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Unformatted text preview: Lecture 4 Lecture 4 Net Present Value (NPV) Net Present Value (NPV) NPV calculation : single period case r C C N P V + + = 1 1 C r C + 1 1 1 C initial cash outflow cash inflow in one period present value of next periods cash flow NPV calculation : multiple periods, annual compounding The interest compounds when the yield on an investment is reinvested 1881 1 $ 09 1 09 1 1 $ . . . = FV of $1 invested for 2 years at the compound interest rate of 9% per year 8 4 2 . $ 0 9 1 1 0 9 1 1 1 $ = . . PV of $1 to be received in 2 years with 9% annual interest rate FV of an investment C after T years of earning compound interest r ( 29 T r C F V + = 1 PV of a cash flow C to be received T years into future ( 29 ( 29 T T r C r C P V + = + = 1 1 1 NPV of a stream of cash flows ( 29 ( 29 ( 29 ( 29 = + + = + + + + + + + = T i i i T T r C C r C r C r C C N P V 1 2 2 1 1 1 1 1 ( 29 T C C C C , , , , 2 1  Present value factor ( 29 T r + 1 1 NPV calculation : multiple periods, annual compounding (continued) NPV calculation : multiple periods, within year compounding Compounding for m periods within the year r m r Stated Annual Interest Rate (SAIR) (SAIR) Interest for each of m periods m m r C + 1 2 1 + m r C + m r C 1 C m periods Next year Now FV of an investment C after T years T m m r C F V + = 1 Example Example ( 29 8 9 . 4 7 0 9 . 1 7 0 0 0 9 . 1 5 0 0 1 0 0 0 2 = + + = N P V What happens if the interest is compounded semi annually ? ( 29 ( 29 8 9 . 4 7 8 6 . 4 4 0 4 5 . 1 7 0 0 0 4 5 . 1 5 0 0 1 0 0 0 2 0 9 . 1 7 0 0 2 0 9 . 1 5 0 0 1 0 0 0 4 2 2 2 2 &lt; = + + = + + + + = N P V Consider an investment of $1,000 that is expected to yield $500 in 1 year and $700 in 2 years. What is the NPV of the investment at an annual discount rate of 9% ? EAIR is defined as ( 29 m m r + = + 1 1 Effective annual interest rate...
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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.
 Spring '06
 Bejan

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