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Present Value of Money

0. 1. 2. 3. 4. 5. Present Value of Money. To find the present value of money, we must know: The Cash Flow Amount (cash inflow or outflow) Time (the “n” # of periods to the future point in time) Discount Rate (“i” to discount back to find the PV) per period. n. PVF. i.

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Present Value of Money

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  1. 0 1 2 3 4 5 Present Value of Money To find the present value of money, we must know: The Cash Flow Amount (cash inflow or outflow) Time (the “n” # of periods to the future point in time) Discount Rate (“i” to discount back to find the PV) per period

  2. n PVF i The Present Value of a Single Lump Sum Amount... … is described as the amount that must be invested today (at time “0”) to produce a known future value 1 PV = Amount x ---------- (1 + i) n

  3. An investment that involves a series of identical cash flows at the end of each year is called an Ordinary Annuity. $100 $100 $100 $100 $100 1 2 3 4 5 The Present Value of an Ordinary Annuity equals ... (AnnualAmnt) x [PVF-OA(n=#, r=%)]

  4. $100 $100 $100 $100 $100 1 2 3 4 5 0 For an Annuity Due, the “rents” or payments occur at the beginning of each period (pay in advance) The Present Value of an Annuity Due equals ... (AnnualAmnt) x [PVF-AD(n=#, i=%)]

  5. Calculating the Present Value of an Annuity Due 1) Find the present value of an ordinary annuity factor (PVF-OA @ n=N-1, i=%) for n-1 periods 2) Multiply that factor time (1+i), that is, 1 plus the interest rate -- to get the “PVF-AD” factor 3) Multiply the periodic “amount” times this PVF-AD to get the present value of payments

  6. $0 $0 $100 $100 $100 1 2 3 4 5 If the cash flows from an ordinary annuitybegin after a period of time, we have a Deferred Ordinary Annuity. Present Value of a Deferred Ordinary Annuity ... “deferred factor” for payments extending through period “#” beginning after period “d” = (PVF-OA N=#, r=%) - (PVF-OA N=d, r=%) PV of DA = (AnnualAmnt) x [deferred factor]

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