LECTURE4 - Lecture 4 Lecture Net Present Value(NPV NPV...

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Lecture 4 Lecture 4 Net Present Value (NPV) Net Present Value (NPV)
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NPV calculation : single period case r C C NPV + + - = 1 1 0 0 C r C + 1 1 1 C initial cash outflow cash inflow in one period present value of next period’s cash flow
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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 842 . 0 $ 09 1 1 09 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 FV + × = 1 PV of a cash flow C to be received T years into future ( 29 ( 29 T T r C r C PV + × = + = 1 1 1
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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 NPV 1 0 2 2 1 0 1 1 1 1 ( 29 T C C C C , , , , 2 1 0 - Present value factor ( 29 T r + 1 1 NPV calculation : multiple periods, annual compounding (continued)
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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 FV + × = 1
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Example Example ( 29 89 . 47 09 . 1 700 09 . 1 500 1000 2 = + + - = NPV What happens if the interest is compounded semi annually ? ( 29 ( 29 89 . 47 86 . 44 045 . 1 700 045 . 1 500 1000 2 09 . 0 1 700 2 09 . 0 1 500 1000 4 2 2 2 2 < = + + - = + + + + - = × NPV 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% ?
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EAIR is defined as ( 29 m m r + = + 1 1 ρ Effective annual interest rate Effective annual interest rate (EAIR) (EAIR) 09 . 0 092 . 0 1 2 09 . 0
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