Chapter 6 Measuring and Calculating Interest Rates and

Chapter 6 Measuring and Calculating Interest Rates and Financial Asset Prices Mc. Graw-Hill/Irwin Copyright © 2008 by The Mc. Graw-Hill Companies, Inc. All Rights Reserved.

Learning Objectives ù To learn how money market interest rates are determined, and how those interest rates are used by dealers when trading money market assets. ù To explore the important relationships between the interest rates on bonds and other financial instruments and their market value or price. 6 -3

Learning Objectives ù To look at the many different ways lending institutions calculate interest rates they charge borrowers for loans. ù To determine how interest rates or yields on deposits in banks, credit unions, and other depository institutions are figured. 6 -4

Introduction ù 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. ù 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

Units of Measurement For Interest Rates ù The Interest rate is the price 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 ù Interest rates usually expressed as annualized percentages ù 360 -day and 365 -day years are common ù Compounding terms may also differ 6 -6

Units of Measurement For Interest Rates ù A basis point equals 1/100 of a percentage point. ù Example 10. 5% = 10% + 50 basis points, or 1050 basis points 6 -7

Interest Rates in the Wholesale Money Markets ù Wholesale money market ù Lending for short period of time ù Large sums of money ù Market details in Chapter 10 and 11 ù This chapter ù How interest rates are computed on these assets ù How are interest rates reported in the financial press 6 -8

Computing Interest Rates on Money Market Assets ù Most money market assets have similar characteristics ù Short-term ù Receives no income until asset matures ù At maturity receive par value (face value) ù Must pay less than par to purchase security ù Return is price appreciation ù Assets sold at a discount to par value 6 -9

Computing Interest Rates on Money Market Assets ù Rate of return on money market instrument ù Coupon-equivalent (or bond-equivalent of investment rate) rate of return ù Need three pieces to estimate ù Par value ù Number of days to maturity ù Purchase price 6 -10

Computing Interest Rates on Money Market Assets The formula for the actual annualized rate of return for a single year: Investment rate(IR) 365 = Par value – Purchase price Days to maturity . 6 -11

Computing Interest Rates on Money Market Assets ù In the money market a different rate is quoted ù Bank discount rate (DR) ù Not the actual annualized rate of return ù Used as trading standard ù Easier to estimate than IR ù Use face value in denominator instead of price ù Use 360 rather than 365 days 6 -12

Computing Interest Rates on Money Market Assets ù The formula for the bank discount rate(DR): = Par value – Purchase price Face value 360 Days to maturity. 6 -13

Holding-Period Yield on Money Market Assets ù Financial assets sold at a discount ù Price tends to rise over time ù Price exactly equal to part at maturity ù Prices do not rise at a steady, uniform rate ù Price changes will be impacted by continuous changes in the market interest rates ù If you hold to maturity, you lock in a nominal return ù If you sell early, then price fluctuations impact your investment return 6 -14

Holding-Period Yield on Money Market Assets The holding period yield (HPY) on assets sold at a discount is: HPY = DR at purchase +/- Change in DR over holding period= (Initial days to maturity-Days held)x. Difference in DR Days Held Difference in DR is the change in the CR between when the asset is purchased and when it is sold 6 -15

Interest Rate Quotations on US Treasury Bills ù Treasury bills are money market assets ù Issued by the U. S. government ù Various maturities ù 4 weeks ù 3 months ù 6 months ù Daily report of information on the bills ù Various financial sources ù For each maturity 6 -16

Interest Rate Quotations on US Treasury Bills ù Security dealers who act as “market makers” usually quote two prices ù The higher ask price is the dealer’s selling price ù The lower bid price is the dealer’s buying price ù The difference between the bid and ask prices is the spread – the dealer’s return for creating a market 6 -17

Interest Rates on Bonds and Other Long-Term Debt Securities ù Yield to maturity (YTM) of a financial asset ù The rate of interest that the market is currently prepared to pay for the financial asset ù It is the rate that equates the purchase price (P) with the present value the stream of coupon payments (C) by the asset ù Coupon = Coupon rate * Par value 6 -18

Interest Rates on Bonds and Other Long-Term Debt Securities ù Adjustments for non-annual rates ù Include a parameter k, the number of times during the year that the interest income is paid to the investor 6 -19

Measures of the Rate of Return (Yield) On a Financial Asset ù The holding-period yield is an investment rate of return ù Over its actual or planned holding period ù It is the discount rate (h) equalizing the purchase price (P) of a financial asset with all the discounted annual payments (C) received until the asset is sold at time m for price Pm 6 -20

Understanding Yield to Maturity Example A 5 -year corporate bond has a face value of $1, 000. Its promised a annual coupon rate is 10% and it pays $50 in interest every 6 months. The bond is currently selling for $900 6 -21

Price Quotations on U. S. Treasury Notes and Bonds ù U. S. Treasury notes (T-notes) and U. S. Treasury bond (T-bonds) ù Original maturities of 2 years to 30 years ù Most are fixed payments ù Typically semi-annually ù Need to know ù Price and maturity ù Date coupons paid ù Amount of coupon payments ù Current yield to maturity 6 -22

Price Quotations on U. S. Treasury Notes and Bonds ù 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% 6 -23

Price Quotations on U. S. Treasury Notes and Bonds ù Characteristics ù Price quotes are on $100 of par value ù Quoted in 32 nd of a dollar ù Annualized rate ù Price quotations provided in financial press ù Including daily trading activity ù Often including bid and asked prices 6 -24

Price Quotations on Corporate Bonds ù Price quotes on corporate bonds are similar ù Same basic information required ù However the need to consider risk ù Unlike what is assumed for the US government, some borrowers may default on all or a portion of their promised payments ù The market value of the risky asset may rise or fall ù Investors require greater returns to compensate them for this risk 6 -25

Yield-Asset Price Relationships ù The price of a financial asset (especially debt securities) and its rate of return are inversely related ù A rise in yield implies a decline in price, and vice versa ù Investing funds in financial assets can be viewed from two different perspectives ù The borrowing and lending of money ù The buying and selling of financial assets 6 -26

Yield-Asset Price Relationships Equilibrium Asset Prices and Interest Rates (Yields) Interest-Rate Determination Interest Demand Rate (borrowing) i. E LFE Asset Price Determination Price Supply (lending) Loanable Funds PE Demand (lending) Supply (borrowing) FAE Assets 6 -27

Rates of Return on Perpetual Financial Instruments ù Some financial instruments never mature ù Perpetuity financial instruments ù May be fixed-income ù Equal payments to its holder every year ù Ad infinitum ù May be variable-return ù Corporate stock ù Future payments may change over time 6 -28

Rates of Return on Perpetual Financial Instruments Perpetuity rate Annual rate of return on a perpetual financial instrument = Annual cash flow promised current price or present value. Or Current Price =Annual cash flow promised Annual rate of return . 6 -29

Rates of Return on Perpetual Financial Instruments ù Key points to consider ù An infinite stream of cash flows has a finite value ù There is an inverse relationship between the current price and the rate of return ù This can be weaker than for bonds ù It does not always hold for common stock 6 -30

Rates of Return on Perpetual Financial Instruments ù Stock pricing formula ù D 0 is current dividend ù EDi is expected future dividend at time I ù R is the minimum rate of return required by a company’s shareholders ù SP is the company’s stock price 6 -31

Rates of Return on Perpetual Financial Instruments ù This simplifies to 6 -32

Yield-Asset Price Relationships demand for loanable funds supply of securities Interest-Rate Determination Interest Rate D’ Asset Price Determination Price D S S’ Loanable Funds Assets 6 -33

Yield-Asset Price Relationships supply of loanable funds demand for securities Interest-Rate Determination Interest Rate Asset Price Determination D’ Price D S S’ Loanable Funds Assets 6 -34

Price Quotation in Corporate Stocks ù There are many professional analysts examining stocks. They can provide information by trading stocks ù Closing price is price at end of prior trading day ù How much the stock price has changed ù Compare to prior year’s high and low ù Determine if the stock pays a dividend and how much ù Price to earnings ratio 6 -35

Interest Rates Charged or Paid by Institutional Lenders ù Simple interest method ù 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 ù The more frequently a borrower makes repayments on a loan, the less the total interest 6 -36

Interest Rates Charged or Paid by Institutional Lenders ù Add-on interest method ù Interest is calculated on the full loan principal ù The sum of interest and principal payments is divided by the number of payments to determine the dollar amount of each payment ù In a single payment loan, the simple interest and add-on methods give the same interest rate ù As the number of installment payments increases, the borrower pays a higher effective rate under the add-on method 6 -37

Interest Rates Charged or Paid by Institutional Lenders ù Discount loan method ù Determines the total interest charged to the customer on the basis of the amount to be repaid ù Loan proceeds are only the difference between the total amount owed and the interest bill ù Hence, the effective interest rate is Interest paid 100 Net loan proceeds 6 -38

Interest Rates Charged or Paid by Institutional Lenders ù Monthly payments of a home mortgage loan ù First covers in full the monthly interest on the outstanding principal ù The remainder is then applied to the principal of the loan where L = total amount owed r = annual loan interest rate t = number of years of the loan 6 -39

Annual Percentage Rate ù The U. S. Consumer Credit Protection Act of 1968 (Truth in Lending) ù Requires lending institutions to calculate and tell the borrower the annual percentage rate (APR) ù Rate borrower actually pays ù APR measures the yearly cost of credit ù Interest costs ù Transaction fees or service charges imposed by the lender 6 -40

Compound Interest The compounding of interest means that the lender or depositor earns interest income on both the principal and 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 6 -41

APY on Deposits The U. S. Truth in Savings Act of 1991 ù Requires depository institutions to use the daily average balance in a customer’s deposit ù Over each interest-crediting period ù 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 6 -42

Markets on the Net ù Bankrate. com at www. bankrate. com ù CNN Money at money. cnn. com/pf/banking ù Compare Interest Rates at www. compareinterestrates. com ù Credit Card Analyzer at www. creditcardanalyzer. com ù Federal Reserve System at www. federalreserve. gov 6 -43

Markets on the Net ù Fin. Aid at www. finaid. org ù Financial Power Tools at www. financialpowertools. com ù Interest Rate Calculator at www. interestratecalculator. com ù Investopedia at www. investopedia. com/calculator ù Lenders. Compete. com at lenderscompete. com 6 -44

Markets on the Net ùLocal Bank Rates on Loans and Savings at www. digitalcity. com ùMortgage Professor’s Web Site at mtgprofessor. com 6 -45

Chapter Review ù Introduction ù Units of measurement for interest rates and asset prices ù Calculating and quoting interest rates ù Basis points ù Prices of stocks and bonds 6 -46

Chapter Review ù Measures of the rate of return, or yield, on a loan, security, or other financial asset ù Rate of return on a perpetual financial instrument ù Coupon rate ù Current yield ù Yield to maturity ù Holding-period yield ù Bank discount rate 6 -47

Chapter Review ù Yield-asset price relationships ù Interest rates and the prices of debt securities ù Interest rates and stock prices 6 -48

Chapter Review ù Interest rates charged by institutional lenders ù Simple interest rate ù Add-on rate of interest ù Discount loan method ù Home mortgage interest rate ù Annual Percentage Rate (APR) ù Compound interest ù Annual Percentage Yield (APY) on deposits 6 -49