1. Chapter McGraw-Hill Ryerson © 2013 McGraw-Hill Ryerson Limited 6 Prepared by Anne Inglis Edited by William Rentz Discounted Cash Flow Valuation

2. 6-1 Key Concepts and Skills Be able to compute the future value and present value of multiple cash flows. Be able to compute loan payments and find the interest rate on a loan. Understand how loans are amortized or paid off. Understand how interest rates are quoted. © 2013 McGraw-Hill Ryerson Limited

3. 6-2 Chapter Outline Future and Present Values of Multiple Cash Flows Valuing Level Cash Flows: Annuities and Perpetuities Comparing Rates: The Effect of Compounding Loan Types and Loan Amortization Summary and Conclusions © 2013 McGraw-Hill Ryerson Limited

4. 6-3 Multiple Cash Flows 6.1 FV Example You currently have $7,000 in a bank account earning 8% interest. You think you will be able to deposit 存 an additional $4,000 at the end of each of the next three years. How much will you have in three years? LO1 © 2013 McGraw-Hill Ryerson Limited

5. 6-4 Multiple Cash Flows FV Example (cont.) Find the value at year 3 of each cash flow and add them together. Formula Approach Today (year 0): FV = $7,000(1.08) 3 = $8,817.98 Year 1: FV = $4,000(1.08) 2 = $4,665.60 Year 2: FV = $4,000(1.08) = $4,320 Year 3: value = $4,000 Total value in 3 years = $8,817.98 + $4,665.60 + $4,320 + $4,000 = $21,803.58 LO1 © 2013 McGraw-Hill Ryerson Limited

6. 6-5 Multiple Cash Flows FV Example (cont.) Calculator Approach with P/Y = C/Y = 1* Year 0 CF: N = 3; I/Y = 8; PV = -7,000; CPT FV = 8,817.98 Year 1 CF: N = 2; I/Y = 8; PV = - 4,000; CPT FV = 4,665.60 Year 2 CF: N = 1; I/Y = 8; PV = - 4,000 PV; CPT FV = 4,320 Year 3 CF: value = 4,000 Total value in 3 years = $8,817.98 + $4,665.60 + $4,320 + $4,000 = $21,803.58 *Factory default is P/Y = C/Y = 12. LO1 © 2013 McGraw-Hill Ryerson Limited

7. 6-6 Multiple Cash Flows FV Example (cont.) Efficient Calculator Approach N = 3, I/Y = 8, PV = - 7,000, PMT = - 4,000 CPT FV = 21,803.58 Here we are taking advantage of an embedded ordinary annuity Later we will discuss annuities in detail. LO1 © 2013 McGraw-Hill Ryerson Limited

8. 6-7 Multiple Cash Flows PV Example You are offered an investment that will pay you $200 in one year, $400 the next year, $600 the year after, and $800 at the end of the following year. You can earn 12% on similar investments. How much is this investment worth today? LO1 © 2013 McGraw-Hill Ryerson Limited

9. 6-8 Multiple Cash Flows – Timeline PV Example 01234 200400600800 178.57 318.88 427.07 508.41 1,432.93 LO1 © 2013 McGraw-Hill Ryerson Limited

10. 6-9 Multiple Cash Flows PV Example continued Find the PV of each cash flow and add them Formula Approach Year 1 CF: $200 / (1.12) 1 = $178.57 Year 2 CF: $400 / (1.12) 2 = $318.88 Year 3 CF: $600 / (1.12) 3 = $427.07 Year 4 CF: $800 / (1.12) 4 = $508.41 Total PV = $178.57 + $318.88 + $427.07 + $508.41 = $1,432.93 LO1 © 2013 McGraw-Hill Ryerson Limited

11. 6-10 Multiple Cash Flows PV Example continued Calculator Approach Year 1 CF: N = 1I/Y = 12 FV = 200 CPT PV = - 178.57 Year 2 CF:N = 2I/Y = 12 FV = 400 CPT PV = - 318.88 Year 3 CF: N = 3I/Y = 12 FV = 600 CPT PV = - 427.07 Year 4 CF: N = 4I/Y = 12 FV = 800 CPT PV = - 508.41 Total PV = $178.57 + $318.88 + $427.07 + $508.41 = $1,432.93 LO1 © 2013 McGraw-Hill Ryerson Limited

12. 6-11 Multiple Uneven Cash Flows – Using the Calculator Another way to use the financial calculator for uneven cash flows is to use the cash flow keys Texas Instruments BA-II Plus Clear the cash flow registers by pressing the CF menu key and then touching the 2 nd and CLR Work key. Enter the cash flows beginning with year 0. You have to press the Enter key for each cash flow. Use the down arrow key to move to the next cash flow. Between cash flows after the year 1 entry, you will encounter the variable “F”. It is the number of times a given cash flow occurs in consecutive years. Use the NPV menu key to compute the Net Present Value by entering the interest rate for I, pressing the down arrow, and then the CPT key. LO1 © 2013 McGraw-Hill Ryerson Limited

13. 6-12 Decisions, Decisions Your broker calls you and tells you that he has this great investment opportunity. If you invest $100 today, you will receive $40 in one year and $75 in two years. If you require a 15% return on investments of this risk, should you take the investment? LO1 © 2013 McGraw-Hill Ryerson Limited

14. 6-13 Decisions Decisions (cont.) Go to the CF menu by touching the CF key and then touching the 2 nd and CLR work keys Now enter the data for the cash flows CF 0 = 0 C01 = 40 F01 = 1 C02 = 75 F02 = 1 Go to the NPV menu by touching the NPV key Enter the data for the interest rate I = 15 CPT NPV = 91.49 NO!!! – the broker is charging more than you would be willing to pay. (If you had set CF 0 = - 100, the NPV would have been – 8.51.) LO1 © 2013 McGraw-Hill Ryerson Limited

15. 6-14 Saving For Retirement You are offered the opportunity to put some money away for retirement. You will receive five annual payments of $25,000 each beginning in 40 years. How much would you be willing to invest today if you desire an interest rate of 12%? LO1 © 2013 McGraw-Hill Ryerson Limited

16. 6-15 Saving For Retirement Timeline 0 1 2 … 39 40 41 42 43 44 0 0 0 … 0 25K 25K 25K 25K 25K Notice that the year 0 cash flow = 0 (CF 0 = 0) The cash flows years 1 – 39 are 0 (C01 = 0; F01 = 39) The cash flows years 40 – 44 are 25,000 (C02 = 25,000; F02 = 5) LO1 © 2013 McGraw-Hill Ryerson Limited

17. 6-16 Saving For Retirement (cont.) Go to the CF menu by touching the CF key and then touching the 2 nd and CLR WORK keys. Now enter the data for the cash flows. CF 0 = 0 C01 = 0 F01 = 39 C02 = 25000 F02 = 5 Go to the NPV menu by touching the NPV key. Enter the data for the interest rate and then touch the down arrow and CPT keys. I = 12 CPT NPV = 1,084.71 LO1 © 2013 McGraw-Hill Ryerson Limited

18. 6-17 Quick Quiz – Part I Suppose you are looking at the following possible cash flows: Year 1 CF = $100; Years 2 and 3 CFs = $200; Years 4 and 5 CFs = $300 The required discount rate is 7%. What is the value of the cash flows at year 5? What is the value of the cash flows today? What is the value of the cash flows at year 3? LO1 © 2013 McGraw-Hill Ryerson Limited

19. 6-18 Annuities and Perpetuities 6.2 Annuity – finite series of equal payments that occur at regular intervals If the first payment occurs at the END of the period, it is called an Ordinary Annuity. If the first payment occurs at the BEGINNING of the period, it is called an Annuity Due. Perpetuity – infinite series of equal payments LO1 © 2013 McGraw-Hill Ryerson Limited

20. 6-19 Annuities and Perpetuities – Basic Formulas Perpetuity: PV = C / r Annuities: LO1 © 2013 McGraw-Hill Ryerson Limited

21. 6-20 Annuities and the Calculator You can use the PMT key on the calculator for the equal payment. The sign convention still holds. Ordinary annuity versus annuity due You can switch your calculator between the two types by using the 2 nd, BGN, 2 nd, and Set keys on the TI BA-II Plus. If you see BGN in the display of your calculator, you have it set for an annuity due. Most problems are ordinary annuities. LO1 © 2013 McGraw-Hill Ryerson Limited

22. 6-21 Annuity: Finding the PV After carefully going over your budget, you have determined that you can afford to pay $632 per month towards a new sports car. Your bank will lend to you at 1% per month for 48 months. How much can you borrow? LO1 © 2013 McGraw-Hill Ryerson Limited

23. 6-22 Annuity: Finding the PV (cont.) You borrow money TODAY so you need to compute the present value. Formula Approach Calculator Approach N = 48; I/Y = 1; PMT = - 632; CPT PV = 23,999.54 LO1 © 2013 McGraw-Hill Ryerson Limited

24. 6-23 Quick Quiz – Part II You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive $5,000 per month in retirement. If you can earn 0.75% per month and you expect to need the income for 25 years, how much do you need to have in your account at retirement? LO1 © 2013 McGraw-Hill Ryerson Limited

25. 6-24 Finding the Annuity Payment Suppose you want to borrow $20,000 for a new car. You can borrow at 8% per year, compounded monthly (8%/12 = 0.66667% per month). If you take a 4 year loan, what is your monthly payment? LO2 © 2013 McGraw-Hill Ryerson Limited

26. 6-25 Finding the Annuity Payment (cont.) Formula Approach $20,000 = C[1 – 1 / 1.0066667 48 ] /.0066667 C = 488.26 Calculator Approach N = 4(12) = 48; PV = 20,000; I/Y =.66667 CPT PMT = - 488.26 LO2 © 2013 McGraw-Hill Ryerson Limited

27. 6-26 Finding the Number of Payments PV Annuty Example You ran a little short on your February vacation, so you put $1,000 on your credit card. You can only afford to make the minimum payment of $20 per month. The interest rate on the credit card is 1.5% per month. How long will you need to pay off the $1,000? LO3 © 2013 McGraw-Hill Ryerson Limited

28. Finding the Number of Payments General Formula for PV Annuity 6-27 PV

29. 6-28 Finding the Number of Payments PV Annuity Example continued Formula Approach t = 93.111 months = 7.76 years Calculator Approach The sign convention matters!!! I/Y = 1.5 PV = 1,000 PMT = - 20 CPT N = 93.111 MONTHS = 7.76 years And this is only if you don’t charge anything more on the card! LO3 © 2013 McGraw-Hill Ryerson Limited

30. 6-29 Finding the Number of Payments – FV Annuity Example Suppose you wish to save $30,000 to buy a car. You are going to make annual deposits of $6,960.35 in an account that pays 5% interest. How long before you buy the car? LO3 © 2013 McGraw-Hill Ryerson Limited

31. Finding the Number of Payments General Formula for FV Annuity 6-30 FV

32. 6-31 Finding the Number of Payments – FV Annuity Example continued Formula Approach t = ln(1.215506404) / ln(1.05) = 4 years Calculator Approach Sign convention matters!!! I/Y = 5 FV = 30,000 PMT = - 6,960.35 CPT N = 4 years LO3 © 2013 McGraw-Hill Ryerson Limited

33. 6-32 Finding the Rate Suppose you borrow $10,000 from your parents to buy a car. You agree to pay $207.58 per month for 60 months. What is the monthly interest rate? LO2 © 2013 McGraw-Hill Ryerson Limited

34. 6-33 Finding the Rate On the Financial Calculator Calculator Approach Sign convention matters!!! N = 60 PV = 10,000 PMT = - 207.58 CPT I/Y =.75% LO2 © 2013 McGraw-Hill Ryerson Limited

35. 6-34 Annuity – Finding the Rate Without a Financial Calculator Trial and Error Process Choose an interest rate and compute the PV of the payments based on this rate. Compare the computed PV with the actual loan amount. If the computed PV > loan amount, then the interest rate is too LOW. If the computed PV < loan amount, then the interest rate is too HIGH. Adjust the rate and repeat the process until the computed PV and the loan amount are equal. LO2 © 2013 McGraw-Hill Ryerson Limited

36. 6-35 Quick Quiz – Part III You want to receive $5,000 per month for the next 5 years. How much would you need to deposit today if you can earn 0.75% per month? What monthly rate would you need to earn if you only have $200,000 to deposit? Suppose you have $200,000 to deposit and can earn 0.75% per month. How many months could you receive the $5,000 payment? How much could you receive every month for 5 years? LO2 & LO3 © 2013 McGraw-Hill Ryerson Limited

37. 6-36 Future Values for Annuities Example You begin saving for your retirement by depositing $2,000 per year in an RRSP. The interest rate is 7.5% per year. How much will you have in 40 years? LO1 © 2013 McGraw-Hill Ryerson Limited

38. 6-37 Future Values for Annuities Example continued Formula Approach FV = $2,000(1.075 40 – 1)/.075 = $454,513.04 Calculator Approach Remember the sign convention!!! N = 40 I/Y = 7.5 PMT = - 2,000 CPT FV = 454,513.04 LO1 © 2013 McGraw-Hill Ryerson Limited

39. 6-38 Annuity Due Example You are saving for a new house. You save $10,000 per year. You earn 8% compounded annually. The first payment is made today. How much will you have at the end of 3 years? LO1 © 2013 McGraw-Hill Ryerson Limited

40. 6-39 Annuity Due Timeline Example 0 1 2 3 $10,000 $10,000 $10,000 $32,464 $35,061.12 LO1 © 2013 McGraw-Hill Ryerson Limited

41. 6-40 Annuity Due Example continued Formula Approach FV = $10,000[(1.08 3 – 1) /.08](1.08) ???? FV = $32,464 x 1.08 = $35,061.12 Calculator Approach 2 nd BGN 2 nd Set (BGN appears in the display) N = 3 PMT = - 10,000 I/Y = 8 CPT FV = 35,061.12 2 nd BGN 2 nd Set (return to an ordinary annuity) LO1 © 2013 McGraw-Hill Ryerson Limited

42. 6-41 Perpetuity Example The Home Bank of Canada wants to sell preferred stock at $100 per share. A very similar issue of preferred stock already outstanding has a price of $40. It pays a dividend of $1 every quarter. What dividend would Home Bank have to offer if its preferred stock is going to sell? LO1 © 2013 McGraw-Hill Ryerson Limited

43. 6-42 Perpetuity Example continued Perpetuity formula: PV = C / r First, find the required return for the comparable issue: 40 = 1 / r r =.025 or 2.5% per quarter Then, using the required return found above, find the dividend for new preferred issue: 100 = C /.025 C = 2.50 per quarter LO1 © 2013 McGraw-Hill Ryerson Limited

44. 6-43 Growing Perpetuity 永久 The perpetuities discussed so far have constant payments. Growing perpetuities have cash flows that grow at a constant rate and continue forever. Growing perpetuity formula: LO1 © 2013 McGraw-Hill Ryerson Limited

45. 6-44 Growing Perpetuity Example Hoffstein Corporation is expected to pay a dividend of $3 per share next year. Investors anticipate that the annual dividend will rise by 6% per year forever. The required rate of return is 11%. What is the price of the stock today? LO1 © 2013 McGraw-Hill Ryerson Limited

46. 6-45 Growing Annuity 年金 Growing annuities have a finite number of growing cash flows. Growing annuity formula: LO1 © 2013 McGraw-Hill Ryerson Limited

47. 6-46 Growing Annuity Example Gilles Lebouder has just been offered a job at $50,000 a year. He anticipates his salary will increase by 5% a year until his retirement in 40 years. The interest rate is 8%. What is the present value of his lifetime salary? LO1 © 2013 McGraw-Hill Ryerson Limited

48. 6-47 Quick Quiz – Part IV You want to have $1 million to use for retirement in 35 years. If you can earn 1% per month, how much do you need to deposit on a monthly basis if the first payment is made in one month? What if the first payment is made today? You are considering preferred stock that pays a quarterly dividend of $1.50. If your desired return is 3% per quarter, how much would you be willing to pay? LO1 © 2013 McGraw-Hill Ryerson Limited

49. 6-48 Work the Web Example Another online financial calculator can be found at MoneyChimp Click on the web surfer and work the following example Choose calculator and then annuity You just inherited $5 million. If you can earn 6% on your money, how much can you withdraw each year for the next 40 years? Payment = $332,307.68 LO1 © 2013 McGraw-Hill Ryerson Limited

50. 6-49 Table 6.2 – Summary of Annuity and Perpetuity Calculations LO1 © 2013 McGraw-Hill Ryerson Limited

51. 6-50 Effective Annual Rate (EAR) 6.3 EAR is the actual rate paid (or received) after accounting for compounding that occurs during the year. If you want to compare two alternative investments with different compounding periods, you need to compute the EAR for each investment and then compare the EARs. LO4 © 2013 McGraw-Hill Ryerson Limited

52. 6-51 Annual Percentage Rate (APR) This is the annual rate that is quoted by law in North America. APR = effective compound period rate times the number of compound periods per year. Consequently, to get the period rate we rearrange the APR equation: Effective compound period rate = APR / number of compound periods per year NEVER divide the EAR by the number of compound periods per year. It will NOT give you the effective compound period rate. LO4 © 2013 McGraw-Hill Ryerson Limited

53. 6-52 Computing APRs What is the APR if the monthly rate is.5%?.5%(12) = 6% What is the APR if the semi-annual rate is.5%?.5%(2) = 1% What is the monthly rate if the APR is 12% with monthly compounding? 12% / 12 = 1% Can you divide the above APR by 2 to get the semiannual rate? NO!!! You need an APR based on semi-annual compounding to find the semi-annual rate by dividing by 2. LO4 © 2013 McGraw-Hill Ryerson Limited

54. 6-53 Things to Remember You ALWAYS need to make sure that the interest rate and the time period match. If you are looking at annual periods, you need an effective annual rate. If you are looking at monthly periods, you need an effective monthly rate. If you have an APR based on monthly compounding, you have to use monthly periods for lump sums, or adjust the interest rate appropriately if you have payments other than monthly LO4 © 2013 McGraw-Hill Ryerson Limited

55. 6-54 Computing EARs Example 1 Suppose you can earn 1% per month on $1 invested today. What is the APR? 1%(12) = 12% How much are you effectively earning? FV = 1(1.01) 12 = 1.1268 EAR = (1.1268 – 1) / 1 =.1268 = 12.68% LO4 © 2013 McGraw-Hill Ryerson Limited

56. 6-55 Computing EARs Example 2 Suppose if you put the $1 in another account, you earn 3% per quarter. What is the APR? 3%(4) = 12% How much are you effectively earning? FV = 1(1.03) 4 = 1.1255 Rate = (1.1255 – 1) / 1 =.1255 = 12.55% LO4 © 2013 McGraw-Hill Ryerson Limited

57. 6-56 EAR - Formula Remember that the APR is the quoted rate m is the number of times the interest is compounded in a year LO4 © 2013 McGraw-Hill Ryerson Limited

58. 6-57 Decisions, Decisions II You are looking at two savings accounts. One pays 5.25%, with daily compounding. The other pays 5.3% with semi-annual compounding. Which account should you use? First account: EAR = (1 +.0525/365) 365 – 1 = 5.39% Second account: EAR = (1 +.053/2) 2 – 1 = 5.37% You should choose the first account (the account that compounds daily), because you are earning a higher effective interest rate. LO4 © 2013 McGraw-Hill Ryerson Limited

59. 6-58 Decisions, Decisions II Continued Let’s verify the choice. Suppose you invest $100 in each account. How much will you have in each account in one year? First Account: Daily rate =.0525 / 365 =.00014383562 FV = $100(1.00014383562) 365 = $105.39, OR, N = 365 I/Y = 5.25 / 365 =.014383562 PV = - 100 CPT FV = 105.39 Second Account: Semi-annual rate =.053 / 2 =.0265 FV = $100(1.0265) 2 = $105.37, OR, N = 2 I/Y = 5.3 / 2 = 2.65 PV = - 100 CPT FV = 105.37 You have more money in the first account. LO4 © 2013 McGraw-Hill Ryerson Limited

60. 6-59 Computing APRs from EARs If you have an effective rate, how can you compute the APR? Rearrange the EAR equation and you get: Note that APR / m is the effective compound period rate. LO4 © 2013 McGraw-Hill Ryerson Limited APR/m =

61. 6-60 APR from EAR Example Suppose you want to earn an effective rate of 12% and you are looking at an account that compounds on a monthly basis. What APR must they pay? LO4 © 2013 McGraw-Hill Ryerson Limited

62. 6-61 Computing Payments with APRs Example Suppose you want to buy a new computer system and the store is willing to allow you to make monthly payments. The entire computer system costs $3,500. The loan period is for 2 years. The interest rate is 16.9% with monthly compounding. What is your monthly payment? LO3 © 2013 McGraw-Hill Ryerson Limited

63. 6-62 Computing Payments with APRs Example continued Formula Approach Monthly rate =.169 / 12 =.01408333333 Number of months = 2(12) = 24 $3,500 = C[1 – 1 / 1.01408333333) 24 ] /.01408333333 C = $172.88 Calculator Approach N = 2(12) = 24I/Y = 16.9 / 12 = 1.408333333 PV = 3,500CPT PMT = - 172.88 LO3 © 2013 McGraw-Hill Ryerson Limited

64. 6-63 Future Values with Monthly Compounding Suppose you deposit $50 a month into an account that has an APR of 9%, based on monthly compounding. How much will you have in the account in 35 years? LO3 © 2013 McGraw-Hill Ryerson Limited

65. 6-64 Future Values with Monthly Compounding Continued Formula Approach Monthly rate =.09 / 12 =.0075 Number of months = 35(12) = 420 FV = $50[1.0075 420 – 1] /.0075 = $147,089.22 Calculator Approach N = 35(12) = 420 I/Y = 9 / 12 =.75 PMT = - 50 CPT FV = 147,089.22 LO3 © 2013 McGraw-Hill Ryerson Limited

66. 6-65 Present Value with Daily Compounding You need $15,000 in 3 years for a new car. You can deposit money into an account that pays an APR of 5.5% based on daily compounding. How much would you need to deposit? LO3 © 2013 McGraw-Hill Ryerson Limited

67. 6-66 Present Value with Daily Compounding continued Formula Approach Daily rate =.055 / 365 =.00015068493 Number of days = 3(365) = 1095 FV = $15,000 / (1.00015068493) 1095 = $12,718.56 Calculator Approach N = 3(365) = 1095 I/Y = 5.5 / 365 =.015068493 FV = 15,000 CPT PV = - 12,718.56 LO3 © 2013 McGraw-Hill Ryerson Limited

68. 6-67 Mortgages 抵押贷款 In Canada, financial institutions are required by law to quote mortgage rates with semi-annual compounding Since most people pay their mortgage either monthly (12 payments per year), semi-monthly (24 payments), bi-weekly (26 payments), or weekly (52 payments), you need to remember to convert the interest rate before calculating the mortgage payment! LO4 © 2013 McGraw-Hill Ryerson Limited

69. 6-68 Mortgage Example Theodore (Theo) D. Kat is applying to his bank for a mortgage of $200,000. The bank is quoting 6% based on semi- annual compounding. Theo would like to have a 25-year amortization period Theo wants to make payments monthly. What will Theodore’s payments be? LO3 © 2013 McGraw-Hill Ryerson Limited

70. 6-69 Mortgage Example continued First, calculate the EAR Second, calculate the effective monthly rate Then, calculate the monthly payment OR, N = 300, I/Y = 0.4939, PV = 200,000, CPT PMT = - 1,279.61 LO3 © 2013 McGraw-Hill Ryerson Limited

71. 6-70 Continuous Compounding Sometimes investments or loans are calculated based on continuous compounding EAR = e APR – 1 The e is a special function on the calculator normally denoted by e x Example: What is the effective annual rate of 7% compounded continuously? EAR = e.07 – 1 =.0725 or 7.25% LO4 © 2013 McGraw-Hill Ryerson Limited

72. 6-71 Quick Quiz – Part V What is the definition of an APR? What is the effective annual rate or EAR? Which rate should you use to compare alternative investments or loans? Which rate do you need to use in the time value of money calculations? LO4 © 2013 McGraw-Hill Ryerson Limited

73. 6-72 Pure Discount Loans 6.4 Treasury bills are excellent examples of Pure Discount Loans. The face value of a T-bill is paid at some future date, without any periodic interest payments. A Bullet Loan is where a borrower repays the amount borrowed plus compound interest in a single lump sum at maturity. A pure discount loan and a bullet loan are really the same type of loan. LO3 © 2013 McGraw-Hill Ryerson Limited

74. 6-73 Pure Discount Loan Example A T-bill promises to pay $10,000 in 12 months. The market interest rate is 4 percent. How much will the bill sell for in the market? PV = $10,000 / 1.04 = $9,615.38, OR N = 1 FV = 10,000 I/Y = 4 CPT PV = - 9,615.38 LO3 © 2013 McGraw-Hill Ryerson Limited

75. 6-74 Bullet Loan Example Sam borrows $20,000. He must repay principal plus compound interest in 12 months. The APR is 6 percent with monthly compounding. How much must Sam repay in 12 months? FV = $20,000 x 1.005 12 = $21,233.56, OR N = 12 PV = 20,000 I/Y =.5 CPT FV = - 21,233.56 LO3 © 2013 McGraw-Hill Ryerson Limited

76. 6-75 Interest Only Loan The borrower pays interest each period and repays the entire principal at some point in the future. This cash flow stream is similar to the cash flows on corporate bonds and we will talk about them in greater detail later. An Interest Only Loan is a type of Balloon Loan, where the final payment is larger than the other payments. LO3 © 2013 McGraw-Hill Ryerson Limited

77. 6-76 Amortized Loan with Fixed Principal Payment - Example Consider a $50,000, 10-year loan at 8% interest. The loan agreement requires the firm to pay $5,000 in principal each year plus interest for that year. Click on the Excel icon to see the amortization table LO3 © 2013 McGraw-Hill Ryerson Limited

78. 6-77 Amortized Loan with Fixed Total Payment - Example Each payment covers the interest expense plus reduces principal. Consider a 4-year loan with annual payments. The interest rate is 8% and the principal amount is $5,000. What is the annual payment? N = 4 I/Y = 8 PV = 5,000 CPT PMT = - 1,509.60 Click on the Excel icon to see the amortization table LO3 © 2013 McGraw-Hill Ryerson Limited

79. 6-78 Work the Web Example There are web sites available that can easily provide you with information on home buying and mortgages Click on the web surfer to check out the Canadian Mortgage and Housing Corporation site LO3 © 2013 McGraw-Hill Ryerson Limited

80. 6-79 Quick Quiz – Part VI What is a pure discount loan? What is a good example of a pure discount loan? What is an interest only loan? What is a good example of an interest only loan? What is an amortized loan? What is a good example of an amortized loan? LO3 © 2013 McGraw-Hill Ryerson Limited

81. 6-80 Summary 6.5 You should know how to: Calculate PV and FV of multiple cash flows Calculate payments Calculate PV and FV of regular annuities, annuities due, growing annuities, perpetuities, and growing perpetuities Calculate EARs and effective rates Calculate mortgage payments Price pure discount loans and amortized loans © 2013 McGraw-Hill Ryerson Limited

82. © 2014 Dr. William F. Rentz & Associates Additions, deletions, and corrections to these transparencies were performed by Dr. William F. Rentz solely for use at the University of Ottawa. The above copyright notice applies to all changes made herein. 6-81