valuation of common stocks & bonds
TRANSCRIPT

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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.
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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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Valuation ModelsContd
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 shortrun
nonconstant 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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Valuation ModelsContd
Link between stock price and EPS
Stock price can be thought of as the capitalized valueof average earning under a nogrowth policy, plus
PVGO, the net present value of growth opportunities:
P0=EPS1/r +PVGO
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Valuation ModelsContd
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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Exercise: Valuing Common Stocks
Our company forecasts to pay a $8.33 dividend next year,
which represents 100% of its earnings. This will provide
investors with a 15% expected return. Instead, we decide to
plow back 40% of the earnings at the firms current return onequity of 25%. What is the value of the stock before and after
the plowback decision?
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56.55$
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).
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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
gRD
gRg)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
11
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 principalonly 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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Exercise: Bond Valuation
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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Exercise: Bond Valuation
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 semiannually?
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Bond Basics: PriceYield 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 risewhich 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
Nonlinear 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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