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Net present value

calculates and then totals the present values of all the expected future cash flows of an investment (using discounting factors based on a pre-determined interest rate to arrive at the ‘present values’), and subtracts these from the original cost of the investment. Example: let us assume that a firm is considering an investment (Project Z) with the following cash flows: Year 0 (£50,000), Year 1 £20,000, Year 2 £30,000, Year 3 £15,000. By the end of the first year, the project is forecast to earn £20,000. To consider the alternative, the firm asks how much it must invest in the bank now, to get £20,000 out in a year. Assuming a 5% interest rate, this can be calculated as follows: £q x 1.05 = £20,000. £q = £20,000 / 1.05. £q = £19,048 (rounded up). The second year sees the project earning £30,000. The firm, therefore, asks how much it must invest in the bank now to get £30,000 in two years time, assuming a 5% interest rate. This is calculated as follows: £q x 1.052 = £30,000; thus £q x 1.1025 = £30,000; £q = £30,000 / 1.1025; £q = £27,211. This means that the firm must invest £27,211 now if it wishes to receive £30,000 in two years time, at compound interest, with a constant rate of 5%. The third year sees the project earning £15,000. To calculate how much the business must invest in the bank now to get £15,000 out in three year’s time, the following formula is used: £q x 1.053 = £15,000; thus £q x 1.157625 = £15,000; £q = £15,000 / 1.157625 = £12,958. NB The factors – 1 / 1.05, 1 / 1.052 and so on, are provided for students in the actual examinations. By adding all these ‘discounted cash flows’ for the three years, the total is £59,217. This figure must be compared with the original investment in Project Z, ie £50,000. Comparison shows that project Z has a return that is more than 5%, ie a return greater than the alternative of putting the money in the bank. Using the figures provided in the discounted cash flow example above, net present value is simply arrived at by deducting the cost of the original investment from the total discounted cash flows (£59,217 – £50,000). In this example Net Present Value is, therefore, £9,217. In general, if the NPV is positive – as in the example we have provided above – then the investment will be accepted. If negative, then the investment will be rejected.

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