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# 393_lecture7 - Discounted Cash Flow Valuation(Multiple Cash...

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Discounted Cash Flow Valuation (Multiple Cash Flows) Lecture 7 Myung Joo Song ECON 393 Fall 2011 Myung Joo Song (ECON 393) Fall 2011 1 / 58

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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 Myung Joo Song (ECON 393) Fall 2011 2 / 58
FV of Multiple Cash Flows FV of Multiple Cash Flows = Sum of all Future Values of Single Cash Flows. You invest in period t 1 , t 2 , ..., t n , and you want to know your future value at time T. First, calculate future value for single cash ﬂow at each period (for t 1 , t 2 , ... ) Note that this is future value at time T. Sum all the future values, you get the FV of all your cash ﬂows at time T. Myung Joo Song (ECON 393) Fall 2011 3 / 58

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Example: FV of Multiple Cash Flows You think you will be able to deposit \$4,000 textcolorblueat the end of each of the next three years in a bank account paying 8% interest. You currently have \$7,000 in the account. How much will you have in 3 years? In 4 years? Today (Year 0): FV = 7000 x (1 . 08) 3 = \$8,817.98 Year 1: FV = 4,000 x (1 . 08) 2 = \$4,665.60 Year 2: FV = 4,000 x (1 . 08) 1 = \$4,320 Year 3: Value = \$4,000 Total FV = 8,817.98 + 4,665.60 + 4,320 + 4,000 = \$21,803.58 Value at year 4 = 21,803.58 x (1.08) = \$23,547.87 Myung Joo Song (ECON 393) Fall 2011 4 / 58
Example: FV of Multiple Cash Flows Suppose you invest \$500 in a mutual fund today and \$600 in one year. If the fund pays 9% annually, how much will you have in two years ? FV of your money today (Year 0) = 500 x (1 . 09) 2 FV of your money next year (Year 1) = 600 x (1.09) In two years what you have is: 500 x (1 . 09) 2 + 600 x (1 . 09) Myung Joo Song (ECON 393) Fall 2011 5 / 58

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Example: FV of Multiple Cash Flows (continued) How much will you have in 5 years if you make no further deposits? First way: FV = 500 x (1 . 09) 5 + 600 x (1 . 09) 4 = \$1 , 616 . 26 Second way: use value at year 2 FV = 1 , 248 . 05 x (1 . 09) 3 = \$1 , 616 . 26 Myung Joo Song (ECON 393) Fall 2011 6 / 58
Example: FV of Multiple Cash Flows Suppose you plan to deposit \$100 into an account in one year and \$300 into the account in 3 years. How much will be in the account in 5 years if the interest rate is 8%? FV = 100 x (1 . 08) 4 + 300 x (1 . 08) 3 = 136 . 05 + 349 . 92 = \$485 . 97 Myung Joo Song (ECON 393) Fall 2011 7 / 58

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Multiple Cash Flows: Present Value PV of Multiple Cash Flows = Sum of all Present Values of Single Future Cash Flows. You receive future payments in period t 1 , t 2 , ..., t n , and you want to know your present value at time t. Firstly calculate present value for single cash ﬂow at each period (for t 1 , t 2 , ... ) Note that this is present value at time t. Sum all the present values, you get the PV at time t of all your future cash ﬂows. Myung Joo Song (ECON 393) Fall 2011 8 / 58
Multiple Cash Flows: Present Value You are oﬀered an investment that will pay you \$200 in one year, \$400 the next year, \$600 the next year and \$800 at the end of the next year. You can earn 12% on very similar investments. What is the most you should pay for this one? Find the PV of each cash ﬂows and add them: 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 Myung Joo Song (ECON 393) Fall 2011 9 / 58

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Example: Timeline Myung Joo Song (ECON 393) Fall 2011 10 / 58
Multiple Cash Flows Using a Spreadsheet

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393_lecture7 - Discounted Cash Flow Valuation(Multiple Cash...

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