1. FIN 614: Financial Management Larry Schrenk, Instructor

2. 1.The Time Value of Money 2.Future Value (FV) 3.Present Value (PV)

3. ‘Cash Flows’ Consider: $100 Today vs. $100 in 1 Year $100 Today vs. $110 in 1 Year $100 in 1 Year vs. $130 in 4 Years Project Comparison 123 Project A100 Project B0160

4. Factors Opportunity Cost Inflation Risk

5. Compounding One-Time Deposit If I invest $100.00 today, how much will I have in… One Year? Ten Years? One Hundred Years?

6. How much is it worth after one year? Interest rate (r) is 10% $100.00 × (1 + 10%) = $100.00 × 1.1 = $110.00 Reasoning: Multiply by 1  Still have Original Deposit Multiply by 0.10  Interest

7. How much do I have in two years? $110.00 at t = 1 and r = 10% $110.00 × (1 + 10%) = $110.00 × 1.1 = $121.00 YearCalculationValue 0$100.00 1$100.00(1.10) =$110.00 2$100.00(1.10)(1.10) =$121.00 3$100.00(1.10)(1.10)(1.10) =$133.10 4$100.00(1.10)(1.10)(1.10)(1.10) =$146.41

8. In Year 2 we have $121.00 $100Original Deposit 10Interest on Deposit in Year 1 10Interest on Deposit in Year 2 1Interest on ‘Year 1 Interest’ in Year 2 $121Total ‘Interest on Interest’ Simple Interest: $120 in Year 2

9. Even better we can construct a formula: In practice, we will use our calculators.

10. $1 Compounded 100 Years = $131.50

11. Discounting Inverse of Compounding One-Time Future Cash Flow If I receive $100.00 in… One Year Ten Years One Hundred Years How much is it worth today?

12. How much is it worth now? Interest rate (r) is 10% $100.00/(1 + 10%) = $100.00/1.1 = $90.91

13. As in compounding, we can repeat this algorithm for multiple years. YearCalculationValue 0$100.00 1$100.00/(1.10) =$90.91 2$100.00/[(1.10)(1.10)] =$82.64 3$100.00/[(1.10)(1.10)(1.10)] =$75.13 4$100.00/[(1.10)(1.10)(1.10)(1.10)] =$68.30

14. Even better we can construct a formula: In practice, we will use our calculators.

15. $100 Discounted100 Years = $0.76

16. FIN 614: Financial Management Larry Schrenk, Instructor