04_Oheads

04_Oheads - Lecture Notes 4 Net Present Value Recipe for...

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1 Lecture Notes 4 Net Present Value Recipe for financial decision makers i. Identify the size and timing of all relevant cash flows. ii. Identify the riskiness of the cash flows in order to determine the appropriate discount rate. iii. Find the NPV of the cash flows. iv. When comparing alternative projects, discount cash flows to the same date. Calculating NPV – the single period case • When the interest rate is r , an investment with an initial negative cash flow of – C 0 and a positive cash flow C 1 in one period is . (1) C 1 /(1+ r ) is the present value of next period’s cash flow. Con- versely, – C 0 (1+ r ) is the future value of the initial investment. NPV C 0 C 1 1 r + ----------- + =
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2 Calculating NPV – multiple periods, annual compounding • When the yield on an investment is re-invested, the interest com- pounds . For example, if we invest $1 for 2 years at the compound interest rate of 9% the future value of the investment will be: $1 & 1.09 & 1.09 = $1.1881. • Conversely, suppose we will receive $1 in 2 years and the cur- rent annual interest rate is 9%. The present value of the income is • The future value of an investment after T years of earning com- pound interest will be (2) • Conversely, the present value of a cash flow C that is to be re- ceived T periods into the future is (3) • The PV is the amount that would have to be invested now at the $1 1.09 1.09 & -------------------------- $0.842 = FV C 0 1 r + () T = PV C 1 r + T ------------------- =
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3 compound interest rate of r per period in order to obtain, in T pe- riods, the same cash flow of C . The term multiplying C in (3), (4) is known as the present value factor . • A stream of cash flows (– C 0 , C 1 , C 2 , …, C T ), representing an in- vestment that will cost C 0 but yield positive amounts in each of T future periods, will have a net present value (5) Calculating NPV – multiple periods, within year compounding • The value next year of an investment C 0 with a stated annual in- terest rate of r but compounding for m periods within the year is . (6) After T years, the value of the investment will be 1 1 r + () T ------------------- NPV C 0 C 1 1 r + ----------- C 2 1 r + 2 ------------------ & C T 1 r + T ++ + + C 0 C i 1 r + i ----------------- i 1 = T + = = FV
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This note was uploaded on 12/20/2011 for the course ECON 448 taught by Professor Bejan during the Spring '06 term at Rice.

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04_Oheads - Lecture Notes 4 Net Present Value Recipe for...

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