Time value of money (continued)

FV = Future value CF = annual cash flow r = interest (decimal) n = number of periods cash is invested

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

Annuity due - occurs at the beginning of the period

FV = CF x ( (1 + r) n - 1 / r )

FV = CF x ( 1 + r) ( ( 1 + r ) n -1 / 1 )

FV = Future value CF = annual cash flow r = interest (decimal) n = number of periods cash is invested

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