valuation of common stocks & bonds

7/21/2019 Valuation of Common Stocks & Bonds

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Financial Management

Session - #

Valuation of Common Stocks & Bonds


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Common (Equity) Stocks

Common stock never matures, todays value is the

present value of an infinite stream of cash flows (i.e.,

dividend). But dividends are not fixed.

Not knowing the amount of the dividends

or even if there will be future dividends makes it difficult to determine the value of common stock.

So what should we do?

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Valuation Models

Dividend Valuation Model (DVM): Let D be the constant dividend paid:

The required rate of return (R) is the returnshareholders demand to compensate them for the time value of money tied up in

their investment and

the uncertainty of the future cash flows from theseinvestments.

3

R

P

RRRP

Div

)1(

Div

)1(

Div

)1(

Div

0

3322110


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Valuation ModelsContd

Gordon Model (Constant Growth Rate)

4

)1(DivDiv 01 g

Since future cash flows grow at a constant rate forever,

the value of a constant growth stock is the present valueof a growing perpetuity:

gRP

1

0

Div

Assume that dividends will grow at a constant rate, g,

forever, i.e.,

2

012 )1(Div)1(DivDiv gg

3

023 )1(Div)1(DivDiv gg .

.

.


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Dividend and Earnings Growth

Growth in dividends occurs primarily as a result ofgrowth in EPS.

Growth in earnings, in turn, results from a number offactors, including (1) retention ratio (2) ROE and (3) inflation.

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Varying Dividend Growth Rate:

For many companies, it is unreasonable to assume

that it grows at a constant rate. P0 = Present value of dividends based on short-run

non-constant rate + Present value of dividends

using constant growth rate.

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Exercise

A companys stock just paid a Rs.11.50

dividend, which is expected to grow at 30%

for next three years. After that, the dividend isexpected to grow at 8% constantly forever. The

stocks required return is 13.4%.

What is the price of the stock today?

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Link between stock price and EPS

Stock price can be thought of as the capitalized valueof average earning under a no-growth policy, plus

PVGO, the net present value of growth opportunities:

P0=EPS1/r +PVGO

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Sometimes when firms finds more opportunities for

the investments, instead of paying all earning as

dividends firms invest a part or full of the earnings inthe firm.

Payout Ratio: Fraction of earnings paid out as dividends

Plowback Ratio: Fraction of earnings retained (reinvested

in the business, also called retention ratio) by the firm

In this case, growth g = ROI * Plowback ratio

This is the steady (or sustainable) rate at which firm

can grow

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Exercise: Valuing Common Stocks

Our company forecasts to pay a $8.33 dividend next

year, which represents 100% of its earnings. This

will provide investors with a 15% expected return.Instead, we decide to plow back 40% of the earnings

at the firms current return on equity of 25%. What is

the value of the stock before and after the plowback

decision?

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11/26

Exercise: Valuing Common Stocks

Our company forecasts to pay a $8.33 dividend next year,

which represents 100% of its earnings. This will provide

investors with a 15% expected return. Instead, we decide to

plow back 40% of the earnings at the firms current return onequity of 25%. What is the value of the stock before and after

the plowback decision?

11

56.55$

15.

33.80 P

No Growth With Growth

00.100$10.15.

00.5

10.40.25.

0

P

g


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Exercise: Valuing Common StocksContd

If the company did not plowback some earnings, the

stock price would remain at $55.56. With the

plowback, the price rose to $100.00.

The difference between these two numbers (PV after

and before the plowback or earning) is called thePresent Value of Growth Opportunities (PVGO).

12

44.44$56.5500.100 PVGO


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Valuing Common StocksEstimating R

The discount rate can be broken into two parts.

The dividend yield

The growth rate (in dividends) In practice, there is a great deal of estimation error

involved in estimatingR.

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gP

Dg

P

g)1(DR

g-RD

g-Rg)1(DP

0

1

0

0

100


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Valuing Common Stocks

For a stock it is expected that the company will pay

the dividends of Rs. 3, Rs. 4 and Rs. 5 over the next

three years respectively. An investor with a

investment horizon of three years expecting that the

price of the stock at the end of three years would be

Rs. 95. If the investor expects a return of 12% pa.

what will be the price of the stock which investor

would be willing to pay now?

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Bond Basics

A bond is a legally binding agreement between

a borrower and a lender that specifies the:

Par (face) value Coupon rate

Coupon payment

Maturity Date

The yield to maturity is the required market

interest rate on the bond.

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Bonds: Basics

Primary Principle:

Value of financial securities = PV of expected future cash

flows

Bond value is, therefore, determined by the present

value of the coupon payments and par value.

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T

T

)(1

FV

R

R)(1

1-1

CValueBond R


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Bonds: ZCB

Make no periodic interest payments (coupon rate =

0%)

The entire yield to maturity comes from thedifference between the purchase price and the par

value.

Cannot sell for more than par value Sometimes called zeroes, deep discount bonds, or

original issue discount bonds (OIDs)

Treasury Bills and principal-only Treasury strips aregood examples of zeroes.

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Bonds: Coupon Bonds

Make periodic coupon payments in addition to thematurity value

The payments are usually equal in each period.Therefore, the bond is just a combination of anannuity of coupons and a terminal (maturity) value.

Coupon payments are typically semiannual.

Effective annual rate (EAR) =

(1 + R/m)m 1

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Exercise: Bond Valuation

Consider a bond with a par value of Rs.1000 payable

after seven years, a coupon rate of 5% and a required

annual yield of 12%. Assume that coupon payments

are made annually to bondholders and that the next

coupon payment is due in another 12 months.

What is the current price of the bond?

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For the bond described in previous exercise, what is

the new required annual yield

If the bond price goes up by 3%?

If it goes down by 3%?

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Suppose you are considering investing in a plain

vanilla coupon bond that

Promises interest of $100, paid at the end of each year

Promises to pay the principal amount of $1000 at the end of

12 years

Investors require an annual yield of 5%

What will be the value of the bond, if the interest is

paid semi-annually?

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Bond Basics: Price-Yield Relationship

A fundamental property of a bond is that its price

changes in the opposite direction of the change in the

interest rates.

Compute the price of a bond with a par value of

Rs.1000 to be paid in ten years, a coupon rate of 10%,

and a required yield of 3%, 5%, 15% and 25%.

Coupon payments are made annually.

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Yield Price

3 1597.11

5 1386.09

15 749.06

25 464.42


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Bond Prices and Interest Rates (1/2)

Bond price = par value,

If coupon rate is equal to the yield required by the market.

Bond price < par value (at a discount) If coupon rate is below the yield required by the market.

Bond price > par value (at a premium)

If coupon rate is above the yield required by the market. If market interest rates increase (decrease), the price

of a bond will decrease (increase).

Price of a bond will fall if rate rise-which is the majorrisk faced by bondholders

23Vivek Rajvanshi,


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Bond Prices and Interest Rates (2/2)

24Vivek Rajvanshi,

Yield (r)

BondPric

e

Non-linear inverse relationship between bond price and interest rate

Longer term bonds are more sensitive to changes in interest rates than

shorter term bonds


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Exercise:

You buy a stock for Rs.230 and you expect the next

years dividend to be Rs.12.42. Furthermore, you

expect the dividend to grow at a constant rate of 8%

p.a. in future

What is the expected return of the stock?

What is the dividend yield?

What is the expected price of the stock in five years?

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Thank You!

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valuation of common stocks & bonds

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