1. Last Study Topics Present Value (PV) – A dollar today is worth more than a dollar tomorrow Net Present Value (NPV) – NPV = PV – INV NPV Rule – Accept the project that makes a net contribution to value. Rate Of Return Rule – Rate of Return is > Cost of Capital 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

2. Topics covered Opportunity Cost of Capital Investment vs. Consumption Managers and the Interests of Shareholders 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

3. Opportunity Cost of Capital The opportunity cost of capital is such an important concept. Theory of valuation endorses that rate of return of the project must always be greater to the rate of return of an alternative opportunity. This alternative rate becomes an opportunity cost of capital. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

4. Opportunity Cost of Capital Example You may invest $100,000 today. Depending on the state of the economy, you may get one of three possible cash payoffs: 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

5. Continue But what’s the right discount rate? You search for a common stock with the same risk as the investment. Stock X turns out to be a perfect match i.e., X’s price next year, given a normal economy, is forecasted at $110. The stock price will be higher in a boom and lower in a slump, but to the same degrees as your investment ($140 in a boom and $80 in a slump). 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

6. Continue Example - continued The stock is trading for $95.65. Depending on the state of the economy, the value of the stock at the end of the year is one of three possibilities: 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

7. Continue Example - continued The stocks expected payoff leads to an expected return. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

8. Continue The amount it would cost investors in the stock market to buy an expected cash flow is $110,000. (They could do so by buying 1,000 shares of stock X @ $110 each) It is, therefore, also the sum that investors would be prepared to pay you for your project. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

9. Opportunity Cost of Capital Example - continued Discounting the expected payoff at the expected return leads to the PV of the project. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

10. Continue To calculate net present value, deduct the initial investment: NPV = 95,650 - 100,000 = -$4,350 The project is worth $4,350 less than it costs. It is not worth undertaking. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

11. Alternative Compare the expected project return with the cost of capital: The 10 % return on project < 15 % return on stock of equal risk. The project is not worthwhile. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

12. Discount rate equals the opportunity cost of capital The opportunity cost of capital is the return earned by investing in the best alternative investment. This return will not be realized if the investment under consideration is undertaken. Thus, the two investments must earn at least the same return. This return rate is the discount rate used in the net present value calculation. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

13. A source of Confusion Bank A will lend you the $100,000 that you need for the project at 8 percent. Does that mean that the cost of capital for the project is 8 %? Or does not? Does Not - First, the interest rate on the loan has nothing to do with the risk of the project. Second, whether you take the loan or not, you still face the choice between the projects. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

14. Case: Norman Norman Gerrymander has just received a $2 million bequest. How should he invest it? There are four immediate alternatives. – Which of these investments have positive NPVs? – Which would you advise Norman to take? Lets have a look each of them! 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

15. Alternative A A - Investment in one-year U.S. government securities yielding 5 percent. Step 1: calculate the payoff after 1 year. = 2.0M X 5% = 2.1 M. Step 2: Discounting the expected payoff at the expected return leads to the PV of the project. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

16. Continue Step 3: To calculate net present value, deduct the initial investment: NPV = $2.0M - $2.0M = $0 The ‘A’ investment has not contributed to the net value. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

17. Alternative B B - A loan to Norman’s nephew Gerald, who has for years aspired to open a big Cajun restaurant in Duluth. Gerald had arranged a one-year bank loan for $900,000, at 10 percent, but asks for a loan from Norman at 7 percent. Step 1: calculate the payoff after 1 year. = 0.9 M X 7% = 0.96 M. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

18. Continue Step 2: Discounting the expected payoff at the expected return leads to the PV of the project. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

19. Continue Step 3: To calculate net present value, deduct the initial investment: NPV = $0.88M - $.9M = -$0.02M The project is worth $0.02M less than it costs. It is not worth undertaking. The ‘B’ investment has brought decline to the net value. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

20. Alternative C C - Investment in the stock market. The expected rate of return is 12 percent. Step 1: calculate the payoff after 1 year. = 2.0 M X 12% = 2.24 M. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

21. Continue Step 2: Discounting the expected payoff at the expected return leads to the PV of the project. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

22. Continue Step 3: To calculate net present value, deduct the initial investment: NPV = $2.0M - $2.0M = $0 The ‘C’ investment has not contributed to the net value nor a decline. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

23. Alternative D B - Investment in local real estate, which Norman judges is about as risky as the stock market. The opportunity at hand would cost $1 million and is forecasted to be worth $1.1 million after one year. Step 1: calculate the payoff after 1 year. = $ 1.1 M. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

24. Continue Step 2: Discounting the expected payoff at the expected return leads to the PV of the project. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

25. Continue Step 3: To calculate net present value, deduct the initial investment: NPV = $0.98M - $1.0M = -$0.02M The project is worth $0.02M less than it costs. It is not worth undertaking. The ‘D’ investment has brought decline to the net value. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

26. Continue Results from four Alternatives; – The ‘A’ investment has not contributed to the net value nor a decline. – The ‘B’ investment has brought decline to the net value. – The ‘C’ investment has not contributed to the net value nor a decline. – The ‘D’ investment has brought decline to the net value. Decision; – Norman should invest in either the risk-free government securities or the risky stock market, depending on his tolerance for risk. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

27. Investment vs. Consumption Some people prefer to consume now. Some prefer to invest now and consume later. Borrowing and lending allows us to reconcile these opposing desires which may exist within the firm’s shareholders. Could a positive-NPV project for Ms. X be a negative-NPV proposition for Mr. Y? Could they find it impossible to agree on the objective of maximizing the market value of the firm? 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

28. Continue This could be answer; Well functioned capital markets allows investors with different time patterns of income and desired consumption to agree on whether investment projects should be undertaken. Lets consider an example ! 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

29. Ant vs Grasshopper A is an ant, who wishes to save for the future; G is a grasshopper, who would prefer to spend all his wealth. Suppose both of them can earn a return of about 14 percent on every $100 investment. The interest rate is 7 percent. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

30. Investment vs. Consumption The grasshopper (G) wants to consume now. The ant (A) wants to wait. But each is happy to invest. A prefers to invest 14%, moving up the red arrow, rather than at the 7% interest rate. G invests and then borrows at 7%, thereby transforming $100 into $106.54 of immediate consumption. Because of the investment, G has $114 next year to pay off the loan. The investment’s NPV is $106.54-100 = +6.54 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

31. Investment vs. Consumption The grasshopper (G) wants to consume now. The ant (A) wants to wait. But each is happy to invest. A prefers to invest 14%, moving up the red arrow, rather than at the 7% interest rate. G invests and then borrows at 7%, thereby transforming $100 into $106.54 of immediate consumption. Because of the investment, G has $114 next year to pay off the loan. The investment’s NPV is $106.54- 100 = +6.54 100 106.54 Dollars Now Dollars Later 114 107 A invests $100 now and consumes $114 next year G invests $100 now, borrows $106.54 and consumes now. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

32. Calculation Return of A: INV = C 0 ; C 1 = Payoff; – r = C 1 -C 0 / C 0 * 100 = = 14% NPV for G: INV = C 0 ; C 1 = Payoff; INT = r; – PV = C 1/ (1+r) t = = $106.54 NPV = PV – C 0 = 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

33. Explanation In our example the ant and the grasshopper placed an identical value on same project and were happy to share in its construction. They agreed because they faced identical borrowing and lending opportunities. Whenever firms discount cash flows at capital market rates, they are implicitly assuming that their shareholders have free and equal access to competitive capital markets. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

34. Continue Despite their different tastes, both A and G are better off by investing in the project and then using the capital markets to achieve the desired balance between consumption today and consumption at the end of the year. If A and G were shareholders in the same enterprise, there would be no simple way for the manager to reconcile their different objectives. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

35. Summary Opportunity Cost of Capital – Rate of an Alternative investment opportunity having a similar risk. Investment vs. Consumption – Manager finds it difficult to reconcile the different objectives of the shareholders. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

36. Calculation of NPV and ROR The opportunity cost of capital is 20 percent for all four investments. Initial CashCash Flow Investment Flow, C0 in Year 1, C1 1 10,000 18,000 2 5,000 9,000 3 5,000 5,700 4 2,000 4,000 a. Which investment is most valuable? b. Suppose each investment would require use of the same parcel of land. Therefore you can take only one. Which one? 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

37. Continue 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

38. Continue Answer to question ‘a’; – Investment 1, since this investment with respect to others has generate highest NPV with Max rate of return. Answer to question ‘b’; – Investment 1, since this investment with respect to others has highest contributed net value. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

39. Decision Rules Here then we have two equivalent decision rules for capital investment; – Net present value rule; Accept investments that have positive net present values. – Rate-of-return rule; Accept investments that offer rates of return in excess of their opportunity costs of capital. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

40. Fundamental Result Our justification of the present value rule was restricted to two periods and to a certain cash flow. However, the rule also makes sense for uncertain cash flows that extend far into the future. The argument goes like this: 1- A financial manager should act in the interests of the firm’s owners, its stockholders. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

41. Continue 2- Stockholders do not need the financial manager’s help to achieve the best time pattern of consumption. 3- How then can the financial manager help the firm’s stockholders? – There is only one way: by increasing the market value of each stockholder’s stake in the firm. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

42. Continue Despite the fact that shareholders have different preferences, they are unanimous in the amount that they want to invest in real assets. This means that they can cooperate in the same enterprise and can safely delegate operation of that enterprise to professional managers. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

43. Continue These managers do not need to know anything about the tastes of their shareholders and should not consult their own tastes. Their task is to maximize net present value. If they succeed, they can rest assured that they have acted in the best interest of their shareholders. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

44. Managers and Shareholder Interests Do managers really looking after the interests of shareholders? This takes us back to the principal–agent problem. – Several institutional arrangements that help to ensure that the shareholders’ pockets are close to the managers’ heart. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

45. Continue Utilizing their Voting power; – If shareholders believe that the corporation is underperforming and that the board of directors is not sufficiently aggressive in holding the managers to task, they can try to replace the board in the next election. E.g; chief executives of Eastman Kodak, General Motors, Xerox, Lucent, Ford Motor, etc were all forced to step aside. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

46. Continue As a result the stock price tumbles. – This damages top management’s reputation and compensation. Part of the top managers’ paychecks comes from bonuses tied to the company’s earnings or from stock options, which pay off if the stock price rises but are worthless if the price falls below a stated threshold. – This should motivate managers to increase earnings and the stock price. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

47. Continue If managers and directors do not maximize value, there is always the threat of a hostile takeover. The further a company’s stock price falls, due to lax management or wrong-headed policies, the easier it is for another company or group of investors to buy up a majority of the shares. – The old management team is then likely to find themselves out on the street and their place is taken by a fresh team. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

48. Continue Should managers look after the interests of shareholders? For this question we need to understand that In most instances there is little conflict between doing well (maximizing value) and doing good. – Profitable firms are those with satisfied customers and loyal employees and vice versa; 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

49. Continue Ethical issues do arise in business as in other walks of life. – when we say that the objective of the firm is to maximize shareholder wealth, we do not mean that anything goes. In business and finance, as in other day-to-day affairs, there are unwritten, implicit rules of behavior. To work efficiently together, we need to trust each other. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

50. Summary Opportunity Cost of Capital – Rate of an Alternative investment opportunity having a similar risk. Investment vs. Consumption – Manager finds it difficult to reconcile the different objectives of the shareholders. Managers and the Interests of Shareholders – Are managers taking care of the interests of the Shareholders or should they? 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

51.  How to Calculate Present Values Principles of Corporate Finance Brealey and Myers Sixth Edition Chapter 3 © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

52. Topics Covered Valuing Long-Lived Assets PV Calculation Short Cuts Compound Interest Interest Rates and Inflation Example: Present Values and Bonds 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

53. Present Values Discount Factor = DF = PV of $1  Discount Factors can be used to compute the present value of any cash flow. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

54. Present Values Discount Factor = DF = PV of $1  Discount Factors can be used to compute the present value of any cash flow. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

55. Present Values  Discount Factors can be used to compute the present value of any cash flow. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

56. Present Values  Replacing “1” with “t” allows the formula to be used for cash flows that exist at any point in time. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

57. Present Values Example Suppose you will receive a certain cash inflow of $100 next year (C 1 = $100) and the rate of interest on one-year U.S. Treasury notes is 7 percent (r 1 = 0.07). What would be the present value of Cash inflow ? 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

58. Present Values Example Suppose you will receive a certain cash inflow of $100 in two year (C 2 = $100) and the rate of interest on two-year U.S. Treasury notes is 7.7 percent (r 1 = 0.077). What would be the present value of year 2 Cash inflow ? 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

59. Present Values Example You just bought a new computer for $3,000. The payment terms are 2 years same as cash. If you can earn 8% on your money, how much money should you set aside today in order to make the payment when due in two years? 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

60. Present Values Example You just bought a new computer for $3,000. The payment terms are 2 years same as cash. If you can earn 8% on your money, how much money should you set aside today in order to make the payment when due in two years? 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

61. Present Values  PVs can be added together to evaluate multiple cash flows. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

62. Present Values  PVs can be added together to evaluate multiple cash flows, and called as discounted cash flow or (DCF) formula; 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

63. Present Values If a dollar tomorrow is worth less than a dollar today, one might suspect that a dollar the day after tomorrow should be worth even less. But, lets assume - given two dollars, one received a year from now and the other two years from now, the value of each is commonly called the Discount Factor. Assume r 1 = 20% and r 2 = 7%. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

64. Present Values Given two dollars, one received a year from now and the other two years from now, the value of each is commonly called the Discount Factor. Assume r 1 = 20% and r 2 = 7%. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

65. Continue If First we lend $1,000 for one year at 20 percent, we have; – FV = PV (1+r t ) t = Go to the bank and borrow the present value of this $1,200 at 7 percent interest, we have; – PV = FV / (1+r t ) t = 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

66. Continue If we going to find out the net present value of our investment we get, – NPV = PV – Investment = “Just imagine in this game of lending and borrowing How much money you can earn without taking risks” 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

67. Continue Of course this story is completely fanciful. – “There is no such thing as a money machine.” In well-functioning capital markets, any potential money machine will be eliminated almost instantaneously by investors who try to take advantage of it. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

68. Present Values Example Assume that the cash flows from the construction and sale of an office building is as follows. Given a 7% required rate of return, create a present value worksheet and show the net present value. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

69. Present Values Example - continued Assume that the cash flows from the construction and sale of an office building is as follows. Given a 7% required rate of return, create a present value worksheet and show the net present value. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

70. NPV Formula Mathematically; PV @ 7% ∑PV = PV of C 1 + PV of C 2 = -$93,500 + $261,900 = $168,400 NPV = ∑ PV - INV = $168,400 - $150,000 = $18,400 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

71. Short Cuts Sometimes there are shortcuts that make it very easy to calculate the present value of an asset that pays off in different periods. These tolls allow us to cut through the calculations quickly. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

72. Short Cuts Perpetuity - Financial concept in which a cash flow is theoretically received forever. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

73. Short Cuts Perpetuity - Financial concept in which a cash flow is theoretically received forever. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

74. Case : Investment A An investment costs $1,548 and pays $138 in perpetuity. If the interest rate is 9 percent, what is the NPV? – PV = C / r = $1533.33 – NPV = PV - INV = $1533.33 - $1548 = -$ 14.67 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

75. Short Cuts Annuity - An asset that pays a fixed sum each year for a specified number of years. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

76. Case: leasing a car Example You agree to lease a car for 4 years at $300 per month. You are not required to pay any money up front or at the end of your agreement. If your opportunity cost of capital is 0.5% per month, what is the cost of the lease? 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

77. Continue Example - continued You agree to lease a car for 4 years at $300 per month. You are not required to pay any money up front or at the end of your agreement. If your opportunity cost of capital is 0.5% per month, what is the cost of the lease? 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

78. Case: Endowment Funds Example - Suppose, for example, that we begins to wonders what it would cost to contribute in a endowment fund with an amount of $100,000 a year for only 20 years ? 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

79. Alternatively We can simply look up the answer in the annuity table given on the next slide. This table gives the present value of a dollar to be received in each of t periods. In our example t = 20 and the interest rate r =.10, and therefore; We look at the twentieth number from the top in the 10 percent column. It is 8.514. Multiply 8.514 by $100,000, and we have our answer, $851,400. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

80. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

81. Compound Interest There is an important distinction between compound interest and simple interest. – When money is invested at compound interest, each interest payment is reinvested to earn more interest in subsequent periods. – In contrast, the opportunity to earn interest on interest is not provided by an investment that pays only simple interest. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

82. Compound Interest 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

83. Compounding Interest Suppose that the bank starts with $10 million of automobile loans outstanding. This investment grows to ; $10 * 1.005 = $10.05 million after month 1, $10 * 1.005 2 = $10.10025 million after month 2, and $10 1.005 12 $10.61678 million after 12 months. Thus the bank is quoting a 6 percent APR but actually earns 6.1678 percent if interest payments are made monthly. In general, an investment of $1 at a rate of r per annum compounded m times a year amounts by the end of the year to [1 + (r/m)] m, and the equivalent annually compounded rate of interest is [1 + (r/m)] m - 1. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

84. Compound Interest i ii iii iv v Periods Interest Value Annually per per APR after compounded year period (i x ii) one year interest rate 1 6% 6% 1.06 6.000% 2 3 6 1.03 2 = 1.0609 6.090 4 1.5 6 1.015 4 = 1.06136 6.136 12.5 6 1.005 12 = 1.06168 6.168 52.1154 6 1.001154 52 = 1.06180 6.180 365.0164 6 1.000164 365 = 1.06183 6.183 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

85. Explanation 1$ at the end of the year can be calculated as; – [1 + (r/m)] m ; Since, we have r = 6%; periods = m = 12, 52; – = ;= – = $1.06168= $1.06180 Annually compounded rate; – [1 + (r/m)] m – 1 – =;= 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

86. Continuous Compounding 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed Eventually one can quote a continuously compounded rate, so that payments were assumed to be spread evenly and continuously throughout the year. In terms of our formula, this is equivalent to letting m approach infinity. As m approaches infinity [1 + (r/m)] m approaches (2.718) r or e r = (2.718) r By the end of t years e rt = (2.718) rt

87. Example 1 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed Suppose you invest $1 at a continuously compounded rate of 11 percent (r=.11) for one year (t =1). The end-year value is e =.11, which can be calculated as; e rt = (2.718).11*1 = $1.116 In other words, investing at 11 percent a year continuously compounded is exactly the same as investing at 11.6 percent a year annually compounded.

88. Example 2 Suppose you invest $1 at a continuously compounded rate of 11 percent (r=.11) for two year (t =2). The end-year value is e =.11, which you can be calculated as; e rt = (2.718).11*2 = $1.246 In other words, investing at 11 percent for 2 years continuously compounded is exactly the same as investing at 24.6 percent a year annually compounded. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

89. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

90. Example 3 Suppose that we start thinking more seriously and decided to found a home for us, which will cost $100,000 a year, starting and spread evenly over 20 years. Annual compounding rate is 10%. What sum should we set aside? Here we going to apply Annuity formula – Step 1: calculate continuously compounded rate – r = 9.53% or ( e.0953 = 1.10) 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

91. Continue Step2: calculate the PV of the annuity; – PV = C [1/r – (1/r*1/e rt )] = = $893,200 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

92. Alternatively we could have cut these calculations short by using PV of annuity Table, given on the next slide. This shows that, if the annually compounded return is 10 percent, then $1 a year spread over 20 years is worth $8.932. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

93. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

94. Inflation Inflation - Rate at which prices as a whole are increasing. Nominal Interest Rate - Rate at which money invested grows. Real Interest Rate - Rate at which the purchasing power of an investment increases. 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

95. Inflation 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

96. Inflation approximation formula 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

97. Inflation Example If the interest rate on one year govt. bonds is 5.9% and the inflation rate is 3.3%, what is the real interest rate? Savings Bond 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

98. Inflation Example If the interest rate on one year govt. bonds is 5.9% and the inflation rate is 3.3%, what is the real interest rate? Savings Bond 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

99. Inflation Example If the interest rate on one year govt. bonds is 5.9% and the inflation rate is 3.3%, what is the real interest rate? Savings Bond 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

100. Valuing a Bond Example If today is October 2000, what is the value of the following bond?  An IBM Bond pays $115 every Sept for 5 years. In Sept 2005 it pays an additional $1000 and retires the bond.  The bond is rated AAA (WSJ AAA YTM is 7.5%). Cash Flows Sept 0102030405 1151151151151115 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

101. Valuing a Bond Example continued If today is October 2000, what is the value of the following bond?  An IBM Bond pays $115 every Sept for 5 years. In Sept 2005 it pays an additional $1000 and retires the bond.  The bond is rated AAA (WSJ AAA YTM is 7.5%). 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed

102. Bond Prices and Yields Yield Price 11/16/2014Instructor: Mr. Wajid Shakeel Ahmed