2+A(1+i)-3 = - A(1+i)-n 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) -100000 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 accounted for, it is useful to make a sketch to represent the various Appendix 2: Financial Calculations Time (years) Figure A2.6 Annual cash flows are discounted in present value methods amounts and when they occur. Such a sketch is shown in Figure A2.6. Income is shown above the line, costs below it. End of year Actual cash flow: Discount factor Discounted cash flow: $ 000 @ 10 % per annum. $ 000 (1000) 1.000 (1000) 0.909 363.6 0.826 413.0 (100) 0.751 (75.1) 0.683 341.5 0.621 372.6 Total 415.6 (Note: The usual condition for the existence of an internal rate of return is that there must be at least one change 