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Outline: Chapter 4 Valuation of Bonds and Stocks

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- Financial Assets
- Determining Bond Values and Yields
- Bond valuation
- Interest rates and bond prices
- Bonds issued by the government
- Bonds issue by firms
- Determining the yield to maturity
- Bonds with semi-annual interest
- Consols and preferred stock
- Bond valuation and financial management

- Determining Common Stock Values
- Dividend valuation
- No growth in cash dividends
- Constant growth in cash dividends
- Nonconstant growth in cash dividends
- To invest or not to invest?
- Non-dividend-paying stocks
- Volatility, liquidity, and stock prices

- The Present Value of Growth Opportunities
- Price/earnings ratios
- Growth opportunities and value creation
- Growth opportunities and bond valuation

- Returns and Financial Management
- Returns
- Expected versus realized returns
- Importance for financial management

- Two major financial assets
- Bonds
- What is a bond?
- A financial asset, or claim against a firm
- Promissory note
- Fixed income security
- Issued by a firm or government
- 10 to 30 years maturity
- Source of funding for corporations

- What is a bond?
- Stock
- What is a stock?
- A financial asset, ownership of the firm

- What is a stock?

- Bonds

- Definitions
- Par (maturity) value is the stated or face value of a bond (usually $1,000)
- Coupon interest rate is the interest, as a percentage of par, that is paid annually
- Maturity is the length or term, expressed in years, at the end of which the firm is legally obligated to redeem the bond at par
- New corporate bond issues are sold in the primary market with the proceeds going to the issuing company
- Outstanding bonds trade in the secondary market between investors

- Market price of a bond
- Equal to the sum of the present values of the series of interest payments and of the maturity value

- Equation

- An example
Consider a $1,000 par value bond that has a 10% coupon rate and a 25 year maturity. If this bond has a required rate of return of 10% and pays interest annually, what is its market value?

Answer:

The market price of the bond is equal to its face value because the market rate (or required rate of return) is equal to the coupon rate

- Market price of bonds fluctuates with changes in
- Risk-free rate
- Compensates for changes is expected inflation
- Best proxy is short term T-Bill rate

- Investors’ risk premium

- Risk-free rate
- Bond prices (returns) are negatively (positively) related to
- Risk-free rate
- Risk premium

- Expected inflation
- An example
Assume that the 25-year, 10% coupon rate, bond from the last example is a Government of Canada bond. Expected inflation jumps by 6%. If you own this bond what is the new market value of your $1,000 par value bond? Is your bond selling at a premium or a discount from its par value?

Answer:

- An example

Your bond is selling at a discount because the market interest rate is greater than the coupon rate

- An example
Assume that expected inflation falls by 2%, such that the required return is 8% for similar government bonds issued today. What is the market value of your $1,000 par value bond? Is it selling at a premium or a discount?

Answer:

Your bond is selling at a premium because the market interest rate is less than the coupon rate

- Interest rate risk and the maturity premium
- An example
Assume you own a government bond with three years to maturity (instead of 25 years). Coupon rate is still 10%. Relative to a 25-year government bond, how will an increase in expected inflation of 6% and a decrease in expected inflation of 2% affect the value of your three year bond? What can we conclude?

- An example

Answer:

Given our previous answers of $634.17 and $1,213.50 we can conclude that bonds of shorter maturity are less sensitive to changes in expected inflation i.e., they have less interest rate risk.

- Bond’s market price, interest, and maturity

Market value of bond ($)

25 - year bond

•

1,400

•

•

•

•

Par value = 1,000

•

3 – year bond

•

•

•

600

Market rate of interest (%)

0

4

8

12

16

- Unlike government bonds, corporate bonds have
- Default premium
- To cover expected costs if firm goes out of business

- Liquidity premium
- To cover expected costs when bonds are not easily traded on secondary markets

- Issue-specific premium
- To cover expected costs from special provisions attached to bond agreements

- Default premium

- Reinvestment risk
- The risk that an investor's income will fall if there is a need to reinvest in another bond issue

- Event risk
- Risk shifting due to a firm's capital structure change

- An example
You are told that your 20-year maturity, $1,000 par value bond with an 8% coupon rate sells for $908.32. What discount rate makes the present value of the interest of $80 per year and the maturity value of $1,000 equal to $908.32?

Answer:

We know your bond is selling at a discount. This implies that the yield to maturity must be more than 8%. The yield to maturity is simply an internal rate of return

By financial calculator, kb = 9%

- Equation

- An example
Consider a bond with 20 years to maturity remaining and with a 14% coupon rate that pays interest semiannually. Assume a 10% annual or a 5% semiannual rate of return is presently required on this bond. What is the value of the bond?

Answer:

- Consol
- Perpetual coupon rate bond
- The value of a perpetual bond is
- An example
If the required rate of return is 7.5% and the coupon rate is 10%, then a $1,000 par value perpetual bond would be worth $100 / 0.075 = $1,333.33

- Preferred stock
- The valuation is similar to consols as long as the preferred has no sinking fund provisions
- An example
If a preferred stock has a $50 par value and the dividend is 6.5% per year and the required rate of return is 9%, then the preferred stock's value is ($50)(0.065) / 0.09 = $36.11

- Bonds, like stocks, are means of providing capital for firms
- Financial managers need to know how to value bonds
- Financial managers need to know the yield to maturity, since it helps determine a firm's opportunity cost of capital
- Knowing bond valuation helps managers decide between stocks and bonds

- Definitions to understand common stock valuation

- Dividend valuation approach
- Common stock value is the present value of all expected cash dividends and future market price
- An example
You expect $5, $6, and $7 in dividends over the next three years, at which time you expect to sell your stock for $100. What is the current market value if the required rate of return on the stock is 14%?

Answer:

P0 = $5/(1.14)1 + $6/(1.14)2 + $107/(1.14)3 = $81.22

- Common stock value is the present value of a perpetuity if infinite constant dividends with no growth is assumed
- An example
What is Po if you expect $1.00 dividend in perpetuity and ks = 16%?

Answer:

P0 = $1.00/0.16 = $6.25

- An example

- Since dividends are expected to grow at a constant rate each year we are valuing a growing perpetuity
- Common stock value is the cash dividend expected in one year (at t = 1) divided by the required return adjusted for expected growth

- Example
The current (t=0) cash dividend of $1.00 is expected to grow to grow at 5% per year to infinity. Your required rate of return is 8%. What price would you place on this common stock?

Answer:

- Employ four steps to solve problems involvingnonconstant growth in cash dividends
- Step 1: Determine the cash dividends until the series reverts to constant growth to infinity or no growth
- Step 2: Determine the first year's dividend after the growth rate changes to constant growth to infinity or no growth
- Step 3: Determine the market price of the stock as of the end of the nonconstant (or rapid) growth period
- Step 4: Use Equation 4.4 and the required rate of return to discount both the expected cash dividends from step 1 and the expected market price from step 3 back to the present

- An example
Assume a required rate of return of 16%, Do = $1.00, and 10% growth in dividends for years 1 through 3, followed by 3% compound growth thereafter to infinity.

Answer:

Step 1:

Step 2:

Step 3:

Step 4: Using Equation 4.4, we discount (by 16%) Dl, D2, D3 and P3 back to t = 0 and get P0 equal to about $9.46

0

1

2

3

4

$1.371

$1.

100

$1.210

$1.331

$0.9483

0.8992

0.8527

6.7565

$9.46 = P0

D

$1.371

4

P

=

=

3

k

- g

0.16 - 0.03

S

= $10.5462

- Relationship between expected growth and market value
- There is a direct relationship between the amount and length of expected growth in cash dividends and a stock's market value, as can be seen from the previous calculations. If we had different conditions, then we would have had different results.

- Resulting P0 assumes D0 = $1 and ks = 16%.
ConditionResulting P0

g = 0% $6.25

10% Compound growth $8.03

for years 1-3, then g = 0%

10% compound growth$9.46

for years 1-3, then g = 3%

to infinity

g = 10% to infinity $18.33

- Applying the concept of net present value (NPV) to stocks
- Criteria for investment
- Invest in all stocks with a NPV > 0
- Do not invest in , or sell, stocks with NPV < 0

- Criteria for investment

- An example
- An investor is considering buying some shares of a stock today when the market price is $20. If it is expected that the current per share dividend (D0) of $1 will grow indefinitely at 10 % per year and the investor has a required rate of return of 16% should he buy the stock?
Answer:

NPV = $18.33 - $20 = -$1.67

He should not buy the shares

- Applying the concept of internal rate of return (IRR) to stocks:
- Calculate the rate of return that we expect to earn from an investment in the stock and compare it to our required rate of return, ks
- Expected rate of return, kx
- Criteria for investment:
- If kx > ks invest in the stock
- If kx < ks do not invest in the stock

- An example
If an investor pays $15 for a share of stock today when it is expected that the current dividend (D0) of $1 will grow indefinitely at 10 percent per year. If the investor has a required rate of return of 16% should she buy the stock?

Since this is greater than her required rate of return of 16%, she should buy this stock.

- Three ways to value non-dividend paying stocks
- Estimate when the firm will start paying dividends, as well as their size, growth rate, etc. Then proceed as previously discussed
- Estimate some future market price and discount it back to the present
- Employ earnings and multiply them by some factor (based on perceived growth, risk and/or estimates from similar firms) to arrive at value

- Three variables affecting stock price volatility
- Unexpected changes in a firm's cash flows and, therefore, cash dividends
- Changes in the discount rate (ks) due to predictable changes in macro forces such as GDP, industrial production, and investment
- Unexpected changes in the discount rate used

- Investors demand additional compensation for investing in less-liquid stocks

- Although most investors do not employ the dividend valuation model directly, the intuition behind the dividend valuation model underlies their decision making process
- Common characteristics between the dividend valuation model and investor's decision making process
- Focus on cash flows and dividends
- Consider the returns needed to compensate them for the risks incurred
- Look for growth opportunities

- Expected growth is valuable
- Other things being equal, the market price of a firm which is expected to grow is higher than the market price of a firm that is not expected to grow

- P/E ratio is the market price per share of common stock divided by the earnings per share, EPS
- Dividend payout ratio
- (Cash dividends paid per share of common stock)/EPS
- D1 = (EPS1)(Dividend payout ratio)

- Using the constant growth model
- This implies that the P/E ratio is a function of the firm's dividend payout ratio, the return demanded by investors, ks, and the expected future growth, g, for the firm
- High P/E ratios may be "good news" or "bad news"

- The value of a firm does not increase or decrease when it accepts zero NPV projects
- To increase the value of the firm, projects with NPV > 0 are necessary
- Investing in projects that provide the return demanded by investors, which is also the firm's opportunity cost of capital, does not create value
- When firms accept projects with NPV < 0 , the firm and its investors suffer a loss in value

- Investing in a project that provides an average rate of return is not growth!

- Convertible bonds
- Allow the bondholder to exchange the bond for a specified number of common stocks
- To value convertible bonds we must recognize:
- The conversion date (not the maturity date) is important
- The conversion value (not the maturity value) at the conversion date is important
- Represent the total value of the shares that the bond will be converted into

- Option to wait
- This option has value and may be an important consideration in valuing convertible bonds

- An example
FSB Inc expects to grow at 8% for the foreseeable future. The firm’s stock is currently trading at $4.63. A years ago the firm issued 15-year bonds with a face value of $1,000 and a coupon rate of 7% that are convertible into 110 shares of common stock. The issue also has a call price of $1,025. FSB will call the bonds when the share price hits $10.87. The current required rate of return is 7.5%. How much would you be willing to pay for one of FSB’s bonds?

Answer:

The growth rate is 8% therefore

You would be willing to pay up to $1,051.75 for the bond

- Returns from investing in any financial asset comes from one of two sources:
- Income from interest, dividends and so forth
- Capital gains or losses

- An example
You own 100 shares of stock in Canada Ltd. and expect to receive cash dividends of $5.00 per share at time t = 1. You pay $50 per share at time t = 0. At time t = 1, the price per share is $51. What is your return?

Answer:

k = [$5.00 + ($51 - $50)]/$50 = 12%

For the 100 shares, your return is $6.00 ($5 dividend and $1 capital gain) per share or $600.00 total during this time period

- Ex-post or realized returns may differ from their expected or ex-ante returns
- Expected returns are always positive, but realized returns are not always positive
- James Thomas buys 100 shares of Acme Ltd. expecting a 12% rate of return. He owns the stock for three years, receives no dividends, and the price he has paid for the 100 shares falls 5%. His realized or ex-post return is negative

- Expected returns are always positive, but realized returns are not always positive
- Over the 1965-1999 time period 31% of the total return on common stocks came from dividend income; the remainder was due to changes in the market price of common stocks

- Relationship among the firm's financial management decisions, investors' actions, and valuation

Influences

1. Magnitude

Influences

financial

2. Timing

investors

management

3. Riskiness of expected

decisions, which affect

cash flows

1. Perceived risk

V = S + B

Determines

2. Required rate of

the size of the pie

return