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Measuring and Calculating Interest Rates and Financial Asset Prices

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6

C h a p t e r

Money and Capital Markets

Financial Institutions and Instruments in a Global Marketplace

Eighth Edition

Peter S. Rose

McGraw Hill / Irwin

Slides by Yee-Tien (Ted) Fu

- To learn how to measure and calculate interest rates and the prices of financial assets.
- To understand the relationship between the interest rate on a financial instrument and its market value.
- To look at the many different ways that banks and other lending institutions 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.

- 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.

- A basis point equals 1/100 of a percentage point.
- Example
10.5% = 10% + 50 basis points, or 1050 basis points

- 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)

- 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.

- Security dealers usually quote two prices for an asset.
- The higher ask price is the dealer’s selling price, while the lowerbid 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.

- The coupon rate of a 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.

- The current yield of a security is the ratio of the annual income (dividends or interest) generated by the security 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%.

- The yield to maturity 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.

- 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.

- 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 n).

- The price of a security and its yield or rate of return are inversely related – a rise in yield implies a decline in price, while a fall in yield implies a rise in the security’s price.
- This inverse relationship can be seen 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 securities.

Interest-Rate Determination

Security Price Determination

Interest

Rate

Price

Demand

(borrowing)

Demand

(lending)

Supply

(lending)

Supply

(borrowing)

rE

PE

Loanable Funds

Securities

QE

VE

Equilibrium Security Prices and Interest Rates (Yields)

Interest-Rate Determination

Security Price Determination

Interest

Rate

D’

Price

D

S

D

S

S’

Loanable Funds

Securities

demand for loanable funds

supply of securities

Interest-Rate Determination

Security Price Determination

Interest

Rate

D’

Price

D

S

D

S

S’

Loanable Funds

Securities

supply of loanable funds

demand for securities

- 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.

- 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.

- The discount 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

- 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

where

L = total amount owed

r = annual loan interest rate

t = number of years of the loan

- 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 constant ratio formula usually gives a close approximation to the true APR.

m= number of payments in a year

c= annual interest cost

N= total number of payments

P= principal of the loan

- 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:

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

- 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.

where

i= interest earned

b= daily average balance

d= term in days

- The measurement or calculation of interest rates is a popular subject on many websites. See, for example,
- http://www.interestratecalculator.com/
- http://www.compareinterestrates.com/
- http://www.digitalcity.com/

- Units of Measurement for Interest Rates and Security Prices
- Definition of Interest Rates
- Basis Points
- Security Prices

- Measures of the Rate of Return, or Yield, on a Loan, Security, or other Financial Asset
- Coupon Rate
- Current Yield
- Yield to Maturity
- Holding-Period Yield

- Yield-Asset Price Relationships

- Interest Rates Charged or Paid by Institutional Lenders
- Simple Interest Rate
- Add-On Rate of Interest
- Discount Method
- Home Mortgage Interest Rate
- Annual Percentage Rate (APR)
- Compound Interest
- Annual Percentage Yield (APY)