e investment value has increased to P2 = Po(1 + +i) = P (1 +i)2 In general, Pn = Po(1 + i)" Discounting a future value: The present value P of a future amount Pn is found from the above equation: In general, P Cost of investment (cash out) Payback time Accumulated cash inflow Figure A2.4 Pay back time Understanding Changing Telecommunications - Building a Successful Telecom Business Figure A2.5 Assumed annual Telecom project (net) cash flows PV of a series of regular equal cash flows: n cash flows (payments or receipts), each of amount A, at the end of years 1, 2, 3 according to Figure A2.5. Po=A(1+i)-1+A(1+i)-2+A(1+i)-3 = + A(1 Discounting can be applied to both money receivable and also to money payable at a future date. And SO by discounting all payments and receipts from a capital investment to a present value, they can be compared on a common basis at a value that takes account of when the various cash flows will take place. Example 1 The estimated cash flows on a project investment (100 000) over the next four years are (60 000, 80000, 40 000 and 30 000). The company cost of capital (or interest) is 15 %. What is the NPV of the project, and should it be undertaken? Cash flow Discount factor (i = 15%) 100 000(investment) -100 000 60 000 0.870 52 200 80 000 0.756 60 480 40 000 0.658 26 340 30 000 0.572 17 160 56 160 Example 2 A telecommunication project is expected to have the following cash flows, where the figures in brackets represent costs and are negative (this is standard accounting practice). The corporate discount rate for new investments is i = 10 %. The discount factor for each amount can be deduced from the formula (1 + i) -n. The sum of the discounted cash flows will be the NPV for the project. The initial cost of $1 million is incurred at the end of year 0, that is; at the beginning of year 1, and hence the discount factor for it is 1.0. If paid at the end of year 1, it would have to be discounted and the PV of the expense reduced. To ensure that the timings of costs and income are correctly acco