Determinants of Interest Rates Wiley

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```					FINANCE IN A CANADIAN
SETTING
Lusztig, Cleary, Schwab
CHAPTER SIX

Bond and Common Share
Valuation
Learning Objectives

1. Name the five variables of a debt contract.
2. Describe how to estimate bond prices and
bond yields.
3. Discuss the three leading theories on the
term structure of interest rates, and explain
how they differ.
4. Explain the dividend discount model (DDM)
and how financial officers use it to value
shares.
Introduction

   Topics explored and discussed include:
•   valuation of bonds and common share
•   Rates at which debt instruments are
discounted and determined through the
financial markets
•   valuation of bonds and common share
without explicit consideration of risk
•   Risk premiums associated with interest rates
Valuation of Bonds

   Bond – a debt instrument that entitles the
owner to specified periodic interest payments
and eventually to the repayment of principle
at the stated date of maturity
   Coupon rate – the rate specified on the
original contract in relation to the face value
of the debt
   Effective yield or yield to maturity – the yield
investors realize by holding to maturity a debt
contract that they bought at a particular
market price
Valuation of Bonds

   Debt contracts are characterized by
• The face value
• Stated interest rate
• Time pattern of repayment under the debt
contract
• Current market price of the debt contract
• Effective yield of the debt contract, based
on its current price
Calculating Market Price

       1       
1             
B  I
1  r n   
F
     r           1  r n

               


Where:
B = current market price of the bond
F = face value of the bond
I = interest or coupon payments
r = yield to maturity
Semi-annual coupons

   In calculating the bond price for semi-annual
coupons the following changes must be
recognized:
•   Divide the annual coupon by two to
determine the amount of semi-annual coupon
•   Divide the market yield by two to obtain the
six-month market yield
•   Multiply the number of years to maturity by
two to obtain the number of semi-annual
periods to maturity
Perpetual Bonds

   Zero-coupon bond (or strip bond) do not pay
any interest during its life
   Zeros are created when financial
the cash flow from them and sell the coupon
and cash flow separately
   Purchaser pays less for zeros and receives
face value at maturity
Bond Yields
    Yield to Maturity - the yield investors realize
by holding to maturity a debt contract that
they bought at a particular market price.
The yield captures both the coupon income
and the capital gain or loss realized by
purchasing the bond at a price different
from its face value

    Two methods in calculating YTM include:
1.   Linear interpolation
2.   Approximation formula
Current Yield

   Current yield – the ratio of annual
coupon interest to the current market
price

Annual interest
CY 
B
Determinants of Interest
Rates
   The effective yield of a debt contract is
established by the general economic
factors that effect the overall level of
interest rates and by such features of
the debt contract as its maturity,
currency denomination, and risk of
default.
Determinants of Interest
Rates

   Interest - the price paid for borrowing
money
• Changes in interest is measured in basis
points.
• One basis point = 1/100th of one percent
Determinants of Interest
Rates
   Loanable fund theory –the relationship
between the supply and demand for
funds where the supply of capital  with
 interest rates and the demand for
funds  as the costs . At equilibrium
interest rates are such that demand
equals supply.
Determinants of Interest
Rates
 Real risk-free rate interest – the basic
interest rate that must be offered to
individuals to persuade them to save
rather than consume and is not affected
by price changes or risk factors
 Nominal interest rates – represent the
real rate (RR) plus the expected
inflation
Determinants of Interest
Rates

RF = RR + EI
where:
RF = short-term treasury bill rate
RR = the real risk-free rate of interest
EI = the expected rate of inflation over
the term of the instrument
Term Structure of Interest
Rates
 Term Structure of Interest Rates – the
relationship between time to maturity
and yields for a particular category of
bonds at a particular time
 Yield curve – the graphical depiction of
the relationship between yields and
time to maturity
Term Structure of Interest
Rates
    The three most common term
structure of interest rate theories
include:
1. Expectations theory
2. Liquidity preference theory
3. Market segmentation theory
Common Share Valuation

   Two basic approaches are used in
fundamental security analysis:
1. Present Value using the DDM
2. Relative valuation methods which values
shares relative to some company
characteristics based on a multiple that is
deemed appropriate
Common Share Valuation

   Dividend discount model (DDM) – uses the
expected future cash flows as the basis for
valuing common shares

    D
1  r 
t
P0
t 1          cs
Where:
Po = estimated price of a common share today
D = the dividends expected to be received for
each future period
rcs = the required rate of return
No-Growth-Rate Version of
the DDM
   The fixed dollar dividend reduces to a
perpetual annuity

P    0
 D0
r   cs
Where:
D0 = the constant-dollar dividend
rcs = the required rate of return
The Constant-Growth-Rate
Version of the DDM
   Dividends are expected to grow at a
constant rate over time

P            D    1
0
r   cs
g

Where:
D1 = the dividend expected to be
received at the end of year 1
Estimating the Growth Rate
in Future Dividends
    Three estimates are required in order to
implement the constant-growth-rate of the
DDM:
1. The expected dividend at the end of the
year
2. The required rate of return by
shareholders
3. The expected growth rate in dividends
Estimating Growth Rates

   Internal growth rate of earnings or
dividends:

g = ROE X (1- Payout ratio)

•   Used where g can be estimated using data
for a particular year using long-term averages
or “normalized” figures for ROE and payout
ratio
Estimating Growth
Opportunities
•   Under the assumptions g=0, D1=EPS1 the
constant-growth-rate version of the DDM is
represented by:

EPS 1
Po 
rcs
Estimating Growth
Opportunities
•   Firms that do have growth opportunities
can have their growth represented in
the PVGO

EPS1
Po        PVGO
rcs
Other Versions of The DDM

   Multiple-growth-rate version

   Two-stage-growth-rate version
Summary
1. Market prices of debt such as bonds are
calculated by discounting future cash flows
specified under the loan contract (periodic
interest payments and eventual repayment
of principle) at the prevailing interest rate.
2. Interest is the price paid for borrowed
money, and in free financial markets, it is
determined by the laws of supply and
demand. Interest rates tend to parallel
inflation, and in an environment of general
price-level changes, we have to distinguish
between nominal and real interest rates.
Summary
3. The liquidity preference theory postulates
that investors prefer short maturities, and
borrowers desire long maturities. Therefore,
the term structure should be upward sloping
and exhibit a built-in liquidity premium.
According to the expectations hypothesis, the
yield curve reflects expectations about the
future levels of interest rates. When investors
expect short-term rates to fall, we must
observe an inverted or downward-sloping
yield curve.
Summary

4. According to the dividend discount model
(DDM), the value of a stock today is the
discounted value of all future dividends. To
account for an infinite stream of dividends,
stocks to be valued are classified by their
expected growth rate in dividends.

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 views: 9 posted: 9/27/2012 language: English pages: 30