Chapter 6 Measuring and Calculating Interest Rates and Financial Asset Prices

6 - 3 McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved.  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.

6 - 4 McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

6 - 5 McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

6 - 6 McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

6 - 7 McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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)

6 - 8 McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

6 - 9 McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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%.

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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 (P 0 ) 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).

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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. Yield to maturity  12.8%

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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. Holding period yield  16.5%

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Yield-Asset Price Relationships Equilibrium Asset Prices and Interest Rates (Yields) Interest Rate Loanable Funds rErE QEQE  Demand (borrowing) Supply (lending) Price Assets PEPE AEAE  Demand (lending) Supply (borrowing) Interest-Rate DeterminationAsset Price Determination

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Yield-Asset Price Relationships  demand for loanable funds Interest Rate Loanable Funds  DS Interest-Rate Determination   supply of securities D’  Price Assets  Asset Price Determination DS S’ 

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Yield-Asset Price Relationships  supply of loanable funds Interest Rate Loanable Funds  DS Interest-Rate Determination   demand for securities Price Assets  Asset Price Determination DS S’  D’ 

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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 where L = total amount owed r = annual loan interest rate t = number of years of the loan

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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.

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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: 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

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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. where i= interest earned b= daily average balance d= term in days

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Markets on the Net Bankrate.com at Compare Interest Rates at Federal Reserve System at Financial Power Tools at

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Markets on the Net Interest Rate Calculator at Local Bank Rates on Loans and Savings at The Credit Card Analyzer at

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Chapter Review Introduction Units of Measurement for Interest Rates and Asset Prices -Calculating and Quoting Interest Rates -Basis Points -Prices of Stocks and Bonds

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Chapter Review Yield-Asset Price Relationships -Interest Rates and the Prices of Debt Securities -Interest Rates and Stock Prices

McGraw-Hill/Irwin Money and Capital Markets, 9/e © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 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