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## Net Present Value (NPV)

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**Net Present Value (NPV)**Payback and ARR methods of investment appraisal ignore the time value of money but, as we know, £100 now is worth more than £100 in 5 years. The NPV method takes this into account; future sums are discounted (reduced) to reflect this lower value. BUT discount rates do vary; for example, a firm with cash-flow problems will have a high discount rate as it needs money NOW, whereas a secure firm will a have lower discount rate. Generally, the current rate of interest shows what can be earned on money received immediately, therefore this acts as a guide to the discount that should be applied to money in the future. Discount Cash Flow (DCF) This is how you reduce the value of future sums, therefore as time goes by the ‘present’ value of a given sum declines. The higher the rate, the lower the value. Example: Present value of £1 at discount rate Yr 5% 10% 15% 0 1.0 1.0 1.0 1 0.952 0.909 0.870 2 0.907 0.826 0.756 3 0.864 0.753 0.658 4 0.823 0.683 0.572 5 0.784 0.621 0.497**Calculating the NPV**Example: Project A costs £100 initially. It then provides an annual return of £25 for 5 years. The discount rate is 5%. What is the NPV? Yr Net return x Discount factor = Present Value 0 -100 x 1.0 = -100 1 +25 x 0.952 = +23.8 2 +25 x 0.907 = +22.675 3 +25 x 0.864 = +21.6 4 +25 x 0.823 = +20.575 5 +25 x 0.784 = +19.6 Present Value of total cash inflow = +108.25 NPV = +8.25 In accounting terms, the investment produces a profit of 125-100= £25. In NPV it is only £8.25. BUT this is still a positive outcome. On financial grounds, any positive NPV is worthwhile (and vice versa). • Advantages of NPV: • Considers the time value of money. • Good for analysis of single projects. • A positive NPV means accept, a negative means reject. • Disadvantages of NPV: • Based on an arbitrary % discount rate. • Time consuming and harder to calculate. • Difficult to understand.