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Chapter 5

Chapter 5. Time Value of Money. After studying Chapter 5 you should be able to:. Understand what is meant by "the time value of money." Understand the relationship between present and future value.

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Chapter 5

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  1. Chapter 5 Time Value of Money

  2. After studying Chapter 5 you should be able to: • Understand what is meant by "the time value of money." • Understand the relationship between present and future value. • Describe how the interest rate can be used to adjust the value of cash flows – both forward and backward – to a single point in time. • Calculate both the future and present value of: (a) an amount invested today; (b) a stream of equal cash flows (an annuity); and (c) a stream of mixed cash flow.

  3. The Time Value of Money • The Interest Rate • Simple Interest • Compound Interest • Compounding More Than Once per Year

  4. Obviously, $10,000 today. You already recognize that there is TIME VALUE TO MONEY!! Which would you prefer -- $10,000 today or $10,000 in 5 years? The Interest Rate

  5. TIME allows you the opportunity to postpone consumption and earn INTEREST. Why is TIME such an important element in your decision? Why TIME?

  6. Compound Interest Interest paid (earned) on any previous interest earned, as well as on the principal borrowed (lent). Types of Interest • Simple Interest • Interest paid (earned) on only the original amount, or principal, borrowed (lent).

  7. Simple Interest Formula FormulaSI = P0(i)(n) SI: Simple Interest P0: Deposit today (t=0) i: Interest Rate per Period n: Number of Time Periods

  8. SI = P0(i)(n)= $1,000(.07)(2) = $140 Assume that you deposit $1,000 in an account earning 7% simple interest for 2 years. What is the accumulated interest at the end of the 2nd year? Simple Interest Example

  9. FV = P0 + SI = $1,000+ $140 =$1,140 Future Valueis the value at some future time of a present amount of money, or a series of payments, evaluated at a given interest rate. What is the Future Value (FV) of the deposit? Simple Interest (FV)

  10. The Present Value is simply the $1,000 you originally deposited. That is the value today! Present Valueis the current value of a future amount of money, or a series of payments, evaluated at a given interest rate. What is the Present Value (PV) of the previous problem? Simple Interest (PV)

  11. examples • If u know that pv=1000 • Interest rate = 6% • Future value = 1180 • How u can caculate number of years for this investment?

  12. examples • If u know that during 3 years • Ur future value is 1180 • Interest rate is 6% • Can u compute ur initial value for this investment

  13. examples • If u invest 1000 dollars by 6% simply interest rate during: • 26 weeks • 9 months • 240 days • How u can calculate ur future value

  14. Why Compound Interest? Future Value (U.S. Dollars)

  15. Distinguish invest 1000 dollars by 6% simply or compounded rate for 3 years • then mention which is bettre for investor ?

  16. Future Value Single Deposit (Graphic) Assume that you deposit $1,000 at a compound interest rate of 7% for 2 years. 0 12 7% $1,000 FV2

  17. Future Value Single Deposit (Formula) FV1 = P0 (1+i)1 = $1,000(1.07) = $1,070 Compound Interest You earned $70 interest on your $1,000 deposit over the first year. This is the same amount of interest you would earn under simple interest.

  18. Future Value Single Deposit (Formula) FV1 = P0(1+i)1 = $1,000 (1.07) = $1,070 FV2 = FV1 (1+i)1 = P0 (1+i)(1+i) = $1,000(1.07)(1.07) = P0(1+i)2 = $1,000(1.07)2 = $1,144.90 You earned an EXTRA$4.90 in Year 2 with compound over simple interest.

  19. General Future Value Formula FV1 = P0(1+i)1 FV2 = P0(1+i)2 General Future Value Formula: FVn = P0 (1+i)n or FVn = P0 (FVIFi,n) -- See Table I etc.

  20. Valuation Using Table I FVIFi,nis found on Table I at the end of the book.

  21. Using Future Value Tables FV2 = $1,000 (FVIF7%,2) = $1,000 (1.145) = $1,145[Due to Rounding]

  22. Story Problem Example Julie Miller wants to know how large her deposit of $10,000 today will become at a compound annual interest rate of 10% for 5 years. 0 1 2 3 4 5 10% $10,000 FV5

  23. Story Problem Solution • Calculation based on general formula:FVn = P0 (1+i)nFV5= $10,000 (1+ 0.10)5 = $16,105.10 • Calculation based on Table I: FV5= $10,000(FVIF10%, 5)= $10,000(1.611) = $16,110 [Due to Rounding]

  24. We will use the “Rule-of-72”. Quick! How long does it take to double $5,000 at a compound rate of 12% per year (approx.)? Double Your Money!!!

  25. Approx. Years to Double = 72/ i% 72 / 12% = 6 Years [Actual Time is 6.12 Years] Quick! How long does it take to double $5,000 at a compound rate of 12% per year (approx.)? The “Rule-of-72”

  26. Example • If you know that price of BMW always 20000 dollars. U like to buy one-currently u have only 7752 dollars-how many years will it take for your initial investment of 7752 dollars to grow 20000- if it is invested at 9% compounded annually using table of ( FVIF) • ALSO IF u have currently 11167 dollars invested for 10 years- what is interest rate u need to get price of BMW –using same table

  27. Present Value Single Deposit (Graphic) Assume that you need $1,000in 2 years. Let’s examine the process to determine how much you need to deposit today at a discount rate of 7% compounded annually. 0 12 7% $1,000 PV0 PV1

  28. Present Value Single Deposit (Formula) PV0 = FV2 / (1+i)2 = $1,000/ (1.07)2 = FV2 / (1+i)2 = $873.44 0 12 7% $1,000 PV0

  29. General Present Value Formula PV0= FV1 / (1+i)1 PV0 = FV2 / (1+i)2 General Present Value Formula: PV0 = FVn / (1+i)n or PV0 = FVn (PVIFi,n) -- See Table II etc.

  30. Valuation Using Table II PVIFi,nis found on Table II at the end of the book.

  31. Using Present Value Tables PV2 = $1,000 (PVIF7%,2) = $1,000 (.873) = $873[Due to Rounding]

  32. Story Problem Example Julie Miller wants to know how large of a deposit to make so that the money will grow to $10,000in 5 years at a discount rate of 10%. 0 1 2 3 4 5 10% $10,000 PV0

  33. Story Problem Solution • Calculation based on general formula: PV0 = FVn / (1+i)nPV0= $10,000/ (1+ 0.10)5 = $6,209.21 • Calculation based on Table I: PV0= $10,000(PVIF10%, 5)= $10,000(.621) = $6,210.00 [Due to Rounding]

  34. example • What is present value of an investment yields 500 dollars to be received in 5 years and 1000 dollars to be received in 10 years if u know that discount rate is 4% for both

  35. example • If present value=676 and future value= 1000 dollars and discount rate was =4% so number of years was 8 years using PVIF table • Mention: true or falce and why.

  36. Types of Annuities • An Annuity represents a series of equal payments (or receipts) occurring over a specified number of equidistant periods. • Ordinary Annuity: Payments or receipts occur at the end of each period. • Annuity Due: Payments or receipts occur at the beginning of each period.

  37. Examples of Annuities • Student Loan Payments • Car Loan Payments • Insurance Premiums • Mortgage Payments • Retirement Savings

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