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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

Types of Bonds

- Pure discount or zero bonds
- Single promised payments (face value) at a maturity date
Examples: Treasury bills, corporate zeros, strips

- Single promised payments (face value) at a maturity date
- 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

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 = $466.51.

FIN 591: Financial Fundamentals/Valuation

Another Example:Pricing Discount Bonds

Example:Suppose we have two discount (zero) bonds:

0 1 2

1-year PV = $93.46 $100 0

2-year PV = $84.17 0 $100

What can we infer about the 1- and 2-year spot interest rates at time 0?

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

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

0 1 2 3 4

Note:

c = r Price = face Par

c < r Price < face Discount

c > r Price > face Premium

FIN 591: Financial Fundamentals/Valuation

Value of Risky Debt

I. Risky Debt = Assets – Equity (call option)

FIN 591: Financial Fundamentals/Valuation

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

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

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 / 1.10 + $5 / (1.10)2 + $90 / (1.10)2

= $3.64 + $4.13 + $74.38 = $82.15.

FIN 591: Financial Fundamentals/Valuation

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

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 / (.10 - .04) = $50.

FIN 591: Financial Fundamentals/Valuation

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 / 1.08 + $3 / (1.08)2 + $4 / (1.08)3

+ [$4 (1.05) / (.08 - .05)] / (1.08)3

= $1.85 + $2.57 + $3.18 + $111.14 = $118.74.

FIN 591: Financial Fundamentals/Valuation

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) / (.08 - .05)

(1.08)3

= $114.31.

FIN 591: Financial Fundamentals/Valuation

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

Valuation and Dividend Policy

- “Dividends do not matter” versus “dividends do matter” views.

FIN 591: Financial Fundamentals/Valuation

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

Some Cautions AboutDividend 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

Conceptual View of the Firm

Balance Sheet

- 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

- Free cash flow, APV model
- Economic value added
- Dividends not a factor.

- Modigliani & Miller model

Assets Debt

Equity

FIN 591: Financial Fundamentals/Valuation

Outline of Valuation Models Economic value added (aka EVA) Market value added Shareholder value added.

- Free cash flow
- Exhibit 5.5, page 77 in text

- i.e., economic profit or residual income

- Market value of firm – book value of firm
- PV of EVA’s
- Exhibits 4.2 – 4.4, pages 60 – 62.

Reconciled:

Exhibit 3.5,

Page 50

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

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

- Financing perspective
- EVA = Operating profits - capital charge.

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

- EVA = (ROIC% - WACC%) * Invested operating capital
- Method 2:
- EVA = (Operating profits after taxes) - WACC% * Invested operating capital
- Similar to the economist’s definition of profit.

- EVA = (Operating profits after taxes) - WACC% * Invested operating capital

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.

- Negative free cash flow could be

- Interpreting annual free cash flow is difficult

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

RelationshipBetween EVA & MVA

EVA EVA EVA EVA

Year 1 Year 2 Year 3 .... Year n

MVA

MVA

Market

Value

Market

value

EVA + EVA + EVA + ... + EVA

1 + r (1 + r)2 (1 + r)3 (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

The End

FIN 591: Financial Fundamentals/Valuation

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