valuing securities. fin 591: financial fundamentals/valuation2 pricing in general investors value...

Valuing Securities

FIN 591: Financial Fundamentals/Valuation

2

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.


3

Types of Bonds

Pure discount or zero bonds Single promised payments (face value) at a

maturity dateExamples: 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.


4

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 = $1,000Discount rate r = 10%Years until maturity T = 81000 / (1.10)8 = $466.51.


5

Another Example:Pricing Discount Bonds

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

0 1 21-year PV = $93.46 $100 02-year PV = $84.17 0 $100What can we infer about the 1- and 2-year spot interest rates at time 0?

%9117.84$/100$

%7146.93$/100$

1/1/

2/12

1

/1

r

r

PVFrrFPV TT


6

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:

t=1 $C / (1 + r)t = $C / r Example:

$50 received monthly, in perpetuityStated annual rate = 8%Monthly rate r = 8% / 12 = .6667%PV = $C / r = $50 / .6667% = $7500.


7

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 $50 1 2 3 4

PV C AT F

1 r T

$5 3.6299 $100 / 1.1699 $103.63

Note:

c = r Price = face Par

c < r Price < face Discount

c > r Price > face Premium


8

Value of Risky Debt

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


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.


10

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 = Divt / (1 + rt)t

Value of stock depends on the size, timing, and riskiness of expected future dividends.


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

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


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.


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


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 / 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.


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) / (.08 - .05)

(1.08)3

= $114.31.


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?


17

Valuation and Dividend Policy

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


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.


19

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.


20

Conceptual View of the Firm

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.

Balance Sheet

Assets DebtEquity


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


22

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.


23

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.


24

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.


25

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.


26

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.


27

RelationshipBetween EVA & MVA

EVA EVA EVA EVAYear 1 Year 2 Year 3 .... Year n

MarketValueMarketvalue

MVA

Capital

=EVA + EVA + EVA + ... + EVA1 + r (1 + r)2 (1 + r)3 (1 + r)n

Market value is based on establishing theeconomic 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.

MVA


28

The End

valuing securities. fin 591: financial fundamentals/valuation2 pricing in general investors value...

Documents

bonds price

discount rate r

r t t value of stock

r t example

c r example

constant discount rate

expected price

face value of f