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Time value of money (continued), FV = Future value CF =…
Time value of money (continued)
PV v FV
Both present value and future value measure how much value of money has changed over time
FV measures what one are more cash flows are worth at the end of specified period
PV measures what one or more cash flows that are to be recieved in the future will be worth in time
FV -- Discounting - - PV
PV -- Compounding -- FV
Ordinary annuity v Annuity due
Ordinary annuity - occurs at the end of the period
FV = CF x ( (1 + r) n - 1 / r )
Annuity due - occurs at the beginning of the period
FV = CF x ( 1 + r) ( ( 1 + r ) n -1 / 1 )
Present value - power of discounting (FV to PV)
Discount factor = PV = FV x discount factor
Single cash flow = 1 / ( 1 + r ) n
PV = CFn / (1 + r ) n
Annuity - 1 / r ( 1 - 1 / ( 1 + r ) n
Perpetuity - 1 / r
Calculating cash payments
we use annuities to calculate cash payments
Cash payment - loan example
Loan - present value
Cash payment - savings example
Savings - future value
Interest rate - terms used
Cost of capital
Discount rate
Required return
How to calculate the monthly or daily rate when annual percentage rate = 365 days
(1 + ry) = ( 1 + rm) 12 or (1 + ry) = ( 1 + rd) 365
FV = Future value CF = annual cash flow r = interest (decimal) n = number of periods cash is invested