Future Value The amount to which a cash flow or series of cash flows will grow over a given period of time when compounded at a given interest rate Present Value The value today of a future cash flow or series of cash flows Compounding the arithmetic process of determining the final value of a cash flow or series of cash flows when compound interest is applied take interest on interest FV PV 1 i N Simple interest when interest is not earned on interest EX 100 100 05 3 Compound interest occurs when interest is earned on prior periods interest Opportunity cost the rate of return you could earn on an alternative investment of similar risk the present value of a cash flow due in N years in the future is the amount which if it were on hand today would grow to equal the given future amount Discounting the process of finding the present value of a cash flow or series of cash flows discounting is the reverse of compounding the higher the interest rate the quicker the value falls at relatively high rates funds due in the future are worth very little today Annuity a series of equal payments at fixed intervals for a specified number of periods Ordinary deferred Annuity an annuity whose payments occur at the end of each period Annuity due an annuity whose payments occur at the beginning of each period will have a higher value than other type because payment occurs one period earlier thus all the payments earn interest for one additional period the PV of the annuity due is larger than the other because it is discounted back one less year FVAN PMT 1 i N 1 i FVA due FVA ordianry 1 i Perpetuity a stream of equal payments at fixed intervals expected to continue forever PV of a perpetuity PMT 1 Uneven Nonconstant Cash Flows a series of cash flows where the amount varies from one period to the next Payment PMT the term designates equal cash flows coming at regular intervals Cash Flow CF the term designates a series of cash flows that s not part of an annuity 1 a stream that consists of a series of annuity payments plus an additional final lump sum a an example is bonds 2 all other uneven streams a an example is stocks and capital investments CF 2 1 i 2 CF 1 1 i 1 P V Find the future value of uneven cash flow streams by compounding rather than discounting Annual compounding The arithmetic process of determining the final value of cash flows when interest is added once a year Semiannual compounding The arithmetic process of determining the final value of cash flows or series of cash flows when interest is added twice a year Periodic rate Iper Stated annual rate number of payments per year I M or I Y Ex States annual rate of 5 compounded semiannually the periodic rate is 2 5 Number of periods number of years periods per year NM or N Nominal Quoted or Stated Interest Rate The contracted or quoted or stated interest rate Annual Percentage Rate APR The periodic rate times the number of periods per year rate that credit card companies student loan officers and so forth tell you they are charging Effective Equivalent Annual Rate EFF or EAR The annual rate of interest actually being earned as opposed to the quoted rate Also called the equivalent annual rate the rate that would produce the same future value under annual compounding as would more frequent compounding at a given normal rate If a loan or investment uses annual compounding its nominal rate is all its effective rate However if compounding occurs more than once a year the EFF is higher than Inom EFF 1 I Nom M M 1 Amortized Loan A loan that is repaid in equal payments over its life like a mortgage Amortization Schedule A table showing precisely how a loan will be repaid It gives the required payment on each payment date and a breakdown of the payment showing how much is interest and how much of the repayment is principal Interest component is relatively high in the first year but it declines as the loan balance decreases Production Opportunities The investment opportunities in productive cash generating assets Time Preferences for Consumption The preferences of consumers for current consumption as opposed to saving for future consumption Risk In a financial market context the chance that an investment will provide a low or negative return Inflation the amount by which prices increase over time The interest rate paid to savers depends on the rate of return that producers expect to earn on invested capital the saver s time preferences for current vs future consumption the riskiness of the loan the expected future rate of inflation Nominal rate r r RF DRP LP MRP Real Risk Free Rate of Interest the rate of interest that would exist on default free US Treasury securities if no inflation were expected Nominal quoted Risk Free Rate rrf The rate of interest on a security that is free of all risk Rrf is proxied by the T bill rate or the T bond rate It includes an inflation premium best example would be a Treasury Inflation Protected Security r RF r IP Inflation Premium A premium equal to expected inflation that investors add to the real risk free rate of return Default Risk Premium The difference between the interest rate on a US Treasury bond and a corporate bond of equal maturity and marketability Liquidity Premium A premium added to the equilibrium interest rate on a security if that security cannot be converted to cash on a short notice and at close to its fair market value Interest Rate Risk the risk of capital losses to which investors are exposed because of changing interest rates Maturity Risk Premium MRP a premium that reflects interest rate risk Reinvestment Rate Risk The risk that a decline in interest rates will lead to lower income when bonds mature and funds are reinvested Term Structure of Interest Rates The relationship between the bond yields and maturities the relationship between long and short term rates important to corporate treasurers deciding whether to borrow by issuing long or short term debt need to see how LT and ST rates related as well as what causes the shifts Yield Curve A graph showing the relationship between bond yields and maturities The main determinants of the slope of the curve are expectations for future inflation and the MRP Normal Yield Curve an upward sloping yield curve long term rates are usually higher than short term rates because of the maturity risk premium Abnormal Yield Curve A downward sloping yield curve Humped Yield Curve a yield curve where interest rates on intermediate term maturities are higher