Zara Mahmood Roberts FE101 Chapter 5 Interest Rates INTEREST RATES QUOTES AND ADJUSTMENTS Interest is paid and interest rates are quotes in different ways Differ depending on investment horizon Differ due to risk The Effective Annual Rate annual percentage yield APY end of one year E g with an EAR of 5 a 100 investment grows to 100 x 1 r 2 100 X 1 05 105 the total amount of interest that will be earned at the Adjusting the discount Rate to Different Time Periods By raising the interest rate factor 1 r to the appropriate power we can compute an equivalent interest rate for a longer period of time Use same method to find equivalent interest rate for periods shorter than one year o E g raise 1 r to appropriate fractional power o 5 r for one year 1 r 5 1 05 5 1 0247 for each 1 invested every 6 months 5 EAR interest rate of 2 47 earned every 6 months o verify by computing interest rate we would earn in one year by investing for 2 6 month periods at this rate convert a discount rate of r for one period to an equivalent discount rate for n periods Equivalent n period Discount Rate 1 r n 1 When computing present or future values you should adjust the discount rate to match the time period of the cash flows Annual Percentage Rates Indicates the amount of interest earned in one year without the effect of compounding o Simple interest interest earned without the effect of compounding Zara Mahmood Roberts FE101 Because no effect of compounding APR quote is typically less than the actual amount of interest you will earn Must convert APR to an EAR If APR does not reflect the true amount you will earn over in one year APR itself cannot be used as a discount rate Interest Rate per Compounding Period APR m m compounding periods in 1 yr EAR increases with frequency of compounding because of the ability to earn interest Compounding more frequently than daily has a negligible impact on the effective on interest sooner annual rate and is rarely observed Compute equivalent interest rate for an other time interval using the first equation APPLICATION DISCOUNT RATES AND LOANS Computing Loan Payments Amortizing loan include interest on the loan plus some part of the loan balance a loan on which the borrower makes monthly payments that when the compounding interval for the APR is not stated explicitly it is equal to the interval between the payments o the loan will be repaid within 60 equal monthly payments computed using a 6 75 APR with monthly compounding Loan payment each month includes interest and repayment of part of the principal reducing the amount you still owe Zara Mahmood Roberts FE101 Loan balance is decreasing each month the interest that accrues on that balance is decreasing Part of that payment needed to cover interest each month is constantly decreasing and part left over to reduce the principal further is constantly increasing Computing the Outstanding Loan Balance Amount you owe at any point in time can be calculated as the present value of your future obligations on the loan Outstanding principal balance PV of remaining future loan payments Calculate outstanding loan balance by determining the present value of the remaining loan payments using the loan rate as the discount rate THE DETERMINANTS OF INTEREST RATE Fundamentally interest rates are determined by market forces based on the relative supply and demand of funds o Determined by the willingness of individuals banks and firms to borrow save and lend Inflation and Real Versus Nominal Rates Inflation measures the purchasing power of a given amount of currency declines due to increasing prices Nominal interest rates o Interest rates quoted by banks and other financial institutions that indicate the rate at which money will grow if invested for a certain period of time o If prices in the economy are also increasing due to inflation the nominal interest rate does not represent the true increase in purchasing power that will result from investing Real interest rate the rate of growth of purchasing power after adjusting for inflation Nominal interest rate tends to move with inflation Individuals willingness to save will depend on the growth in purchasing power they can expect o When inflation rate is high a higher nominal interest rate is needed to induce individuals to save Zara Mahmood Roberts FE101 Investment and Interest Rate Policy Affect firms incentive to raise capital and invest Discounting positive cash flows at a higher rate which reduces their present value When costs of an investment precede the benefits and increase in the interest rate will make the investment less attractive High interest rates will shrink the set of good investments available to firms Fed will lower interest rates in an attempt to stimulate investment if the economy is slowing The Yield Curve and Discount Rates Term structure Yield curve the relationship between the investment term and the interest rate a plot of bond yields as a function of the bonds maturity date o Interest rate depends on the horizon Risk free interest rate without risk over a given period the interest rate at which money can be borrowed or lent Risk free cash flow of Cn received in n years has the present value Rn is risk free interest rate for an n year term o Must match the term of cash flow and term of the discount rate Use different discount rate for each cash flow based on the rate from the yield curve with the same term When interest rates are similar across maturities we say that the yield curve is flat The Yield Curve and the Economy Sometimes short term rates are close to long term rates but can also be very different Interest Rate Determination o Federal funds rate the overnight loan rate charged by banks with excess reserves at a Federal Reserve bank to banks that need additional funds to meet reserve requirements o Short term long term rates interest rates expected to rise in future investors would not want to make long term investments o Invest on short term basis and reinvesting after the rise of rates Yield Curve Shape o Influenced by interest rate expectations Zara Mahmood Roberts FE101 o Steep curve with long term rates much higher than short term rates generally indicated that interest rates are expectrd to rise in the duture o Interpreted as negative forecast for economic growth interest rates tend to drop in economic slow down o Normal shape is upward sloping If interest rates were always going to rise in future o Have to be other forces at work to cause long term