1. The Time Value of Money By R. S. Miolla

2. Agenda Time value of money Future value Present value Annuities

3. 1) Future Value (FV) Investing or FV – A lump sum of cash (Present Value) – Rate of return (i), % – Number of periods (n), usually years – Compounding – You compute the FV

4. Computing FV - Manually Given $1,000 to invest (PV) 5% rate of return (i) Three years (n) Manually: FV = 1000 * 1.05 = 1050, year 1 1050* 1.05 = 1102.50, year 2 1102.50*1.05 = 1157.63 year 3

5. Computing FV - Equation FV = PV(1+i)^n FV = 1000(1 +.05)^3 FV = 1157.63

6. 2) Present Value (PV) Cash to be received in the future is worth how much now? – FV or amount to be received – Discount rate or i (%); inflation and loss of use – Number of years to wait (n)

7. Computing PV - Equation PV = FV/(1+i)^n Example: Will receive 2,000 in 4 years – i = 7% PV = 2000/(1+.07)^4 PV = 2000(1.31) PV = 1526.72

8. Annuity A repeating set of cash flows in different time periods. You can compute the FV of an annuity and the PV of an annuity.

9. Tools Present value and future value tables Excel Online calculators Financial calculators Smart phone apps.

10. Summary Time value of money (cash) Future value and present value Computation and tools