The Time Value of Money

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