Chapter 6
Measuring and Calculating
Interest Rates and
Financial Asset Prices
6-2
 Learning Objectives 
• To explore the important relationships between the interest
rates on bonds and other financial instruments and their market
value or price.
• To look at the many different ways lending institutions may
calculate the interest rates they charge borrowers for loans.
• To determine how interest rates or yields on deposits in banks,
credit unions, and other depository institutions are figured.
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Introduction
• Many different interest-rate measures attached to different
types of financial assets have been developed, leading to
considerable confusion, especially for small borrowers and
savers.
• In this chapter, we will examine the methods most frequently
used to measure interest rates and the prices of financial assets
in the money and capital markets.
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Units of Measurement
For Interest Rates and Asset Prices
• The interest rate is the price that is charged to a borrower for
the loan of money.
• Interest
Fee required by the lender for
rate on = the borrower to obtain credit  100
loanable
Amount of credit made
funds
available to the borrower
• Interest rates are usually expressed as annualized percentages.
However, both 360-day and 365-day years are commonly
used. The compounding terms may also differ.
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Units of Measurement
For Interest Rates and Asset Prices
• A basis point equals 1/100 of a percentage point.
• Example
10.5% = 10% + 50 basis points, or 1050 basis points
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Units of Measurement
For Interest Rates and Asset Prices
• The prices of common and preferred stock are measured today
in many markets in terms of dollars and decimal fractions of a
dollar (or some other currency unit).
• Example
$40.25 per share (versus $40 1/4 in the recent past)
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Units of Measurement
For Interest Rates and Asset Prices
• Bond prices are usually expressed in points and fractions of a
point, with each point representing $1 on a $100 basis or $10
for a $1000 bond.
• Example
A bond priced at 97 is selling for $97 on a $100 basis, or $970 for
each $1000 in face value.
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Units of Measurement
For Interest Rates and Asset Prices
• Many security dealers who act as “market makers” usually
quote two prices for an asset.
• The higher ask price is the dealer’s selling price, while the
lower bid price is the dealer’s buying price.
• The difference between the bid and ask prices – known as the
spread – provides the dealer’s return for creating a market for
the security.
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Measures of the Rate of Return (Yield)
On a Financial Asset
• The interest rate on a loan or other financial asset is not
necessarily a true reflection of the yield or rate of return
actually earned by the lender during the life of the asset.
- Some borrowers may default on all or a portion of their
promised payments.
- The market value of the financial asset may rise or fall.
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Measures of the Rate of Return (Yield)
On a Financial Asset
• The perpetuity rate is the return on a financial instrument that
never matures, but promises a fixed income to its holder every
year ad infinitum into the future.
• Annual rate of return on a perpetual financial instrument =
Annual cash flow promised
.
current price or present value
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Measures of the Rate of Return (Yield)
On a Financial Asset
• The coupon rate of a bond or some other debt security is the
contracted interest rate that the security issuer agrees to pay at
the time the security is issued.
• Example
A bond with a par value of $1000 and a coupon rate of 9% pays an
annual coupon of $90.
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Measures of the Rate of Return (Yield)
On a Financial Asset
• The current yield of a financial asset is the ratio of the annual
income (dividends or interest) generated by the asset to its
market value.
• Example
The current yield of a share of common stock selling for $30 in the
market and paying an annual dividend of $3 to the shareholder is
$3/$30 = 0.10, or 10%.
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Measures of the Rate of Return (Yield)
On a Financial Asset
• The yield to maturity (YTM) of a financial asset is the rate of
interest that the market is prepared to pay today for the
financial asset.
• It is the rate that equates the purchase price (P) with the
present value of all the expected annual net cash flows (CF)
from the asset.
CFn
CF1
CF2
P


1
2
n
1  YTM  1  YTM 
1  YTM 
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Measures of the Rate of Return (Yield)
On a Financial Asset
• A bond trades at a discount from par if its price is less than its
par value, i.e. if its current yield to maturity is higher than its
coupon rate.
• A bond trades at a premium over par if its price is more than its
par value, i.e. if its current yield to maturity is lower than its
coupon rate.
• A bond trades at par if its price equals its par value, i.e. if the
current market interest rate on comparable securities equals its
coupon rate.
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Measures of the Rate of Return (Yield)
On a Financial Asset
• The holding-period yield is the rate of return from an
investment over its actual or planned holding period.
• It is the discount rate equalizing the purchase price (P0) of a
financial asset with all the discounted net cash flows (CF)
received from the asset from the time the asset is purchased
until the time it is sold (in period m).
CFm
Pm
CF1
CF2
P0 



1
2
m
1  hpy  1  hpy 
1  hpy  1  hpy m
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Measures of the Rate of Return (Yield)
On a Financial Asset
• Example
A 5-year corporate bond has a face value of $1,000. Its promised
annual coupon rate is 10% and it pays $50 in interest every 6
months. The bond is currently selling for $900.
$50
$50
$50
$1000
$900 



1
9
10
1  YTM 
1  YTM  1  YTM  1  YTM 10
Yield to maturity  12.8%
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Measures of the Rate of Return (Yield)
On a Financial Asset
• Example
Shares of common stock issued by General Electric Corporation
are currently selling for $40 per share. Dividends of $2 per share
are expected each year. An investor plans to hold the stock for two
years and then sell out at an expected price of $50 per share.
$2
$2
$50
$40 


1
2
1  hpy  1  hpy  1  hpy 2
Holding period yield  16.5%
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Measures of the Rate of Return (Yield)
On a Financial Asset
• The bank discount rate is widely used for short-term loans and
securities traded daily in the money market on which there is
no intermediate payment before the asset matures.
• The discount rate =
face value  purchase price
face value
360 days/year
 days
to maturity
.
• The YTM-equivalent return measure =
face value  purchase price
purchase price
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365 days/year
 days
to maturity
.
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Yield-Asset Price Relationships
• The price of a financial asset (especially for a bond or some
other debt security) and its yield or rate of return are inversely
related – a rise in yield implies a decline in price, and vice
versa.
• This principle can be reinforced by noting that investing funds
in financial assets can be viewed from two different
perspectives –
 the borrowing and lending of money,
and  the buying and selling of financial assets.
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Yield-Asset Price Relationships
Equilibrium Asset Prices and Interest Rates (Yields)
Interest-Rate Determination
Interest
Demand
Rate (borrowing)

rE
QE
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Asset Price Determination
Price
Supply
(lending)
Loanable
Funds
PE
Demand
(lending)

AE
Supply
(borrowing)
Assets
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Yield-Asset Price Relationships
 demand for loanable funds
  supply of securities
Interest-Rate Determination
Asset Price Determination
Interest
Rate
D’
Price
D
S
D
S
S’




Loanable
Funds
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Assets
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Yield-Asset Price Relationships
 supply of loanable funds
  demand for securities
Interest-Rate Determination
Asset Price Determination
Interest
Rate
D’
Price
D
S
D
S
S’




Loanable
Funds
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Yield-Asset Price Relationships
• Interest rates and corporate stock (equity) prices also
frequently move in opposite directions (though by no means is
this always the case).
• For example, if interest rates rise, bonds and other debt
instruments now offering higher yields become more attractive
relative to stocks, resulting in increased stock sales and
declining equity prices.
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Interest Rates
Charged or Paid by Institutional Lenders
• The simple interest method assesses interest charges on a loan
only for the period of time that the borrower has actual use of
the borrowed funds.
• Interest = principal  rate  term
• The more frequently a borrower makes repayments on a loan,
the lesser the total interest will be.
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Interest Rates
Charged or Paid by Institutional Lenders
• In the add-on rate approach, interest is calculated on the full
principal of the loan, and the sum of interest and principal
payments is divided by the number of payments to determine
the dollar amount of each payment.
• In a single payment loan, the simple interest and add-on
methods give the same interest rate. However, as the number
of installment payments increases, the borrower pays a higher
effective rate under the add-on method.
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Interest Rates
Charged or Paid by Institutional Lenders
• The discount loan method determines the total interest charged
to the customer on the basis of the amount to be repaid.
However, the borrower receives as proceeds of the loan only
the difference between the total amount owed and the interest
bill.
• Hence, the effective interest rate is
Interest paid
 100
Net loan proceeds
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Interest Rates
Charged or Paid by Institutional Lenders
• Each monthly payment of a home mortgage loan first covers in
full the monthly interest on the outstanding principal. The
remainder is then applied to the principal of the loan, such that
the amount owed is reduced progressively.
• The monthly payment
t 12
r 
r 
 1  
12  12 
 L
t 12
r 

1    1
 12 
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where
L = total amount owed
r = annual loan interest rate
t = number of years of the loan
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Interest Rates
Charged or Paid by Institutional Lenders
• The U.S. Consumer Credit Protection Act of 1968 (Truth in
Lending) requires lending institutions to calculate and tell the
borrower the annual percentage rate (APR) he or she is
actually paying.
• The APR, which measures the yearly cost of credit, includes
not only interest costs but also any transaction fees or service
charges imposed by the lender.
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Interest Rates
Charged or Paid by Institutional Lenders
• The compounding of interest means that the lender or
depositor earns interest income on both the principal amount
and any accumulated interest.
• The formula for calculating the future value of a financial asset
earning compound interest is:
r

FV  P 1  
 m
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tm
FV = future value of the asset
P = principal value of the asset
r = annual interest rate
m = annual compounding frequency
t = term of the asset in years
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Interest Rates
Charged or Paid by Institutional Lenders
• The U.S. Truth in Savings Act of 1991 requires depository
institutions to use the daily average balance in a customer’s
deposit over each interest-crediting period to determine the
customer’s annual percentage yield (APY) for that deposit
account.
365


d
i



APY  1    1 100
 b 



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where
i = interest earned
b = daily average balance
d = term in days
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Markets on the Net
•
•
•
•
Bankrate.com at www.bankrate.com
Compare Interest Rates at www.compareinterestrates.com
Federal Reserve System at www.federalreserve.gov
Financial Power Tools at www.financialpowertools.com
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Markets on the Net
• Interest Rate Calculator at www.interestratecalculator.com
• Local Bank Rates on Loans and Savings at
www.digitalcity.com
• The Credit Card Analyzer at www.creditcardanalyzer.com
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Chapter Review
• Introduction
• Units of Measurement for Interest Rates and Asset Prices
- Calculating and Quoting Interest Rates
- Basis Points
- Prices of Stocks and Bonds
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Chapter Review
• Measures of the Rate of Return, or Yield, on a Loan, Security,
or other Financial Asset
-
Rate of Return on a Perpetual Financial Instrument
Coupon Rate
Current Yield
Yield to Maturity
Holding-Period Yield
Bank Discount Rate
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Chapter Review
• Yield-Asset Price Relationships
- Interest Rates and the Prices of Debt Securities
- Interest Rates and Stock Prices
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Chapter Review
• Interest Rates Charged by Institutional Lenders
-
Simple Interest Rate
Add-On Rate of Interest
Discount Loan Method
Home Mortgage Interest Rate
Annual Percentage Rate (APR)
Compound Interest
Annual Percentage Yield (APY) on Deposits
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