# BOND VALUATION

```Group 06
Habiba Mustafa
Sumaiya Nishan
Hafiz Aamir Sohail
Altaf Hussain
BOND VALUATION
BOND: long term debt
A security that pays a stated amount of
interest to the investor, period after
period until its maturity.
Face value
Coupon
maturity
BOND VALUE
 PV(bond)=PV(coupon payments)+PV(final payment)
PV= PMT(1-1/(1+i)^n)/i + MV/(1+i)^n
Factors affecting Bond prices
Credit Quality
Interest Rate
Yield
Tax Status
Interest rate
yield
Yield is a figure that shows the return you get
on a bond.
Simplest version
Yield= coupon amount/price
• Most important thing to remember!!!!
**When prevailing interest rates rise, prices of
outstanding bonds fall to bring the yield of
older bonds into line with higher-interest new
issues
**When prevailing prices fall, prices of
outstanding bonds rise, until the yield of older
bonds is low enough to match the lower
interest rate on new issues.
BOND VOLATILITY
Volatility refers to the amount of
uncertainty or risk about the size of
changes in security’s value.
Volatility=Duration/1+yield
BOND DURATION
• Duration is a weighted measure of the length
of time the bond will pay out.
• Unlike maturity,
duration takes into account interest payments
that occur throughout the course of holding
the bond.
Cont’d…
Term structure/Yield Curve
A "term structure of interest rates,“ also
known as yield curve is a graph that plots the
yield/spot rates of bonds against their
maturities, ranging from shortest to longest.
Forms of yield curve
Cont’d…
EXPECTATION THEORY
The expectation theory says that:
“Bonds are priced so that an investor who holds
a succession of short bonds can expect the same
return as another investor who holds a long
bond.”
INTRODUCING RISK
In expectation theory risk factor must
be considered. If predicted future
level of interest rates, select strategy
offering highest return.
Inflation and Term structure
• Suppose u are saving for your retirement.
which of the following strategies is the more
risky?
• Invest in one-year or invest in 20-year bond?
Inflation and nominal interest rates
• How does inflation affect the nominal rate of
interest?
FISHER’S THEORY
“A change in the expected inflation rate will
cause the same proportionate change in the
nominal interest rate; no effect on the required
real interest rate”.
1+rnominal=(1+rreal)(1+i)
REAL & NOMINAL INTEREST RATE
In Real interest rate no inflation factor while in
Nominal interest rate inflation factor exists.
Inflation rate higher real return will be lower.
NOMINAL INTEREST RATE
Real cash flowt=nominal cash flowt/1+inflation
rate)t
FOR EXAMPLE:
If u were to invest \$1,000 in a 20-year bond
with a 10% coupon, final payment would be
\$1,100.
if inflation rate=6% then real value would be
=1,100/1.0620=\$342.99
INDEXED BONDS
Bonds promised you a fixed nominal rate
of interest.
Valuation of common
stock
• Primary Market
• Secondary Market
How Common Stocks are valued
• PV(stock) = PV(expected future dividends)
• Today’s Price
The cash payoff to the owners of common
stocks comes in two forms
• Cash dividends
• Capital gains or losses
Conti…d
• Expected return = r = Divi1 + p1-p0/p0
Example
Suppose Fledgling Electronics stock is selling for
\$100 a share (p0=100). Investors expect a \$5
cash dividend over the next year (Div1=5).
They also expect stock to sell for \$110 a year
(p1=110)
Conti’d
Expected return = r = 5+(110-100)/100
r = 0.15 or 15%
On the other hand, if you are given investors
forecasts of dividend and price and the
expected return is same then you can predict
today’s price.
Price = po = Div1+p1/(1+r)
Conit’d
• If DIV1=5 and p1=110 and r=15%, then today's
price should be 100:
P0 = 5+110/1.15 =\$100
But what determines the Next Year’s
Price
• P1 = DIV2 + P2/(1+r)
That is, a year from now investor will be looking
out at dividends in year 2 and price at the end
of year 2. thus we can forecast p1 by
forecasting DIV2 and p2 and we can express
po in terms of DIV1, DIV2, and p2:
Conit…’d
• Po=1/1+r(DIV1+p1)=1/1+r(DIV1+DIV2+p2/1+r)
=DIV1/(1+r) + DIV2+p2/(1+r)*2
Example
Suppose they are looking today for dividends of
\$5.5 in year 2 and subsequent price of \$121.
that implies a price at the end of the year 1 of
P1 = 5.50+121/1.15
= \$110
Conti…d
• From our expended formula
P0 = 5/1.15 + 5.50+121/(1.15)*2
= \$100
Estimating the Cost of Equity Capital
• Po = DIV1/ (r-g)
•
r = (DIV 1/p0) + g
Danger lurk in Constant-Growth
formula
• Dividend growth rate = plowback ratio*ROE
The link between stock price and
Earning per share
• Growth stock
• Income stock
Expected return =dividend yield=earning-p ratio
If dividend is \$10 a share and stock price is \$100
then:
Expected return=DIV1/P0
= 10/100 = .10
Conti..d
The price equals
P0= DIV1/r = EPS1/r = 10/.10 =100
Po =EPS1/r+PVGO
So,
EPS/Po= r ( 1- PVGO/Po)
It will underestimate r if PVGO is +ve and
overestimate it if PVGO is -ve
Calculating PV of Growth
Opportunities
• Po= DIV1/r-g
• Payout ratio = DIV1/EPS1
• Growth rate= g = plowback ratio*ROE
• Present value of level stream of earnings= EPS/r
• PVGO = NPV1/r-g
• Share price = EPS1/r +PVGO
Valuing a Business by Discounting Cash Flow
• In this you forecast dividend per share or total
free cash flow of a business.
• Value today always equals future cash flow
discounted at the opportunity cost of capital
• PV= FCF/1+r + FCF2/(1+r)^2 +….+FCF/(1+r)^H
+ PV/(1+r)^H
Estimating Horizon Value
• Forecasting reasonable horizon is particularly
difficult. The usual assumption is moderate
long rum growth after the horizon, which
allow us to growing-perpatuity DCF formula.
• It can also be calculated normal price-earnings
or market-book ratios at the horizon date
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21 cards