Finance 300 Chapter Six Discounted Cash Flow Valuation Assessment Preparation Key Terms amortized loan A loan that has identical payments throughout the contract Payments are applied first towards reducing the interest balance and any remaining sum towards the principal balance As a consequence the proportion of each payment that pays interest decreases while the proportion applied to principal increases throughout the loan annual percentage rate APR A simple interest rate that laws require banks to state on all consumer loans annuity due A finite stream of identical recurring payments whose payments occur at the beginning of each period Rent and lease payments are examples closing costs Expenses separate from the purchase price that buyers and sellers normally incur to complete a real estate transaction Examples include appraisal fees title searches and insurance loan processing fees a k a origination fees by the bank and many more Closing costs run somewhere between 2 and 5 of the purchase price consistent In TVM calculations involving the annuity and perpetuity formulae you must define both the payment frequency and the periodic rate over the same unit of time Start with the payment then determine the rate continuously compounded interest Interest paid constantly and immediately begins earning interest on itself effective annual rate EAR or annual percentage yield APY An interest rate that reflects all the compound interest paid or earned in one year effective rate A low frequency rate that is equivalent to a high frequency rate For example an effective annual rate of 12 682503 low frequency is the same as 1 per month high frequency growing annuity An annuity whose payments grow at a constant rate per period for the length of the contract hedge fund Hedge funds pool money from sophisticated investors known as accredited investors then pursue a wide range of investment strategies chasing alpha unusually large returns Typically investors can only withdraw their money once per year known as the lock up period The Securities and Exchange Commission does not heavily regulate hedge funds because from its point of view accredited investors should know what they are getting themselves into The typical hedge fund has a two and twenty fee structure a two percent annual management fee plus 20 of overall profits In summary hedge funds pool the resources of a small number of wealthy backers charge large fees and adopt relatively unconstrained investment strategies due to limited regulation lease A contract that allows a party to temporarily rent an asset for a fixed period under a set of prespecified conditions A lease can differ from rent in the case of large capital assets because generally accepted accounting principles may require the lessor renter to book the asset and the lease on its balance sheet loan amortization schedule A payment by payment table that shows the beginning balance interest and principal paid per payment and the resulting ending balance for an amortized loan such as a mortgage or car loan 1 Mark J Laplante Ph D Wisconsin School of Business University of Wisconsin Madison ordinary annuity A finite stream of identical recurring payments whose payments occur at the end of each period Car loans and mortgages are examples mutual fund Mutual funds pool money from small investors then pursue a wide range of investment strategies usually enabling the investors to diversify easily Since many mutual fund investors are unsophisticated the Securities and Exchange Commission acts in the public interest to regulate mutual funds and enforce rigorous public disclosures For example SEC regulation restricts mutual fund strategies and requires quarterly public disclosure of equity positions Mutual funds charge relatively low fees for their investment services in fact some charge no fees In summary mutual funds pool the resources of a large number of small backers charge small fees and adopt relatively constrained investment strategies due to SEC regulation net present value NPV The difference between the present value of cash inflows and the present value of cash outflows pension fund An investment pools that pay for employee retirement benefits Employers whether private sector or government provide the money for the fund though in some cases employees may contribute as well Federal laws provide specific guidelines for plan fiduciaries to protect the pension assets thus plan managers pursue constrained investment strategies in the best interests of the beneficiaries perpetuity An infinite stream of cash flows that are paid or received with a regular frequency In general the word perpetuity refers to a stream where all the cash flows are the same Level perpetuity or constant perpetuity are other names preferred stock Stock with dividend priority over common stock normally with a fixed dividend rate and most often without voting rights Typically financial companies issue preferred stock and pay a level quarterly dividend 2 Key Equations Variables FV PV r t g m future value of a lump sum later on the timeline than the present value present value of a lump sum earlier on the timeline than the future value periodic rate expressed in decimal form a growth rate in dollars number of periods payments must be consistent with the interval of time over which a contract defines the periodic rate the growth rate in a growing annuity expressed in decimal form the number of compounding periods per year BAII Enter t payments N r 100 I Y C PMT Solve CPT FV The future value lump sum occurs at the time when the last payment in the ordinary annuity stream occurs That s what the subscripts are trying to tell you 2 PV C 0 1 BAII Enter t payments N r 100 I Y C PMT Solve CPT PV The present value lump sum occurs one period prior to the first payment in the ordinary annuity stream note the subscripts BAII Enter r 100 I Y C PMT PV PV Solve CPT N 4 C PV 0 1 BAII Enter t payments N C PMT PV PV Solve CPT I Y Ordinary annuity 1 FV C t t 1 1t r r 1 1 tr 1 r ln C C r PV 1 r ln 3 t 1 1 1 tr 1 r Annuity due 5 FV C t t 1 1t r r BAII Enter t payments N r 100 I Y C PMT Solve CPT FV The future value lump sum occurs at the time when the last payment in the annuity due stream occurs note the subscripts 6 PV due PV ordinary 1 r 3 The present value lump sum occurs when the first payment in the annuity due stream occurs an important difference from the present value of the ordinary annuity formula The periodic rate cannot