# 44 net present value future value pv 1 i n where i

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44 Net Present Value Future Value PV = ----------------- (1 + i) n Where i = interest rate n = number of years The PV of £1 @ 10% in 1 years time is 0.9090 If you invested 0.9090p today and the interest rate was 10% you would have £1 in a year’s time Process referred to as: ‘Discounting Cash Flow’

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23 45 Net Present Value Cash flow x discount factor = present value e.g. PV of £500 in 10 years time at a rate of interest of 4.25% = 500 x .6595373 = £329.77 • £329.77 is what you would have to invest today at a rate of interest of 4.25% to earn £500 in 10 years time PVs can be found through valuation tables (e.g. Parry’s Valuation Tables) 46 Discounted Cash Flow An example: A firm is deciding on investing in an energy efficiency system. Two possible systems are under investigation One yields quicker results in terms of energy savings than the other but the second may be more efficient later Which should the firm invest in?
24 47 Discounted Cash Flow – System A Year Cash Flow (£) Discount Factor (4.75%) Present Value (£) (CF x DF) 0 - 600,000 1.00 -600,000 1 +75,000 0.9546539 71,599.04 2 +100,000 0.9113641 91,136.41 3 +150,000 0.8700374 130,505.61 4 +200,000 0.8305846 166,116.92 5 +210,000 0.7929209 166,513.39 6 +150,000 0.7569650 113,544.75 Total 285,000 NPV =139,416 48 Discounted Cash Flow – System B Year Cash Flow (£) Discount Factor (4.75%) Present Value (£) (CF x DF) 0 - 600,000 1.00 -600,000 1 +25,000 0.9546539 23,866.35 2 +75,000 0.9113641 68,352.31 3 +85,000 0.8700374 73,953.18 4 +100,000 0.8305846 83,058.46 5 +150,000 0.7929209 118,938.10 6 +450,000 0.7569650 340,634.30 Total 285,000 NPV = 108,802.70

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25 49 Discounted Cash Flow System A represents the better investment System B yields the same return after six years but the returns of System A occur faster and are worth more to the firm than returns occurring in future years even though those returns are greater 50 Advantages and disadvantages of using NPV Advantages Theoretically the NPV method of investment appraisal is superior to all others. This is because it: • considers the time value of money • is an absolute measure of return • is based on cash flows not profits • considers the whole life of the project • should lead to maximisation of shareholder wealth. Disadvantages • It is difficult to explain to managers • It requires knowledge of the cost of capital • It is relatively complex.
26 51 Internal rate of return (IRR) Internal rate of return (IRR) The internal rate of return is the discount rate, which, when applied to the future cash flows of a project, will produce an NPV of precisely zero. 52 What is IRR? The discounted rate that equates the present value of a project’s expected cash inflows to the present value of the project’s costs

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27 53 Internal Rate of Return Allows the risk associated with an investment project to be assessed The IRR is the rate of interest (or discount rate) that makes the net present value = to zero Helps measure the worth of an investment Allows the firm to assess whether an investment in the machine, etc. would yield a better return based on internal standards of return Allows comparison of projects with different initial outlays Set the cash flows to different discount rates Software or simple graphing allows the IRR to be found 54 So now what? Once you’ve calculated IRR If IRR is greater than the cost of capital, then you’ve got a GOOD project on your hands (go for it!).
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