Valuation

Bonds

&

Stocks

Bonds and Interest rates• Bond taxonomy

– Definition– Grading– Quotes

• Bond valuation– Discounted cash flow – Bond Properties and risks

• Yields– Calculation and assumption– Interest rates components– Interest rates term structure

Bond taxonomy

• Bond = Long Term Debt from state, government or corporation-Contractual agreement (Default = bankruptcy)

• Face value or maturity value• Market value or proceed • Coupon or payment• Maturity• Yield or discount rate

Indenture

• Term and amount of issue• Date of issue and maturity• Face value and Ask price• Coupon and payment date• Collateral and seniority• Sinking fund • Call provision and call premium• Covenants on dividends, asset restriction

and financing restrictions

Rating

Quotation

Bond Valuation

• PV=Present of future payments

+ Present value of maturity value

Then, intuitively

• PV=PMT x PVIFA(n x m, i/m)

+ FV/FVIF(n x m, i/m)

• Calculator:

FV I n PMT CPT PV

Example

A bond has 5 years to maturity and a coupon rate of 10%. Interest rates are compounded semi-annually

Joe thinks that such bond is expected (as of now) to return 12%, Cindy thinks it should yield 8%, and for Charles it must return 10%.

What is the bond value for each individuals?

Solution• Variables:FV=1000; m=2; n=5PMT=%C x FV/m=10% x 1000/2=$50 • For Joe: PV=50 PVIFA(10,6%)+1000/FVIF(10,6%)=926.7• For Cindy:PV=50 PVIFA(10,4%)+1000/FVIF(10,4%)=1081.2• For Charles:PV=50 PVIFA(10,5%)+1000/FVIF(10,5%)=1000

Yields• Reinvestment rate=Yield• Calculating yield: calculator (PV is “-”)• Approximation:

• “Nominal” Rate=Risk-free rate + Risk Premium

Real rate + Inflation + Risk Premium

32

iyieldFVPVnPVFV

PMTm

Bond Properties

• Par, Premium and Discount• Bond prices and yield are inversely related• As Coupon is greater, Price sensitivity to yield

decreases• As Maturity gets greater, Price sensitivity to yield

increases• Price risk and reinvestment risk• Q: with an expected change interest rates, which

bond would you pick?

Term-structure• Cross-section of short versus long-term rates• Relationship with capital markets• 3 possible shapes

– Normal

– Flat

– Inverted

• Remember: k = k* + IP + risk premium• What conclusion(s) can you draw from a yield curve?

STOCKS

• Taxonomy

• Valuation

• Growth revisited

Stocks’ features• Features

– C/S: Voting rights; classes (control of the firm); dividends; prospectus

– P/S: Dividends right; fixed income; rating; convertibility

– Q: How do P/S differ or resemble bonds?• Markets

– Spread for Dealers; transaction costs for Brokers– NYSE and other auction markets: Floor Brokers,

Commission Brokers, floor traders and Specialists; S-DOT

– Dealers’ market: Bid-ask quotations at Levels 1, 2, and 3

Households-Direct

Insurance Companies

Private Pensions

State & Local

Pensions

Mutual Funds

Foreign Holders

Banks, Brokerage

Firms

EQUITY MARKET OWNERSHIP

Source: Federal Reserve Board Data as of 9/30/98

$5.3 tril

$800 mil$1.7 tril

$1.3 tril

$2.0 tril

$900 mil

$800 mil

Total Equity Market Value $12.8 trillion

Valuation• Same stuff as before: today’s price is the present

value of all expected future cash flows:

• PV= PV(future dividends for ever and ever…)

• Mathematically,

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Growth factor...• Technically, we cannot really “simplify” nor use

the previous equation. Then, we use a trick: DIVIDENDS GROW!

• That is, Next years dividend is proportional to this year’s dividends:

• PMT1=PMT0 x (1+g)

• PMT2=PMT1 x (1+g)=PMT0 x (1+g)2

• PMT3=PMT2 x (1+g)=PMT0 x (1+g)3

• Q: What is growth?

Three models...• Zero growth: same dividend amount for ever…

• Constant growth: same growth for ever…

• Non-constant growth: growth changes…

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Example • Calculate the market value of the following companies:

– ABC corp. will pay the same dividends of $1/share in the future. Such company has been returning 10% per year on average.

– DEF corp. has paid $1/share in dividends this year. This amount will grow at 6% per annum. Such company is required to return 10% per annum.

– GHI corp. has paid $1/share in dividends this year. This amount will grow at 12% per annum for the next three years and remain at 6% after. Such company is expected to return 10% per annum.

Solution• ABC: zero growth; PV=1/10%=$10

• DEF:constant growth; PV=1 x (1+6%)/(10%-6%)=$26.5

• GHI: non-constant growth

– Dividend 1=PMT1=1 x (1+12%)=1.12

– Dividend 2= PMT2= 1.12 x (1+12%)=1.2544

– Dividend 3= PMT3= 1.2544 x (1+12%)=1.4049

– Then, Price at year 3=PV3= PMT3 x (1+g1)/(R-g2)=$37.23

Finally,

PV(today)=1.12/(1.1)+1.25/(1.1)2+ 1.41/(1.1)3 + 37.23/(1.1)3 =$31.09

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Growth and Return...

• Growth is the growth in dividends; it is also assumed as the growth in earnings. Why?

• Growth, if constant, can be estimated by “b x ROE”. Why?

• What is i? What is a ”required rate of return”; it is a discount factor that includes inflation and risk. What does it mean?

Think further…R= PMT1/PV + g

R= dividend yield + growth in earnings

R= dividend gain + capital gain

R= additional + perception of

dividend growth in ROE• What is the effect of risk and inflation on stock

prices?

U.S. Yield Curve Inverts Before Last Five Recessions(5-year Treasury bond - 3-month Treasury bill)

-6

-4

-2

0

2

4

6

8

Mar-

69M

ar-71

Mar-

73M

ar-75

Mar-

77M

ar-79

Mar-

81M

ar-83

Mar-

85M

ar-87

Mar-

89M

ar-91

Mar-

93M

ar-95

Mar-

97M

ar-99

Mar-

01

% GDP Growth/Yield Curve

% Real annual GDP growth

Yield curve

?RecessionCorrect 2 Recessions

Correct

RecessionCorrect

RecessionCorrect

RecessionCorrect

Data though 12/20/00