# Finance Chp 5

 How are interest rates set? By the market forces of supply and demand When are interest rates low? When savings (supply) is high and borrowing (demand) is low When are interest rates high? When savings (supply) is low and borrowing (demand) is high EAR stands for Effective annual rate EAR, or… APY annual percentage yield EAR -The actual rate paid (or received) after accounting for compounding that occurs during the year.-The total amount of interest that will be earned at the end of one year What can you NOT do to calculate monthly payments with EAR? You can’t find the annual cash flows using EAR and divide by 12 To find an equivalent interest rate for periods shorter than one year… Raise the interest rate factor (1 + r) to the appropriate fractional powerEX: 6 months is 0.5 periods To convert a discount rate r for one period to an equivalent discount rate for n periods… Use the Equivalent n-period Discount Rate Equivalent n-period Discount Rate (1 + r)^N – 1 APR stands for Annual percentage rate APR indicates what Indicates the amount of SIMPLE INTEREST earned in one year without the effect of compounding Simple Interest Interest earned without the effect of compounding APR quote vs actual interest APR is usually less due to the lack of compounding How to find the actual interest rate when you have the APR quote Convert APR to EAR APR with monthly compounding A way to quote a monthly interest rate Key Points about APR (1) Doesn’t reflect the true amount you will earn (no compounding)(2) APR itself cannot be used as a discount rate Interest/Period Rate APR / m(m = number of compounding periods in a year) APR to EAR EAR = (1 + [APR/M])^m – 1EAR = (1 + Period Rate)^m – 1**APR must be in decimal form APR Period Rate * Number of Periods per Year What is APR if the monthly rate is 0.5% 0.5% * 12 What is APR if semi-annual rate is 0.5% 0.5% * 2 What does APR not take into account? Compounding What is the rate all lenders must repeat to customers? APR Key Point Interest rate and time period MUST match Even if accounts have the same APR They may have different EAR As compounding becomes more frequent… EAR increases, but it doesn’t got to infinite The closer to zero that EAR gets… The EAR is given by e^APR – 1 Continuous Componding e^APR – 1 How to find APR if you have EAR APR = m [ (1 + EAR)^1/m – 1 ] Which rate do you need to use in time value of money calculations? Period rate (which is APR / m) EAR increases when? With the frequency of compounding Amortizing Loans Loans on which the borrower makes monthly payments that include interest on the loan plus some part of the loan balance- Each monthly payment is the same, and the loan is repaid in full at the end of the period- Because loan balance is decreasing each period, interest decreases What is different with amortizing loans? The outstanding balance How to calculate the Outstanding Balance on an Amortizing Loan The PV of your future obligations Outstanding Balance or… Outstanding Principal Factors that influence interest rates InflationCurrent economic activityExpectations of future growth Types of Interest Rates ~Nominal Interest Rates~Real Interest Rates Nominal Interest Rate Interest rate quoted by banks and other financial institutions that indicate the rate at which money will grow if invested for a certain period of time (change in actual # of dollars) Real Interest Rate The rate of growth of purchasing power, after adjusting for inflation What is the interest rate quoted in real life? Always the nominal interest rate What does the nominal interest rate include? Our desired real rate of return plus an adjustment for expected inflation Always discount real cash flows with… Real discount rates Always discount nominal cash flows with… Nominal discount rates The relationship between real interest rates,nominal interest rates, and inflation is… EXACT (1 + R) = (1 + r)(1 + h)APPROXIMATE For “small” rates: R = r + hR = nominal interest rater = real interest rateh = inflation Growth in Purchasing Power AKA Real Interest Rate (1 + r)= (1 + R) / (1 + h) = Growth of Money / Growth of Prices= (R – h) / (1 + h)= R – h (APPROXIMATE) At any given point in time… Short-term interest rates differ from long-term interest rate Term Structure of Interest Rates The relationship between the investment term (time to maturity) and the interest rate (yield) In essence, what does the Term Structure of Interest Rates give us? The time value of money for different maturities Yield Curve A plot of the term structure of interest rates(EX: a plot of bond yields as a function of the bonds’ maturity) Normal Yield Curve Moderately upward-sloping; long-term yields are higher than short-term yields (called steep when the slope ishigh). Inverted Yield Curve Downward-sloping; long-term yields are lower than short-term yields Yield Curve + Economy: If interest rates are expected to rise… Long-term interest rates are expected to be higher than short-term interest rates to attract investors (normal yield curve) Yield Curve + Economy: If interest rates are expected to fall.. Long-term interest rates will be lower than short-term interest rates to attract borrowers (inverted yield rate) Risk-free cash flow of Cn received in n years has the present value: PV = Cn / (1 + rn)^n How do you compare nominal and real rates? You cannot do it directly; you need to convert both to either nominal EARs to real EARs Steps in converting to nominal rate (1) Find EAR of real rate (2) Plug EAR of real rate and inflation into formula (1 + EAR of Nominal Rate) = (1 + EAR of Real Rate)(1 + Inflation Rate) Nominal Cash Flow The quoted rate multiplied by inflation rate (1 + h) EX: In order to have \$5000 real dollars in one year, adjust for one year of inflation of 3% (5000 * 1.03) You expect interest rates to decline in the near future even though the bond market is not indicating any sign of this change. Which type of bond should you buy to maximize your gains if the rate decline does occur? Long-term, zero-coupon If interest rates increase and the bond market doesn’t expect it.. All bond prices will decline, but some bond prices will decline more than others, as different bonds have different exposure to interest rate risk, so we want to buy bonds that have the least exposure to interest rate risk. As we know from class, those are the bonds that have low maturities (short-term) and high coupon rates, as those are the bonds that return your money earlier so that you can re-invest your money at the higher interest rate. If interest rates decrease and the bond market doesn’t expect it… … Opportunity Cost is… The cost of lost options (like wages, when you go to college) Sunk Cost is… Costs that have accrued in the past or will occur anyway, regardless of the project (e.g. fixed overhead expenses, past R&D expenditures)
Share