1. DADSS Lecture 3: Using Excel with Time Value Calculations John Gasper

2. Administrative Homework 1 due today (now) Homework 2 due Wednesday. Homework 3 due January 29 (posted tonight) Bring laptops again next class. Start Decision Analysis next week

3. Last Time Basic introduction to Net Present Value and how to calculate it in Excel.

5. Graphical Comparison of NPV

6. Examples Choosing a project Valuing an investment Evaluating the effectiveness of a decision or strategy over time Basically: How can I value things? Given values, what do they mean? 6

7. Specific Problem Types Corporate Finance Plant A requires a $100 million investment, but will return $50 million/yr for 10 years Plant B requires only $50 million now, but another $75 million in 5 years. It will return $45 million/yr for 10 years Which plant should the firm invest in? 7

8. Specific Problem Types Should I go to College? (too late!) Decision #1: Skip college and start work No college costs and you start earning immediately, but your salary is (probably) lower Decision #2: Go to college College is expensive; you miss out on 4 years of earning power However, you will (probably) earn more once you graduate What should you do? What salary premium would you have to earn in order to justify going to college?

9. Specific Problem Types Retirement Planning I want to retire in 20 years with an income of $100,000/yr I have no current savings, but a large income How much should I save if I want to meet my goal? What kind of return do I need to get? How does return trade off against the savings amount required? 9

10. The Key Elements Value over time Choices or Alternatives Uncertainty We’ll ignore uncertainty for now

11. Example: Borrowing Money To buy some equipment for your business, you need to borrow $100,000 The bank offers you a choice of 4 different payment arrangements, each with different terms How should you choose between them? Do you care? Does the bank care? 11

12. Example: Borrowing Money Option #1: Capitalized interest at 6%, balloon payment in 10 years Option #2: Interest-only for 10 years at 8%, then balloon payment at end Option #3: Principal amortized, level payments for 10 years at 10% Option #4: Constant paydown of $10,000/year plus interest, for ten years at 12% 12

13. Valuing Loan Options Option #1 is a single payment in 10 years: CF/(1+0.06) 10 Option #2 is just interest (r × Loan) for 10 years, then you return the loan Option #3 requires calculation of a finite stream of equal payments (sound familiar?) Option #4 makes constant payments, but interest is reduced as the balance is paid down 13

14. Some Preliminary Thoughts… Option 1 has the lowest interest rate and gives you the longest time to pay Option 4 has the highest interest rate and you have to start paying a large amount immediately #1 sounds much better than #4, right? Always ask: What is the money worth right NOW? 14

15. Valuing Loan Options Some observations: Option #1 suffers from compounding – in the banks favor Option #2 requires you to pay interest, but never reduce the principal Option #3 means you have to start paying more now, but that means less interest later Option #4 is like Option #2 with principal, or like Option #3 with the fixed amount set to $10,000 What do the numbers say? The purpose of modeling is insight! We have carefully defined the problem, putting the different options into quantitative terms 15

16. Loan Options The borrower (you) wants to pay as little in interest as possible The bank wants you to pay as much in interest as possible In light of these facts, what might we expect to be the case for each of the options given to the firm? Why might this expectation be wrong? 16

17. Calculating Present Values 17

18. Conclusion? The bank would be more than happy to have you accept Option #2 Ever had your credit card company offer for you to “skip a payment”? You should pick Option #3 (in the absence of any other considerations) Why might some firms or managers prefer a different option? Cash flow constraints Revenue/Liability matching Taxes 18

19. Back for More? Grad School… One option available to you after you graduate is continuing on for a graduate degree Is it worth it? More informatively, under what circumstances would it be worthwhile?

20. Step 1: Make Some Assumptions What to assume? You’ll retire at the same age, whether or not you get an advanced degree Post-graduate school compensation can be represented as a linear multiple of pre- graduate school pay What alternative assumptions could we make? Would such other assumptions have a big impact?

21. Step 1 Continued 21

22. Step 2: Putting the Model Together 22

23. Step 3: Analysis 23

24. Step 3: Analysis 24 Measuring the Benefit (in present dollars) from Grad School

25. More and More Analysis This is just the beginning Creating a model of the decision problem allows us to explore an enormous variety of assumptions One goal for good decisions? Robustness

26. What’s Left Out? Uncertainty How do you trade off a certain value today for an uncertain value in the future? Utility Utility is a way of incorporating different attitudes toward risk (for or against) Measures for Comparing Cash Flows So far we’ve just valued cash flows. NPV, IRR, MIRR, EUAC, Payback, etc. 26