448_04NetPV

448_04NetPV - Lecture Notes 4 Net Present Value The single...

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28 Lecture Notes 4 Net Present Value The single period case • Recall from the previous set of notes that, when the interest rate per period is r , the net present value of an investment that has a negative cash flow of – C 0 now and a positive cash flow one period in the future of C 1 is . (1) • The amount C 1 /(1+ r ) is the present value of the cash flow that will be earned next period. • Conversely, we could calculate everything in terms of next period’s values. The future value of the cash investment this period will be – C 0 (1+ r ). Multiple periods • When the interest earned on an investment is re-invested, the interest compounds . An investment of C 0 becomes C 0 (1+ r ) after the first year. If this entire sum is re-invested, the value at the end of two years will be C 0 (1+ r ) 2 . More, generally the future value of the investment after T years of earning compound interest will be (2) • Conversely, the present value of a cash flow C that is to be received T periods into the future is (3) The PV represents the amount of money that would have to be invested now at the compound interest rate of r per period in order to obtain, in T periods, the same cash flow of C . The term multiplying C in (3), NPV C 0 C 1 1 r + --------- + = FV C 0 1 r + () T = PV C 1 r + T ---------------- =
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29 (4) is known as the present value factor . • A stream of cash flows (– C 0 , C 1 , C 2 , …, C T ), representing an investment opportunity that will cost money immediately but will yield positive amounts in each of T future periods, will have a net present value (5) • Often one sees investments where there is a stated annual interest rate but compounding occurs more frequently than once a year. For example, most mortgages have interest paid at monthly in- tervals but the return is given as a stated annual interest rate. The future value of an investment C 0 with a stated annual interest rate of r but compounding for m periods within the year will be (6) The effective annual interest rate
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448_04NetPV - Lecture Notes 4 Net Present Value The single...

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