Time Value of Money An Introduction Zara Mahmood Roberts FE101 VALUING A STREAM OF CASH FLOWS Steam of Cash Flows A series of cash flows lasting several periods Represented on a timeline Applying the Rules of Valuing Cash Flows to a Cash Flow Stream Most 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 combined o To calculate future value we must compound the cash flow o To calculate present value we must discount future value Allow us to compare and combine cash flows of different times Eg Two ways to calculate value in three years Both methods give us the same result General formula for valuing a stream of cash flows Compute present value of each individual cash flow o 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 flow PERPETUITIES Perpetuities 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 constant Consol A bond that promises its owner a fixed cash flow every year forever Zara Mahmood Roberts FE101 Bank interest rate is like perpetuities Invest 100 each year and take 5 from interest each year o Present value of 5 per year in perpetuity is this do it yourself cost of 100 Annuity A stream of equal cash flows arriving at regular interval and ending after specified time period Value of annuity initial investment PV of principal that will be left in account ANNUITIES Perpetuity continues forever annuity ends after specific time Present Value of an Annuity Find a way to create your own annuity after n years Future Value of an Annuity The value N years in the future GROWING CASH FLOWS Growing Perpetuity Zara Mahmood Roberts FE101 Growing Perpetuity A stream of cash flows that occurs at regular intervals and grows at a constant rate forever Must increase the amount we reinvest each year o Withdraw less than the full amount of interest earned each period Growing Annuity Growing Annuity A stream of cash flows growing at a constant rate and paid at regular intervals that end after a specified number of periods SOLVING FOR VARIABLES OTHER THAN PRESENT VALUE OR FUTURE VALUE Use PV or FV as inputs and solve for variable we are interested in Solving for the Cash Flows Eg 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 year Rate of Return What interest rate would you need so that the present value of what you get is equal to the present value of what you give Solving for the Number of Periods Solve for the amount of time it will take a sum of money to grow to a known rate