1. Valuing Securities

2. FIN 591: Financial Fundamentals/Valuation
Pricing in General
Investors value financial instruments based on discounting expected future cash flows
Why?
Financial markets provide an alternative to real investments
Discounting the cash flows allows you to compare the alternatives
Three types of securities:
Bonds
Stocks
Derivatives.
FIN 591: Financial Fundamentals/Valuation

3. FIN 591: Financial Fundamentals/Valuation
Types of Bonds
Pure discount or zero bonds
Single promised payments (face value) at a maturity date
Examples: Treasury bills, corporate zeros, strips
Consols
Pay a fixed “coupon” each period forever
Coupon bonds
Pay regular (6 month) coupon payments + face value at maturity
Coupons = interest for tax purposes
Examples: Most corporate and long-term government bonds.
FIN 591: Financial Fundamentals/Valuation

4. FIN 591: Financial Fundamentals/Valuation
Pricing Zero Bonds
Price is equal to PV
For a zero coupon bond with T years to maturity and a face value of F and a constant discount rate of r, price equals:
F / (1 + r)T
Example:
Face value = $1,000
Discount rate r = 10%
Years until maturity T = 8
1000 / (1.10)8 = $
FIN 591: Financial Fundamentals/Valuation

5. Another Example: Pricing Discount Bonds
Example: Suppose we have two discount (zero) bonds:
1-year PV = $ $
2-year PV = $ $100
What can we infer about the 1- and 2-year spot interest rates at time 0?
FIN 591: Financial Fundamentals/Valuation

6. FIN 591: Financial Fundamentals/Valuation
Pricing Consol Bonds
Receive coupon payments in perpetuity
Face amount is never paid
For a consol with T years to maturity and a face value of F and a constant discount rate of r, price equals:
St=1 $C / (1 + r)t = $C / r
Example:
$50 received monthly, in perpetuity
Stated annual rate = 8%
Monthly rate r = 8% / 12 = .6667%
PV = $C / r = $50 / .6667% = $7500.
FIN 591: Financial Fundamentals/Valuation

7. FIN 591: Financial Fundamentals/Valuation
Pricing Coupon Bonds
What is the PV of a two-year $100 par value bond paying 10% interest semi-annually if the required return is 8% compounded semiannually? $100
$5 $5 $5 $5
Note:
c = r Price = face Par
c < r Price < face Discount
c > r Price > face Premium
FIN 591: Financial Fundamentals/Valuation

8. FIN 591: Financial Fundamentals/Valuation
Value of Risky Debt
I. Risky Debt = Assets – Equity (call option)
FIN 591: Financial Fundamentals/Valuation

9. Common Stock Valuation
Different valuation models exist
All follow time value of money concepts:
Discount all expected future cash flows at an appropriate market risk-adjusted rate
Future cash flows consist of:
Dividends
Future selling price.
FIN 591: Financial Fundamentals/Valuation

10. FIN 591: Financial Fundamentals/Valuation
Determining Price
For a single holding period:
P0 = (Div1 + P1) / (1 + r1)
But what determines P1?
P1 = (Div2 + P2) / (1 + r2)
But what determines P2?
Well, doing this over and over again, we get
P0 = S Divt / (1 + rt)t
Value of stock depends on the size, timing, and riskiness of expected future dividends.
FIN 591: Financial Fundamentals/Valuation

11. Valuation of a Non-constant Dividend Stream...
Value = PV dividends in period 1
+ PV dividends in period 2
PV dividends in period n
+ PV expected price in period n
Example:
A stock is expected to pay dividends of $4 in 1 year and $5 in 2 years. Expected price of the stock in 2 years is $90. The discount rate is 10%. How much is the stock worth today?
Answer:
$4 / $5 / (1.10)2 + $90 / (1.10)2
= $ $ $74.38 = $82.15.
FIN 591: Financial Fundamentals/Valuation

12. Valuation of Constant, No-Growth Perpetual Dividend Stream
All future dividends are expected to be constant in perpetuity
A simple model emerges:
Price = Expected dividend next period
Required market rate
Example: Dividend next period is forecasted to be $3. The market’s required return is 10%. How much is the stock worth today?
Answer: $3 / .10 = $30.
FIN 591: Financial Fundamentals/Valuation

13. Valuation of Constant Growth Dividend Stream in Perpetuity
All future dividends are expected to grow at a constant rate in perpetuity
A simple model emerges:
Price = Expected dividend next period .
Required market rate - growth rate
Example: Dividend next period is forecasted to be $3 and grow in perpetuity at 4%. The market required return is 10%. How much is the stock worth today?
Answer: $3 / ( ) = $50.
FIN 591: Financial Fundamentals/Valuation

14. Valuation of a Two-Stage Dividend Growth Stream
Combine the non-constant stream and perpetual stream models
Example:
A stock is expected to pay dividends of $2 and $3 each of the next 2 years. The dividend in year 3 will be $4 and grow thereafter at 5%. The market rate is 8%. How much is the stock worth?
Answer:
$2 / $3 / (1.08)2 + $4 / (1.08)3
+ [$4 (1.05) / ( )] / (1.08)3
= $ $ $ $ = $
FIN 591: Financial Fundamentals/Valuation

15. Valuing a Stock that Pays No Dividends for a Period of Time
Example:
A stock is expected to pay no dividends the next 2 years. The dividend in year 3 will be $4 and grow thereafter at 5%. The market rate is 8%. How much is the stock worth?
Answer:
$4 + $4 (1.05) / ( )
(1.08)3
= $
FIN 591: Financial Fundamentals/Valuation

16. Ex-Dividend Behavior of Price
Stock price should drop by the amount of the dividend on the ex-date
Evidence indicates that it declines by a lesser amount
Tax reasons?
Clientele effects?
FIN 591: Financial Fundamentals/Valuation

17. Valuation and Dividend Policy
“Dividends do not matter” versus “dividends do matter” views.
FIN 591: Financial Fundamentals/Valuation

18. Why Dividends May Matter
Informational signaling
Change in dividends signals a corresponding change in management’s expectations for the firm
Agency considerations
Free cash flow argument and shirking by management
Other factors
Debt covenants; institutional constraints; IRS; state laws.
FIN 591: Financial Fundamentals/Valuation

19. Some Cautions About Dividend Growth Models
Many firms have “life cycles”.
When young, they grow fast, then slow and grow at a “normal” rate
Finally, they may shrink or go out of business
These growth rates are difficult to predict
The chosen range has a large impact on value
Important to discount dividends and not earnings
Cash flows received by shareholders represent value
If you use earnings, you may double count some cash flows.
FIN 591: Financial Fundamentals/Valuation

20. Conceptual View of the Firm
Balance Sheet
Assets Debt
Equity
Value of firm = Value of debt + value of stock
Analyze from several perspectives:
Modigliani & Miller model
Free cash flow, APV model
Dividends not a factor
Economic value added
Dividends not a factor.
FIN 591: Financial Fundamentals/Valuation

21. Outline of Valuation Models
Free cash flow
Exhibit 5.5, page 77 in text
Economic value added (aka EVA)
i.e., economic profit or residual income
Market value added
Market value of firm – book value of firm
PV of EVA’s
Exhibits 4.2 – 4.4, pages 60 – 62.
Shareholder value added.
Reconciled:
Exhibit 3.5,
Page 50
FIN 591: Financial Fundamentals/Valuation

22. FIN 591: Financial Fundamentals/Valuation
Free Cash Flow
Definition:
After-tax operating earnings + non-cash charges - investments in operating working capital, PP&E and other assets
It doesn’t incorporate financing related cash flows
Operating free cash flow
Represents cash flow available to service debt and equity.
FIN 591: Financial Fundamentals/Valuation

23. FIN 591: Financial Fundamentals/Valuation
Economic Value Added
Reorders cash flows to allow shareholders to relate company operating performance directly to shareholder value
Adjusts capital to eliminate distortions
Financing perspective
Capital = Debt + equity
Operating perspective
Capital = Fixed assets + working capital
EVA = Operating profits - capital charge.
FIN 591: Financial Fundamentals/Valuation

24. FIN 591: Financial Fundamentals/Valuation
Calculating EVA
Two methods lead to the same answer
Method 1:
EVA = (ROIC% - WACC%) * Invested operating capital
Profitability captured by the spread: ROIC% - WACC%
Growth captured by the invested operating capital
Method 2:
EVA = (Operating profits after taxes) - WACC% * Invested operating capital
Similar to the economist’s definition of profit.
FIN 591: Financial Fundamentals/Valuation

25. FIN 591: Financial Fundamentals/Valuation
Advantage of EVA
Investment objective:
Maximize the NPV of all available projects
Issue is how to measure cash flow generating abilities?
Interpreting annual free cash flow is difficult
Negative free cash flow could be
Value depleting or value enhancing
Temporary
EVA aids the understanding
Will be examined in greater detail later.
FIN 591: Financial Fundamentals/Valuation

26. FIN 591: Financial Fundamentals/Valuation
EVA & Market Value
Market value of a company reflects:
Value of invested capital
Value of ongoing operations
Present value of expected future economic profits
Captures improvement in operating performance
EVA related to market value by:
Measuring all the capital
Seeing what the firm is going to do with the capital
Turn those free cash flow forecasts into EVA forecasts
Discount EVA to find market value added.
FIN 591: Financial Fundamentals/Valuation

27. Relationship Between EVA & MVA
EVA EVA EVA EVA
Year Year Year Year n
MVA
MVA
Market
Value
Market
value
EVA EVA EVA EVA
1 + r (1 + r)2 (1 + r) (1 + r)n =
Capital
Market value is based on establishing the
economic investment made in the company
(capital), making a best guess about what
economic profits (EVA) will be in the future, and discounting those EVAs to the present.
FIN 591: Financial Fundamentals/Valuation

28. FIN 591: Financial Fundamentals/Valuation
The End
FIN 591: Financial Fundamentals/Valuation