Lecture 2

1. Lecture 2 DADSS Engineering Economics Net Present Value

2. Administrative Details • Bring laptops next class • Homework #1 Due Monday. • Homework #2 due Wednesday.

3. 2015

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

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

6. Engineering Economics • Why “engineering”? • Economic Analysis • Corporate Finance • Capital Budgeting • …

7. Engineering Economics • Why “engineering”? • Economic Analysis • Corporate Finance • Capital Budgeting • … • The tools and models used to evaluate investments in both physical and financial assets (especially physical)

8. Value Over Time • Now vs Later • $100 now is worth $100 now, but what would $100 in 1 year be worth? • Two concepts: • Indifference: What would I need to receive in 1 year to give up $100 for certain today? • 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

9. Time Value of Money in Action

10. Time and Money: Salaries

11. 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?

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

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

14. Extension to Multiple Periods • “Money makes money, and the money that money makes makes more money”

15. 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!

16. Multiperiod Cash Flows where: r is the discount rate n is the year number FV is the future value PV is the present value

17. Multiple Payments over Time Year CF Today 50 / (1+.10) 0 $ (100.00) $ (100.00) 50 / (1+.10)^2 1 $ 50.00 $ 45.45 50 / (1+.10)^3 2 $ 50.00 $ 41.32 Net Present Value (NPV) 3 $ 50.00 $ $ $ 50.00 37.57 24.34

18. Multiple Payments over Time Year CF Today 50 / (1+.10) 0 $ (100.00) $ (100.00) 50 / (1+.10)^2 1 $ 50.00 $ 45.45 50 / (1+.10)^3 2 $ 50.00 $ 41.32 Net Present Value (NPV) 3 $ 50.00 $ $ $ 50.00 24.34 37.57 Year CF 0 $ (100.00) Indifferent $24.34 today 1 $ 50.00 2 $ 50.00 3 $ 50.00

19. Cash Flows Over Time • Let CFt represent a cash flow realized in period t

20. Different Discount Rates

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

23. Graphical Comparison of NPV

24. 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?

25. 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?

26. 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?

27. 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?

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

29. 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?

30. 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%

31. Calculating Present Values

32. 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?

33. 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?

34. 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

35. 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

36. Calculating Present Values

37. 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

38. 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?

39. Step 1: Make Some Assumptions • 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?

40. Step 1 Continued

41. Step 2: Putting the Model Together

42. Step 3: Analysis

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

44. 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

45. 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.