Transcript FINANCIAL MARKETS AND INSTITIUTIONS: A Modern Perspective

Chapter Two
Determinants of
Interest Rates
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Interest Rate Fundamentals
• Nominal interest rates - the interest
rate actually observed in financial
markets
– directly affect the value (price) of most
securities traded in the market
– affect the relationship between spot and
forward FX rates
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Time Value of Money and Interest Rates
• Assumes the basic notion that a dollar
received today is worth more than a dollar
received at some future date
• Compound interest
– interest earned on an investment is reinvested
• Simple interest
– interest earned on an investment is not
reinvested
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Calculation of Simple Interest
Value = Principal + Interest (year 1) + Interest (year 2)
Example:
$1,000 to invest for a period of two years at 12 percent
Value = $1,000 + $1,000(.12) + $1,000(.12)
= $1,000 + $1,000(.12)(2)
= $1,240
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Value of Compound Interest
Value = Principal + Interest + Compounded interest
Value = $1,000 + $1,000(.12) + $1,000(.12) + $1,000(.12)
= $1,000[1 + 2(.12) + (.12)2]
= $1,000(1.12)2
= $1,254.40
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Present Value of a Lump Sum
• PV function converts cash flows received
over a future investment horizon into an
equivalent (present) value by discounting
future cash flows back to present using
current market interest rate
– lump sum payment
– annuity
• PVs decrease as interest rates increase
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Calculating Present Value (PV) of a Lump
Sum
PV = FVn(1/(1 + i/m))nm = FVn(PVIFi/m,nm)
where:
PV = present value
FV = future value (lump sum) received in n years
i = simple annual interest rate earned
n = number of years in investment horizon
m = number of compounding periods in a year
i/m = periodic rate earned on investments
nm = total number of compounding periods
PVIF = present value interest factor of a lump sum
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Calculating Present Value of a Lump Sum
• You are offered a security investment that pays
$10,000 at the end of 6 years in exchange for a fixed
payment today.
•
PV = FV(PVIFi/m,nm)
•
at 8% interest - = $10,000(0.630170) = $6,301.70
•
at 12% interest - = $10,000(0.506631) = $5,066.31
•
at 16% interest - = $10,000(0.410442) = $4,104.42
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Calculation of Present Value (PV) of an
Annuity
nm
PV = PMT  (1/(1 + i/m))t = PMT(PVIFA i/m,nm)
t=1
where:
PV = present value
PMT = periodic annuity payment received
during investment horizon
i/m = periodic rate earned on investments
nm = total number of compounding periods
PVIFA = present value interest factor of an annuity
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Calculation of Present Value of an Annuity
You are offered a security investment that pays $10,000 on
the last day of every year for the next 6 years in exchange
for a fixed payment today.
PV = PMT(PVIFAi/m,nm)
at 8% interest - = $10,000(4.622880) = $46,228.80
If the investment pays on the last day of every quarter for
the next six years
at 8% interest - = $10,000(18.913926) = $189,139.26
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Future Values
• Translate cash flows received during
an investment period to a terminal
(future) value at the end of an
investment horizon
• FV increases with both the time
horizon and the interest rate
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Future Values Equations
FV of lump sum equation
FVn = PV(1 + i/m)nm = PV(FVIF i/m, nm)
FV of annuity payment equation
(nm-1)
FVn = PMT

(1 + i/m)t = PMT(FVIFAi/m, mn)
(t = 0)
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Calculation of Future Value of a Lump Sum
• You invest $10,000 today in exchange for a
fixed payment at the end of six years
–
–
–
–
at 8% interest = $10,000(1.586874) = $15,868.74
at 12% interest = $10,000(1.973823) = $19,738.23
at 16% interest = $10,000(2.436396) = $24,363.96
at 16% interest compounded semiannually
• = $10,000(2.518170) = $25,181.70
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Calculation of the Future Value of an Annuity
• You invest $10,000 on the last day of every year
for the next six years,
– at 8% interest = $10,000(7.335929) = $73,359.29
• If the investment pays you $10,000 on the last day
of every quarter for the next six years,
– FV = $10,000(30.421862) = $304,218.62
• If the annuity is paid on the first day of each
quarter,
– FV = $10,000(31.030300) = $310,303.00
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Relation between Interest Rates and
Present and Future Values
Present
Value
(PV)
Future
Value
(FV)
Interest Rate
Interest Rate
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Effective or Equivalent Annual Return
(EAR)
Rate earned over a 12 – month period
taking the compounding of interest into
account.
EAR = (1 + r) c – 1
Where c = number of compounding
periods per year
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Loanable Funds Theory
• A theory of interest rate determination
that views equilibrium interest rates in
financial markets as a result of the
supply and demand for loanable funds
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Supply of Loanable Funds
Demand
Supply
Interest
Rate
Quantity of Loanable Funds
Supplied and Demanded
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Funds Supplied and Demanded by Various
Groups (in billions of dollars)
Funds Supplied Funds Demanded
Households
Business - nonfinancial
Business - financial
Government units
Foreign participants
McGraw-Hill/Irwin
$34,860.7
12,679.2
31,547.9
12,574.5
8,426.7
2-19
$15,197.4
30,779.2
45061.3
6,695.2
2,355.9
Net
$19,663.3
-12,100.0
-13,513.4
5,879.3
6,070.8
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Determination of Equilibrium Interest Rates
D
S
Interest
Rate
IH
i
E
IL
Q
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Quantity of Loanable Funds
Supplied and Demanded
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Effect on Interest rates from a Shift in the
Demand Curve for or Supply curve of
Loanable Funds
Increased supply of loanable funds
Interest
Rate
Increased demand for loanable funds
SS
DD
DD
SS*
DD*
i**
i*
McGraw-Hill/Irwin
i*
E*
Q* Q**
E*
E
E
i**
SS
Quantity of
Funds Supplied
2-21
Q* Q**
Quantity of
Funds Demanded
©2007, The McGraw-Hill Companies, All Rights Reserved
Factors Affecting Nominal Interest
Rates
•
•
•
•
•
•
Inflation
Real Interest Rate
Default Risk
Liquidity Risk
Special Provisions
Term to Maturity
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Inflation and Interest Rates: The
Fisher Effect
The interest rate should compensate an investor
for both expected inflation and the opportunity
cost of foregone consumption
(the real rate component)
i = RIR + Expected(IP)
RIR = i – Expected(IP)
or
Example: 3.49% - 1.60% = 1.89%
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Default Risk and Interest Rates
The risk that a security’s issuer will default
on that security by being late on or missing
an interest or principal payment
DRPj = ijt - iTt
Example for December 2003:
DRPAaa = 5.66% - 4.01% = 1.65%
DRPBaa = 6.76% - 4.01% = 2.75%
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Term to Maturity and Interest Rates:
Yield Curve
(a) Upward sloping
(b) Inverted or downward
sloping
(c) Flat
Yield to
Maturity
(a)
(c)
(b)
Time to Maturity
McGraw-Hill/Irwin
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Term Structure of Interest Rates
• Unbiased Expectations Theory
• Liquidity Premium Theory
• Market Segmentation Theory
McGraw-Hill/Irwin
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Forecasting Interest Rates
Forward rate is an expected or “implied” rate
on a security that is to be originated at some
point in the future using the unbiased
expectations theory
_
_
1/2 - 1
R
=
[(1
+
R
)(1
+
(
f
))]
1 2
1 1
2 1
where
2 f1
McGraw-Hill/Irwin
= expected one-year rate for year 2, or the implied
forward one-year rate for next year
2-27
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