1. Decision Analysis & Decision Support Systems: DADSS Lecture 2: Introduction to Time Value of Money John Gasper

2. Administrative Homework 1 due Sunday Homework 2 due Tuesday

3. 2017

4. Time and Money TodayIn 1 Year indifferent 100.00$ 100 x (1+.10) 110.00$

5. Time and Money TodayIn 1 Year indifferent 100.00$ 100 x (1+.10) 110.00$ TodayIn 1 Year indifferent 50.00$ 50 / (1+.10) 45.45$

6. Time Value Sometimes referred to as “Engineering Economics” Economic Analysis Corporate Finance Capital Budgeting … The tools and models used to evaluate investments in both physical and financial assets (especially physical)

7. Value Over Time Now vs Later $100 now is worth $100 now, but what would $100 in 1 year be worth? Two concepts: 1. Indifference: What would I need to receive in 1 year to give up $100 for certain today? 2. Arbitrage: Through some trade, what could I assure myself of getting in 1 year with a $100 investment today? Indifference allows for risk preferences; arbitrage is risk-neutral

8. Time Value of Money in Action

9. Example 2: Salaries

10. Arbitrage and Fair Returns Arbitrage = Free Money, Riskless Profit Why should future money be worth less (or no more) than current money? Opportunity costs (“preferred habitat”) Inflation (“rational expectations”) Liquidity (“liquidity preference”) Could the opposite ever be true?

11. Value of Money over Multiple Years Today In 2 Years indifferent 100.00$ 100 x (1+.10)110 x (1+.10) 110.00$ In 1 Year $121.00 100 x (1+.10) x (1+.10) or 100 x (1+.10)^2

12. Bringing Future to the Present Today In 2 Years indifferent 50.00$ 45.45 / (1+.10)50 / (1+.10) 45.45$ In 1 Year 41.32$ (50 / (1+.10)) / (1+.10) or 50 / (1+.10)^2

13. Extension to Multiple Periods “Money makes money, and the money that money makes makes more money” Compounding Now = 100 In one year: 100 × (1 + r) But, in the second year: [100 × (1 + r)] × (1 + r) You get to earn a return on the first year’s return in addition to your original capital!

14. Multi-period Cash Flows where: r is the discount rate n is the year number FV is the future value PV is the present value

15. Multiple payments over time YearCFToday 0(100.00)$ 150.00$ 2 $ 3 $ (100.00)$ 45.45$ 50 / (1+.10) 41.32$ 50 / (1+.10)^2 50.00$ 50 / (1+.10)^3 37.57$ 24.34$ Net Present Value (NPV)

16. Cash flows over time Let represent a cash flow realized in period t

17. Different Discount Rates Why does the NPV decrease with increasing rates? How can the NPV be negative? Meaning? NPV

19. Graphical Comparison of NPV