Ch06

Chapter 4

Measuring and Calculating Interest Rates and

Financial Asset Prices

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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 MeasurementFor 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 100loanable Amount of credit madefunds 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 MeasurementFor 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 MeasurementFor 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 MeasurementFor 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.

• ExampleA 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 MeasurementFor 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.

• ExampleA 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.

• ExampleThe 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.

nn

YTMYTMYTM

1

CF

1

CF

1

CFP 2

21

1

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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).

mm

mm

hpyhpyhpyhpy

1

P

1

CF

1

CF

1

CFP 2

21

10

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Measures of the Rate of Return (Yield)On a Financial Asset

• ExampleA 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.

101091 1

1000$

1

50$

1

50$

1

50$900$

YTMYTMYTMYTM

Yield to maturity 12.8%

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Measures of the Rate of Return (Yield)On a Financial Asset

• ExampleShares 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.

221 1

50$

1

2$

1

2$40$

hpyhpyhpy

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 360 days/year .

face value days to maturity

• The YTM-equivalent return measure =face value purchase price 365 days/year .

purchase price 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)

InterestRate

Loanable Funds

rE

QE

Demand(borrowing)

Supply(lending)

Price

Assets

PE

AE

Demand(lending)

Supply(borrowing)

Interest-Rate Determination Asset Price Determination

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Yield-Asset Price Relationships

demand for loanable funds

InterestRate

Loanable Funds

D S

Interest-Rate Determination

supply of securities

D’

Price

Assets

Asset Price Determination

D SS’

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Yield-Asset Price Relationships

supply of loanable funds

InterestRate

Loanable Funds

D S

Interest-Rate Determination

demand for securities

Price

Assets

Asset Price Determination

D SS’

D’

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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 RatesCharged 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 RatesCharged 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 RatesCharged 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 RatesCharged 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

112

1

121

12L 12

12

t

t

r

rr whereL = total amount owedr = annual loan interest ratet = number of years of the loan

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Interest RatesCharged 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 RatesCharged 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:

tm

m

r

1 PFV

FV = future value of the assetP = principal value of the assetr = annual interest ratem = annual compounding frequencyt = term of the asset in years

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Interest RatesCharged 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.

10011APY

365

d

b

iwherei = interest earnedb = daily average balanced = 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