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DCFValuation_Notes

DCFValuation_Notes - Discounted Cash Flow Valuation BUAD...

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Discounted Cash Flow Valuation BUAD 306 - Spring 2009 Jesus Sierra USC- FBE January 27, 2009 Jesus Sierra (USC- FBE) Discounted Cash Flow Valuation January 27, 2009 1 / 64
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Key concepts and skills Determine future and present value of investments with multiple cash flows. Understand the concept of annuity and perpetuity. Calculate loan payments. Find interest rates on loans. Understand how loans are amortized or paid off. Understand how interest rates are quoted: EAR, APR. Jesus Sierra (USC- FBE) Discounted Cash Flow Valuation January 27, 2009 2 / 64
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Outline 1 Future and Present values of multiple cash flows. 2 Valuing level cash flows: annuities and perpetuities 3 Comparing rates: the effect of compounding periods. 4 Loan types and loan amortization. Jesus Sierra (USC- FBE) Discounted Cash Flow Valuation January 27, 2009 3 / 64
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Future value with multiple cash flows So far we have only worked with a single cash flow. Now, we will study multiple cash flows. Ex: Suppose you deposit $100 today in an account paying 8% interest, and in one year, you deposit another $100. How much will you have in 2 years ? One way to solve this is to calculate the balance at the start of each period. At the end of the first year, you will have: $100 × (1 . 08) + $100 = $208 If you leave this on deposit for another year at the same rate, at the end of 2 years you will have $208 × (1 . 08) = $224 . 64 Jesus Sierra (USC- FBE) Discounted Cash Flow Valuation January 27, 2009 4 / 64
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Future value with multiple cash flows One of the most useful tools for solving present value problems is the time line . The most important thing when working with time lines is that you write the cash flows when they occur. Jesus Sierra (USC- FBE) Discounted Cash Flow Valuation January 27, 2009 5 / 64
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Future value with multiple cash flows In the last example, we calculated the balance at the beginning of each period and then rolled the amount forward to the next year. However, there is another way to do it. Notice that once you put the first $100 in the bank @8%, it stays there for 2 years(periods), so its FV is $100 × (1 . 08) 2 = $116 . 64 Then, you deposit another $100 for one year again @8%, so its FV must be $100 × (1 . 08) = $108 So that in total, you have $116 . 64 + $108 = $224 . 64 Jesus Sierra (USC- FBE) Discounted Cash Flow Valuation January 27, 2009 6 / 64
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Future value with multiple cash flows In general, there are 2 ways to calculate FV of multiple cash flows: 1 compound the accumulated balance forward one period at a time. 2 calculate the FV of each cash flow first and then add these up. Both give the same answer. Jesus Sierra (USC- FBE) Discounted Cash Flow Valuation January 27, 2009 7 / 64
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Future value with multiple cash flows Let’s do another example. Consider the FV of $2000 invested at the end of each of the next 5 years. The current balance is 0, and the rate is 10%. First, draw a time line. The correct depiction of the cash flows is illustrated on the following time line : Notice that: 1 Nothing happens until the end of the first year 2 The first investment earns interest for 4 not 5 years 3 The last $2000 is invested at the end of the 5 th year, so it earns no interest at all.
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