18 35 present value of an annuity due cont therefore

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18 35 Present Value of an Annuity Due (cont.) Therefore, the present value of our example annuity due is: PV AD 100 1 1 110 010 100 416 98 5 1 . . . ± Note that this is higher than the PV of the, otherwise equivalent, regular annuity 36 Future Value of an Annuity Due To calculate the FV of an annuity due, we can treat it as regular annuity, and then take it one more period forward: FV Pmt i i i AD N 1 1 1 0 1 2 3 4 5 Pmt Pmt Pmt Pmt Pmt

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19 37 Future Value of an Annuity Due (cont.) The future value of our example annuity is: FV AD 100 110 1 010 110 67156 5 . . . . ± Note that this is higher than the future value of the, otherwise equivalent, regular annuity 38 Present Value, Future Value Future Value = Present Value + Interest Amount Interest amount = Principal amount x Interest rate Future Value of a Single Present Amount Future value = Present amount x (1 + r) n r = interest rate n = number of periods Future Value of an Ordinary Annuity Future value = Annuity Amount x [(1 + r) n - 1] / r r = interest rate n = number of periods
20 39 Present Value, Future Value Present Value of a Single Future Amount Present value = Future Amount x 1 / (1 + r) n r = interest rate n = number of periods Present Value of an Ordinary Annuity Present value = Annuity Amount x [1 - 1/(1 + r) n ] / r r = interest rate n = number of periods Ordinary Annuity : Same amount is paid at the end of each period. Annuity due : Same amount is paid at the beginning of each period. 40 Net Present Value The NPV represents the surplus funds (after funding the investment) earned on the project, therefore: • if the NPV is positive – the project is financially viable • if the NPV is zero – the project breaks even • if the NPV is negative – the project is not financially viable • if the company has two or more mutually exclusive projects under consideration it should choose the one with the highest NPV • the NPV gives the impact of the project on shareholder wealth.

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21 41 Net Present Value To appraise the overall impact of a project using DCF techniques involves discounting all the relevant cash flows associated with the project back to their PV. If we treat outflows of the project as negative and inflows as positive, the NPV of the project is the sum of the PVs of all flows that arise as a result of doing the project. 42 Net Present Value e.g. Project A costs £1,000,000 After 5 years the cash returns = £100,000 (10%) If you had invested the £1 million into a bank offering interest at 12% the returns would be greater You might be better off re-considering your investment!
22 43 Net Present Value The principle: How much would you have to invest now to earn £100 in one year’s time if the interest rate was 5%? The amount invested would need to be: £95.24 Allows comparison of an investment by valuing cash payments on the project and cash receipts expected to be earned over the lifetime of the investment at the same point in time, i.e the present.

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