1. Valuing Shares and Bonds
Chapter Six
Valuing Shares and Bonds

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.

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.

4. The 4 Primary Types of Bonds
Government Bonds (Treasuries)
Agency Bonds (Agencies)
Municipal Bonds (Munis)
Corporate Bonds (Corporates)
A debt security is a financial instrument issued by a company and sold to an investor.

5. Government Bonds (Treasuries)
Types of Bond
Government 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. Agency Bonds (Agencies)
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. 

7. Municipal Bonds (Munis)
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.

8. Corporate Bonds (Corporates)
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. 

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.

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.

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.

12. Bond Price Sensitivity to Interest Rates (YTM)
$1 800
Coupon = $ years to maturity $1000 face value
$1 600
Key Insight: Bond prices and YTMs are inversely related.
$1 400
$1 200
$1 000
$ 800
$ 600
Yield to maturity, YTM 4% 6% 8%
10%
12%
14%
16%

13. Bond Value

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?

15. Example 2—Bond Value
Assume now that the bond’s coupons are paid half-yearly.

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.

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.

18. Interest Rate Risk and Time to Maturity
Interest rate year years
5% $ $
Time to Maturity

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).

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 $
Will the yield be more or less than 8 per cent?
Enter:
N I/Y PV FV PMT
Solve for →
YTM = 9%

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.

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.

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.

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.

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

26. 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.
where
P0 = the stock price at time 0,
D0 = the current dividend,
D1 = the next dividend (i.e., at time 1),
g = the growth rate in dividends, and
r = the required return on the stock, and
g < r.

27. Example—Constant Growth Dividend
Company 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?

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.
Many firms enjoy periods of rapid growth. These periods may result from the introduction of a new product, a new technology, or an innovative marketing strategy. However, the period of rapid growth cannot continue indefinitely. Eventually, competitors will enter the market and catch up with the firm.

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.
P0 = the stock price at time 0,
Dt = the expected dividend at time t,
T = the number of years of non-constant growth,
gc = the long-term constant growth rate in dividends, and
r = the required return on the stock, and
gc < r.

30. Solution—Non-constant Growth Dividend

31. Solution—Non-constant Growth Dividend (continued)

32. Solution—Non-constant Growth Dividend (continued)

33. Share Price Sensitivity to Dividend Growth, g50 45
D1 = $1
Required return, R, = 12% 40 35 30 25 20 15 10 5
Dividend growth rate, g 2% 4% 6% 8%
10%

34. Share Price Sensitivity to Required Return, r
100 90 80
D1 = $1
Dividend growth rate, g, = 5% 70 60 50 40 30 20 10
Required return, R 6% 8%
10%
12%
14%

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.

36. Components of Required Return

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.