Unit 1 Valuation

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Business risk

Financial risk

Liquidity risk

Exchange rate risk

Country risk

Risk - Types


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Business Risk

Uncertainty of income flows caused

by the nature of a firms business Sales volatility and operating

leverage determine the level of

business risk.


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Financial Risk

Uncertainty caused by the use of debtfinancing.

Borrowing requires fixed paymentswhich must be paid ahead of paymentsto stockholders.

The use of debt increases uncertainty ofstockholder income and causes anincrease in the stocks risk premium.


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Liquidity Risk

Uncertainty is introduced by thesecondary market for an investment.

How long will it take to convert aninvestment into cash?

How certain is the price that will be

received?


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Exchange Rate Risk

Uncertainty of return is introduced byacquiring securities denominated in a

currency different from that of theinvestor.

Changes in exchange rates affect the

investors return when converting aninvestment back into the home

currency.


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Country Risk

Political risk is the uncertainty of returnscaused by the possibility of a majorchange in the political or economic

environment in a country.

Individuals who invest in countries that

have unstable political-economicsystems must include a country risk-premium when determining their

required rate of return


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Valuation

How to determine the correctprice??


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Basics

Risk Return Relationship

Req return = Rf + Risk Prem(Rp)

Fixed Deposits Bonds

Preference Shares

Equity Shares

Present Value Concept

How to calculate Price??


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Maturity value(MV)

Coupon rate Discount Rate

Bonds

A bond is a long-term debtinstrument issued by acorporation or government.


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A perpetual bond is a bond that nevermatures.It has an infinite life.

(1 +kd)1 (1 + kd)

2 (1 + kd)V = + + ... +

I II

= St=1

(1 + kd)t

Ior I (PVIFA kd, )

V = I / kd [Reduced Form]

Valuation for Different Bonds


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Bond P has a Rs.1,000 face value and provides an8% coupon. The appropriate discount rate is 10%.

What is the value of the perpetual bond?

I = Rs.1,000 ( 8%) = Rs.80.

kd = 10%.

V = I / kd [Reduced Form]

= Rs.80 / 10% = Rs.800

Perpetual Bond Example


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Bond C has a Rs1,000 face value and provides an 8%annual coupon for 3 years. The appropriate discount rate

is 10%. What is the value of thecoupon bond?

V = [80/1.10] + [80/(1.10)^2] + [(80+1000)/1.10^3]

Coupon Bond Example


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V = 1,000 (PVIF10%, 30

)

=1,000 (.057)

= Rs.57.00

Bond Z has a Rs.1,000 face valueand a 30-year life. The appropriate

discount rate is 10%. What is thevalue of thezero-coupon bond?

Zero Coupon Bond Example


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V = Rs.40 (PVIFA5%, 30) + Rs.1,000 (PVIF5%, 30)

=Rs.40 (15.373) + Rs.1,000 (.231)= Rs.614.92 + Rs.231.00= Rs.845.92

Bond C has a Rs.1,000 face value and providesan 8% semiannual coupon for 15 years. The

appropriate discount rate is 10% (annual rate).What is the value of thecoupon bond?

Semiannual Coupon BondExample


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Preferred Stock is a type of stock thatpromises a (usually) fixed dividend, but

at the discretion of the board ofdirectors.

Preferred Stock has preference overcommon stock in the payment ofdividends and claims on assets.

Preferred Stock


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This reduces to a perpetuity!

(1 +kP)1 (1 + kP)

2 (1 + kP)V = + + ... +

DivP DivPDivP

= St=1 (1 + kP)

t

DivP or DivP(PVIFA kP, )

V = DivP / kP

Preferred Stock Valuation


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DivP = Rs.100 ( 8% ) = Rs.8.00.

kP = 10%.V = DivP /kP = Rs.8.00 /10%

= Rs.80

Stock PS has an 8%, Rs.100 par valueissue outstanding. The appropriate

discount rate is 10%. What is the valueof the preferred stock?

Preferred Stock ValuationExample


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(1) Future dividends

(2) Future sale of the commonstock shares

What cash flows will a shareholder receivewhen owning shares of common stock?

Common Stock Valuation


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Basic dividend valuation model accounts for the PVof all future dividends.

(1 +ke)1 (1 + ke)

2 (1 + ke)V = + + ... +

Div1 DivDiv2

= St=1

(1 + ke)t

Divt Divt: Cash dividendat time t

ke: Equity investors

required return

Dividend Valuation Model


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The basic dividend valuation model adjusted for the

future stock sale.

(1 +ke)1 (1 + ke)

2 (1 + ke)nV = + + ... +

Div1 Divn + PricenDiv2

n: The year in which the firmsshares are expected to be sold.

Pricen: The expected share price in year n.

Adjusted Dividend Valuation

Model


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The dividend valuation model requires the forecast ofallfuture dividends. The following dividend growth

rate assumptions simplify the valuation process.Constant Growth

No Growth

Growth Phases

Dividend Growth Patterns


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The constant growth model assumes that dividendswill grow forever at the rate g.

(1 +ke)1 (1 + ke)

2 (1 + ke)V = + + ... +

D0(1+g) D0(1+g)

=(ke- g)

D1D1: Dividend paid at time 1.

g: The constant growth rate.

ke: Investors required return.

D0(1+g)2

Constant Growth Model


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Stock CG has an expected growth rate of 8%.Each share of stock just received an annualRs.3.24 dividend per share. The appropriate

discount rate is 15%. What is the value of thecommon stock?

D1 = Rs.3.24 ( 1 + .08 ) = Rs.3.50

VCG = D1 / ( ke - g ) = Rs.3.50 / ( .15 - .08 ) =Rs.50

Constant Growth ModelExample


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The zero growth model assumes that dividends willgrow forever at the rate g = 0.

(1 +ke)1 (1 + ke)

2 (1 + ke)VZG = + + ... +

D1 D

=ke

D1 D1: Dividend paid at time 1.ke: Investors required return.

D2

Zero Growth Model


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Stock ZG has an expected growth rate of 0%.Each share of stock just received an annualRs.3.24 dividend per share. The appropriate

discount rate is 15%. What is the value of thecommon stock?

D1 = Rs.3.24 ( 1 + 0 ) = Rs.3.24

VZG = D1 / ( ke - 0 ) = Rs.3.24 / ( .15 - 0 )= Rs.21.60

Zero Growth Model Example


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D0(1+g1)t Dn(1+g2)t

The growth phases model assumes thatdividends for each share will grow at two or

more differentgrowth rates.

(1 +ke)t (1 + ke)

tV =St=1

n St=n+1

+

Growth Phases Model


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D0(1+g1)t Dn+1

Note that the second phase of the growth phasesmodel assumes that dividends will grow at a

constant rate g2. We can rewrite the formula as:

(1 +ke)t (ke- g2)

V =St=1

n

+1

(1 +ke)n

Growth Phases Model


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Stock GP has an expected growth rate of16% for the first 3 years and 8% thereafter.

Each share of stock just received an annualRs.3.24 dividend per share. Theappropriate discount rate is 15%. What isthe value of the common stock under this

scenario?

Growth Phases Model


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Stock GP has two phases of growth. The first, 16%, starts at time t=0for 3 years and is followed by 8%thereafter starting at time t=3. Weshould view the time line as two separate time lines in the valuation.

0 1 2 3 4 5 6D1 D2 D3 D4 D5 D6

Growth of 16% for 3 years Growth of 8% to infinity!

Growth Phases Model


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Note that we can value Phase #2 using the Constant GrowthModel

0 1 2 3

D1 D2 D3

D4 D5 D6

0 1 2 3 4 5 6

Growth Phase#1 plus the infinitely

long Phase #2

Growth Phases Model


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Note that we can now replace all dividends from Year 4 to infinity withthe valueat time t=3, V3! Simpler!!

V3 =

D4 D5 D6

0 1 2 3 4 5 6

D4

k-g

We can use this model becausedividends grow at a constant 8%

rate beginning at the end of Year 3.

Growth Phases Model


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Now we only need to find the first four dividends to calculate thenecessary cash flows.

0 1 2 3

D1 D2 D3

V3

0 1 2 3

New Time

Line

D4

k-g

Where V3 =

Growth Phases Model

Unit 1 Valuation

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