Mishkin/Serletis
The Economics
of Money, Banking,
and Financial Markets
Fifth Canadian Edition
Chapter 4
UNDERSTANDING INTEREST RATES
Copyright © 2014 Pearson Canada Inc.
Learning Objectives
1. Detail the present value concept and the meaning of
the term interest rate
2. Discern among the ways of measuring the interest
rate
3. Illustrate how bond prices and interest rates are
negatively related
4. Explain the difference between nominal and real
interest rates
5. Assess the difference between interest rates and rates
of return
Copyright © 2014 Pearson Canada Inc.
4-2
Measuring Interest Rates
• Present Value:
– a dollar paid to you one year from now is less valuable than a
dollar paid to you today
– why?
• a dollar deposited today can earn interest and become
$1 x (1+i)n
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4-3
Discounting the Future
Let i = 0.10
In one year
$100 x (1+0.10)= $110
In two years
$110 x (1+0.10)=$121
In three years
$121 x (1+0.10)= $133
In general
$100 dollars in n years:
$100 x (1+i)n
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4-4
Simple Present Value
PV = today’s present value
CF = future cash flow or payments
i = interest rate
CF
PV 
n
(1  i )
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4-5
Time Line
Year
PV
$100
$100
$100
$100
0
1
2
n
100
100/(1+i)
100/(1+i)2
100/(1+i)n
Copyright © 2014 Pearson Canada Inc.
4-6
Four Types of Credit Market Instruments
1. Simple Loan
– principal is repaid at the maturity date with interest
2. Fixed Payment Loan
– principal is repaid by making the same payment (principal +
interest) every period for a set period of time
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4-7
Four Types of Credit Market Instruments
3. Coupon Bond
–
a coupon bond pays the owner of the bond a fixed interest
payment (coupon payment) every year until the maturity
date, when a specified final amount (face value or par
value) is repaid
4. Discount Bond
–
a discount bond (also called a zero-coupon bond) is bought
at a price below its face value (at a discount), and the face
value is repaid at the maturity date
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4-8
Yield to Maturity
• YTM
– the interest rate that equates the present value of cash flow
payments received from a debt instrument with its value
today
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4-9
Simple Loan
PV = amount borrowed = $100
CF = cash flow in one year = $110
n = number
$110
$100 
(1  i)1
(1  i)1 x $100  $110
$110
(1  i) 
$100
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4-10
Fixed Payment Loan
LV = loan value
FP = fixed yearly payment
N = number of years until maturity
FP
FP
FP
LV 

 ... 
2
1  i (1  i)
(1  i)n
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4-11
Coupon Bond
P = price of coupon bond
C = yearly coupon payment
F = face value of the bond
n = years to maturity
C
C
C
C
F
P


 ... 

2
3
n
n
1  i (1  i) (1  i)
(1  i) (1  i)
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4-12
Yields to Maturity on a 10%-Coupon-Rate Bond
Maturing in Ten Years (Face Value = $1,000)
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4-13
Three Facts About Coupon Bonds
1. When the coupon bond is priced at its face value, the
yield to maturity equals the coupon rate
2. The price of a coupon bond and the yield to maturity
are negatively related
3. The yield to maturity is greater than the coupon rate
when the bond price is below its face value
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4-14
Consol or Perpetuity
Pc = price of the consol
C = yearly interest payment
ic = yield to maturity of the consol
C
ic 
Pc
• A bond with no maturity date that does not repay
principal but pays fixed coupon payments forever
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4-15
Discount Bond
F = face value of the discount bond
P = current price of the discount bond
F P
i
P
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4-16
Yield on a Discount Basis
• Yield on a discount basis:
F P
365
idb 

P
days to maturity
idb = yield on a discount basis
F= face value
P= purchase price
Copyright © 2014 Pearson Canada Inc.
4-17
The Distinction Between Interest Rates and
Returns
RET  return from holding the bond from time t to t  1
Pt  price of bond at time t
Pt 1  price of the bond at time t  1
C  coupon payment
C Pt 1  Pt
RET  
Pt
Pt
C
 current yield  i c
Pt
Pt 1  Pt
 rate of capital gain  g
Pt
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4-18
The Distinction Between Interest Rates and
Returns (cont’d)
• The return equals the yield to maturity only if the
holding period equals the time to maturity
• A rise in interest rates is associated with a fall in bond
prices, resulting in a capital loss if time to maturity is
longer than the holding period
• The more distant a bond’s maturity, the greater the
size of the percentage price change associated with an
interest-rate change
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4-19
The Distinction Between Interest Rates and
Returns (cont’d)
• The more distant a bond’s maturity, the lower the rate
of return the occurs as a result of an increase in the
interest rate
• Even if a bond has a substantial initial interest rate, its
return can be negative if interest rates rise
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4-20
One-Year Returns on Different-Maturity 10%-CouponRate Bonds When Interest Rates Rise from 10% to 20%
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4-21
Interest-Rate Risk
• Prices and returns for long-term bonds are more
volatile than those for shorter-term bonds
• There is no interest-rate risk for any bond whose time
to maturity matches the holding period
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4-22
Real and Nominal Interest Rates
• Nominal interest rate makes no allowance for inflation
• Real interest rate is adjusted for changes in price level
so it more accurately reflects the cost of borrowing
• Ex ante real interest rate is adjusted for expected
changes in the price level
• Ex post real interest rate is adjusted for actual changes
in the price level
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4-23
Fisher Equation
i = nominal interest rate
r = real interest rate
πe = expected inflation rate
i  r  e
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4-24
Fisher Equation (cont’d)
• When the real interest rate is low, there are greater
incentives to borrow
• Low interest rates reduces the incentives to lend
• The real interest rate is a better indicator of the
incentives to borrow or lend
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4-25
Real and Nominal Interest Rates
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4-26