1. DISCOUNTING PROCEDURE WHEREBY THE PRESENT VALUE OF FUTURE INCOME IS DETERMINED. PRESENT VALUE OF A FUTURE PAYMENT PRESENT VALUE OF A SERIES OF PAYMENTS

2. PRESENT VALUE OF A FUTURE PAYMENT PV O = FV N /(1+i) n OR PRESENT VALUE = FUTURE VALUE / (1 + COMPOUND RATE) CONVERSION PERIODS

3. $5,000 2 years. Assume that you need $5,000 in 2 years. Let’s examine the process to determine how much you need to deposit today at a discount rate of 7%. 2 0 1 2 $5,000 7% PV 1 PV 0 Present ValueSingle Deposit (Graphic)

4. PV 0 FV 2 $5,000 FV 2 $4367.19 PV 0 = FV 2 / (1+i) 2 = $5,000 / (1.07) 2 = FV 2 / (1+i) 2 = $4367.19 Present Value Single Deposit (Formula) 2 0 1 2 $5,000 7% PV 0

5. PV 0 FV 1 PV 0 = FV 1 / (1+i) 1 PV 0 FV 2 PV 0 = FV 2 / (1+i) 2 Present Value General Present Value Formula: PV 0 FV n PV 0 = FV n / (1+i) n PV 0 FV n PVD See Table A2 or PV 0 = FV n (PVD i,n ) -- See Table A2 General Present Value Formula etc.

6. PVD PVD i,n is found on Table A2 Valuation Using Table A2

7. PV 2 $5,000 $5,000 $4365.00 PV 2 = $5,000 (PVD 7%,2 ) = $5,000 (.873) = $4365.00 Using Present Value Tables

8. PROBLEM: $6298.56 DISCOUNTED @ 8% FOR 3 YEARS PV O = 6298.56/(1.08) 3 PV O = 6298.56/(1.259712) PV O = 5000

9. $10,0005 years Julie Miller wants to know how large of a deposit to make so that the money will grow to $10,000 in 5 years at a discount rate of 10%. Example Problem 5 0 1 2 3 4 5 $10,000 PV 0 10%

10. PV 0 FV n PV 0 $10,000 $6,209.21 Calculation based on general formula: PV 0 = FV n / (1+i) n PV 0 = $10,000 / (1+ 0.10) 5 = $6,209.21 PV 0 $10,000PVD $10,000 $6,209.00 Calculation based on Table A2: PV 0 = $10,000 (PVD 10%, 5 ) = $10,000 (.6209) = $6,209.00 Problem Solution