The NPV approach, or Net Present Value, was called ‘fictitious capital’ by socialist Karl Marx. It is the sum of the present values (PVs) of individual cash flows. When all future cash flows are incoming (such as coupons and principal of a bond) and the only outflow of cash is the purchase price, the NPV is simply the PV of future cash flows minus the purchase price. NPV uses the value of money over time to appraise long-term projects, measuring the excess or shortfall of cash flows. All, irrelevant or relevant, have a potential to interfere, so all flows are used to calculuate the NPV, which are added to a discount rate or discount curve and outputs a price; indeed, bond trading finds a yield through the converse process, taking a sequence of cash flows and a price as input and inferring as output a discount rate. NPV, unlike when one employs the monorating internal rate of return (IRR), has multiple discount rates to evaluate investments and discount each cash flow in accordance with envisaged conditions. Though IRR is simpler and needs fewer assumptions as to the likelihood of yield, NPV is preferred as it is more accurate. One can use the total cost or incremental cost approach through using NPV and compare investment projects. The formula divides the net cash flow by the time-exponential of ‘one plus the discount rate’; the discount rate is commonly the weighted average cost of capital, and variable rates are chosen to better reflect the calculations in a real-life situation. NPV must be positive to have a positive bearing on the decision, as this will significantly minimise risk, though NPV may not account for any changes along the way as the project takes hold.
