Lecture3 - LECTURE 3 TIME VALUE OF MONEY PRESENT VALUE OF...

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28 L ECTURE 3 T IME V ALUE OF M ONEY P RESENT V ALUE OF P ERPETUITIES AND A NNUITIES Readings: Chapter 4 (sections 4.3-4.6), Chapter 5 section 5.2. Practice Problems: Lecture 3 Online Objectives: Compute the present values of a series of multiple cash flows, such as annuities and perpetuities Compute the future value of an annuity Solve for an annuity amount Set up and solve problems
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29 C ALCULATING PRESENT VALUE OF MULTIPLE CASH FLOWS For many investments, you will pay some money up front in exchange receive a stream of cash flows in the future. How do we determine the present value of such a cash flow stream? Example: How much would you pay to receive two payments, $10,000 the next year and 20,000 in 3 years? Think of each payment as a separate CD. How much would you have to pay for this pair of CD’s? PV (CD1 + CD2) = PV (CD1) + PV (CD2) This is called “value additivity”. Draw a cash flow timeline Suppose 1 and 3 year CD’s have an interest rate of 6%. Compute their present values and sum. $10,000 $20,000 PV = (1+0.06) + (1+0.06) 3 The PV is how much you would have to invest in 2 CD’s to replicate the cash flows. By the Law of One Price, the PV is the market value of the right to receive these two cash flows.
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30 V ALUING AN A NNUITY What is the PV of $100 to be received every year for 10 years starting in 1 year? Market interest rates are 10%. 1. Sum the present values of the ten cash flows of $100. 2. Multiply 100 times the present value of a $1 annuity for ten years. 46 . 614 ) 100(6.1446 = ) 1 . 1 ( 1 100 ... ) 1 . 1 ( 1 100 ) 1 . 1 ( 1 100 10 2 1 = + + + = PV An annuity is a series of identical fixed payments to be made for a specified number of years.
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31 V ALUING A PERPETUITY What is the PV of a $1 perpetuity. time 0 1 2 3 4 ... payment 0 $1 $1 $1 $1 ... The valuation of perpetuities: ... ) 1 ( 1 ... ) 1 ( 1 ) 1 ( 1 ) 1 ( 1 1000 3 2 1 + + + + + + + + + = r r r r PV How do we figure this one? A perpetuity is a series of identical fixed payments to be made forever .
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32 H OW TO VALUE A PERPETUITY ? PV = CF r where the first C ash F low is received one full period from today. For the curious, we can formally derive this formula as follows: r CF r CF PV CF r PV CF r PV PV r r r CF r PV r r r CF PV r r r CF r PV r r r r r r CF r PV r r r CF PV = = = = + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + = + + + + + + + = ) 1 1 ( ) 1 ( ) 1 ( 1 ... ) 1 ( 1 ) 1 ( 1 1 = ) + 1 ( 2B) ) 1 ( 1 ... ) 1 ( 1 ) 1 ( 1 0 = 1) : 2B equation minus 1 Equation ) 1 ( 1 . ... ) 1 ( 1 ) 1 ( 1 1 = ) + 1 ( 2B) ) 1 ( ) 1 ( . ... ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( 2A) ) 1 ( 1 . ... ) 1 ( 1 ) 1 ( 1 ) 1 2 1 2 1 1 2 1 2 1 2 1 or you can take my word for it. T OOL
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33 E XAMPLES OF P ERPETUITIES Endowed chairs for professors Scholarship funds British Consol Bonds
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34 B ACK TO V ALUING ANNUITIES : A N EASIER WAY An annuity is actually the difference of 2 perpetuities.
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This note was uploaded on 12/02/2009 for the course FIN 350 taught by Professor Schonlau during the Spring '08 term at University of Washington.

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Lecture3 - LECTURE 3 TIME VALUE OF MONEY PRESENT VALUE OF...

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