Chapter 4 The Time Value of Money

1. Chapter 4The Time Value of Money

2. Question: Would you rather Receive $1000 today; or Receive $1000 10 years from today? Answer: Of course today! Why? I could invest $1000 today to make more money I could buy a lot of stuff today with $1000 Who knows what will happen in 10 years Computing Cash Flows

3. Because money is more valuable today than in the future, we need to describe cash receipts and disbursements at time they occur. Computing Cash Flows

4. Money has purchasing power Money has earning power Money is a valuable asset People are will to pay some charges (interests) to have money available for their use Time Value of Money

5. Simple Interest Interest is computed only on the original sum, and not on accrued interest

6. Compound Interest Interest is computed on the unpaid balance, which includes the principal and any unpaid interest from the preceding period Common practice for interest calculation, unless specifically stated otherwise

7. Compound Interest Calculation Loan of $5000 for 5 yrs at interest rate of 8%

8. Repaying a Debt Repay of a loan of $5000 in 5 yrs at interest rate of 8% Plan #1: Pay $1000 principal plus interest due

9. Repaying a Debt Repay of a loan of $5000 in 5 yrs at interest rate of 8% Plan #2: Pay interest due at end of each year and principal at end of 5 years

10. Repaying a Debt Repay of a loan of $5000 in 5 yrs at interest rate of 8% Plan #3: Pay in 5 equal end-of-year payments

11. Repaying a Debt Repay of a loan of $5000 in 5 yrs at interest rate of 8% Plan #4: Pay principal and interest in one payment at end of 5 years

12. A Closer Look at the 4 Repayment Differences: Repayment structure (repayment amounts at various points in time) Total payment amount Similarities: All interest charges were calculated at 8% They all achieved the same purpose of repaying the loan within 5 years

13. Equivalence If a firm believes 8% was reasonable, it would have no preference about whether it received $5000 now or was paid by any of the 4 repayment plans. The 4 repayment plans are equivalent to one another and to $5000 now at 8% interest

14. Use of Equivalence inEngineering Economic Studies Using the concept of equivalence, one can convert different types of cash flows at different points of time to an equivalent value at a common reference point Equivalence is dependent on interest rate

15. Single Payment Compound Interest Formulas Notation: i = interest rate per compounding period N = number of compounding periods P = a present sum of money F = a future sum of money

16. Single Payment Compound Interest Formulas Notation: i = interest rate per compounding period N = number of compounding periods P = a present sum of money F = a future sum of money

17. Single Payment Finding i, or N

18. Uniform Series Compound Interest Formulas Notation: A = an end-of-period cash flow in a uniform series, continuing for N periods

19. Uniform Series Compound Interest Formulas Uniform Series Compound Amount Factor

20. Uniform Series Compound Interest Formulas Uniform Series Capital Recovery Factor

21. Relationships Between Compound Interest Factors Single Payment

22. Relationships Between Compound Interest Factors

23. Arithmetic Gradient

24. Arithmetic Gradient Notation: G = a fixed amount increment or decrement per time period

25. Arithmetic GradientCompound Interest Formulas Arithmetic Gradient Present Worth Factor

26. Application of Arithmetic Gradient Interest Factors

27. Application of Arithmetic Gradient Interest Factors

28. Application of Arithmetic Gradient Interest Factors

29. Geometric Gradient Notation: g = a constant growth rate (+ or -) per period A1 = cash flow at period 1

30. Geometric GradientCompound Interest Formulas Geometric Gradient Present Worth Factor

31. Application of Geometric Gradient Interest Factors Using 8% interest rate, calculate the Present Worth of maintenance cost of the first 5 years where the first year’s cost is estimated at $100, and it increases at a constant rate of 10% per year.

32. Nominal and Effective Interest Rates Notation: r = Nominal interest rate per year without considering the effect of any compounding i = Effective interest rate per compounding period ia = Effective annual interest rate taking into account the effect of compounding m = Number of compounding periods per year

33. Nominal and Effective Interest

34. Application of Nominal and Effective Interest Rates “If I give you $50, you owe me $60 on the following Monday.”

35. Continuous Compounding Interest Formulas Single Payment Compound Amount

36. Continuous Compounding Interest Formulas

37. Application of Continuous Compounding How much would be in the account for $2000 deposit in a bank that pays 5% nominal interest, compounding continuously?

38. Application of Continuous Compounding How long will it take for money to double at 10% nominal interest, compounding continuously?

39. Application of Continuous Compounding $500 were deposited in a credit union (pays 5% compounded continuously) at the end of each year for 5 years, how much do you have after the 5th deposit?

40. Spreadsheets for Economic Analysis Constructing tables of cash flows Using annuity functions to calculate P, F, A, N, or i Using block functions to find the present worth or internal rate of return for a table of cash flows Making graphs for analysis and presentations Calculating “what-if” for different scenarios

41. Spreadsheet Annuity Functions

42. Spreadsheet Block Functions