of Required Return

yield gains capital yield dividend r

g 0

P1

D r

0P

1D

g r

g r 1

D

0P

6-37

Summary and Conclusions• Bonds are issued when an organisation wishes to

borrow money from the public on a long-term basis.• An inverse relationship exists between market

interest rates and bond price.• The market value of a share is the present value of

all expected net cash flows to be received from the share, discounted at a rate of return that reflects the risk of those cash flows.

• Dividend growth is an important aspect of share valuation.