BFIN620_PPT_CH4_sp09-4

BFIN620_PPT_CH4_sp09-4 - 4- 1The Time Value of MoneyThe...

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Unformatted text preview: 4- 1The Time Value of MoneyThe Time Value of MoneyChapter 4Brealey-Myers-Marcus5thEditionBusiness Finance 6204- 2General OverviewRules for Single Cash FlowsCompounding and discountingEffective rates of interestInterest Rates and InflationRules for Streams of Cash FlowsGeneral streams of (uneven) cash flowsStreams with special characteristics•Perpetuities•AnnuitiesAmortization and amortizing loans4- 3Part 1 Topics CoveredFuture values (FV) and compoundingSimple and compound interestFV of a single cash flow todayFV of a stream of cash flowsEffective annual rates of interestPresent values (PV) and discountingPV of a single cash flow in the futurePV of a stream of cash flowsInterest rates and inflation4- 4FV with Simple InterestSimple interest is earned at an annual rate of 6% for 5 years on a principal balance of $100.YearBeginning BalanceInterestEnding Balance1$ 100$ 6$ 106210661123112611841186124512461304- 5FV with Compound InterestCompound Interest is earned at an annual rate of 6% for 5 years on a principal balance of $100.YearBeginning BalanceInterestEnding Balance1$ 100.00$ 6.00$ 106.002106.006.36112.363112.366.74119.104119.107.15126.255126.257.57133.824- 6Ending balance comparison:With compound interest133.82With simple interest130.00Difference3.82Compound interest generates:interest of $30.00 on the original $100 investmentinterest of $3.82 in Years 2-5 on interest credited during Years 1-4The $3.82 difference is called “interest on interest” and is the hallmark of interest compounding.Simple and Compound Interest4- 7FV of a Single Cash FlowFV of Single Cash Flow:In this formula:FV is future valuePV is present value (not always today)R is the constant interest rate (%)K is the number of time periods separating FV and PVK can be any unit of time (e.g., years, months)KR)+(1PV =FV 4- 8FV of Single Cash FlowApplicationWhat is the FV of $1,500 if interest is compounded at a rate of 8% annually for seven years?2,570.74$(1.08)1,500FV7=×=1,5002,570.740 1 2 3 4 5 6 7 How much of the total interest earned represents interest earned on interest?4- 91020304050607024681121416182222426283Number of YearsFV of $10%5%10%15%Effect of Compound Interest on FVInterest RatesR)(1$1FVK+×=4- 10FV of a Stream of Cash FlowsThe FV of each cash flow in the stream can be added to calculate the FV of the stream.The FV of a stream of multiple cash flows is the sum of the FV of each cash flow in the stream.The general formula for a stream of T cash flows (Ci) over T periods, compounded at a rate of R% per period:where Ci(1+R)T-irepresents the FV of the ithcash flow in the stream....
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This note was uploaded on 10/10/2011 for the course BUSINESS 620 taught by Professor Paul during the Spring '11 term at Ohio State.

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BFIN620_PPT_CH4_sp09-4 - 4- 1The Time Value of MoneyThe...

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