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Zara MahmoodRobertsFE101Time Value of Money: An IntroductionVALUING A STREAM OF CASH FLOWSSteam of Cash Flows – A series of cash flows lasting several periods- Represented on a timelineApplying the Rules of Valuing Cash Flows to a Cash Flow StreamMost investments have multiple cash flows occurring at different times- Rules to value cash flows:o Only values at the same point in time can be compared/combinedo To calculate future value we must compound the cash flowo To calculate present value we must discount future value- Allow us to compare and combine cash flows of different timesEg: Two ways to calculate value in three years- Both methods give us the sameresultGeneral formula for valuing a stream of cash flows- Compute present value of each individual cash flowo Once they are in units of today we combine them- Present value of cash flow stream is the sum of present value of each cash flowPERPETUITIESZara MahmoodRobertsFE101Perpetuities – A stream of equal cash flows that occur at regular intervals and last forever- First cash flow arrives at the end of the first period (payment in arrears)- All the cash flows (C) are the same  perpetuities are constantConsol – A bond that promises its owner a fixed cash flow every year, foreverBank interest rate is like perpetuities- Invest $100 each year and take $5 from interest each yearo Present value of $5 per year in perpetuity is this “do it yourself” cost of $100ANNUITIESAnnuity – A stream of equal cash flows arriving at regular interval and ending after specified time period- Perpetuity continuesforever, annuity endsafter specific timePresent Value of an AnnuityFind a way to create your own annuity- Value of annuity  initial investment – PV of principal that will be left in account after nyearsFuture Value of an AnnuityThe value N years in the futureGROWING CASH FLOWSGrowing PerpetuityZara MahmoodRobertsFE101Growing Perpetuity – A stream of cash flows that occurs at regular intervals and grows at a constant rate forever- Must increase the amount we reinvest eachyearo Withdraw less than the full amount ofinterest earned each periodGrowing AnnuityGrowing Annuity – A stream of cash flows, growing ata constant rate and paid at regular intervals, that endafter a specified number of periodsSOLVING FOR VARIABLES OTHER THAN PRESENT VALUE OR FUTURE VALUEUse PV or FV as inputs and solve for variable we are interested inSolving for the Cash FlowsEg: Know present value of investment but don’t know cash flows (loan)- Know how much to borrow (PV) and interest rate, but not how much you repay each yearRate of ReturnWhat interest rate would you need so that the present value of what you get is equal to the present value of what you giveSolving for the Number of PeriodsSolve for the amount of time it will take a sum of money to grow to a known

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