CHAPTER 2 Key points and concepts Time value of money has three component parts each requiring compensation for a delay in the receipt of cash: (i) the pure time value, or impatience to consume, (ii) inflation, and (iii) risk.Opportunity cost of capital is the yield forgone on the best available investment alternative – the risk level of the alternative being the same as for the project under consideration.Taking account of the time value of money and opportunity cost of capital in project appraisal leads to discounted cash flow analysis (DCF).Net present value (NPV) is the present value of the future cash flows after netting out the initial cash flow. Present values are achieved by discounting at the opportunity cost of capital. The net present value decision rules are: NPV 0 accept NPV < 0 reject Internal rate of return (IRR) is the discount rate which, when applied to the cash flows of a project, results in a zero net present value. It is an ‘r’ which results in the following formula being true: The internal rate of return decision rule is:IRR opportunity cost of capital – accept, IRR < opportunity cost of capital −– rejectIRR is poor at handling situations of unconventional cash flows. Multiple solutions can be the result.There are circumstances when IRR ranks one project higher than another, whereas NPV ranks the projects in the opposite order. This ranking problem becomes an important issue in situations of mutual exclusivity.The IRR decision rule is reversed for financing-type decisions.NPV measures in absolute amounts of money. IRR is a percentage measure.IRR assumes that intra-project cash flows can be invested at a rate of return equal to the IRR. This biases the IRR calculation. ANSWERS TO QUESTIONS 3 Confused plc a Project C IRRs at 12.1% and 286%. See Fig. 2.1. Fig. 2.1 Project D No solution using IRR. See Fig. 2.2. Fig. 2.2 b This problem illustrates two disadvantages of the IRR method. In the case of project C multiple solutions are possible, given the non-conventional cash flow. In the case of project D there is no solution, no IRR where NPV = 0. c NPV Project C: +£646 Project D: –−£200 Using NPV, the accept/reject decision is straightforward. Project C is accepted and Project D is rejected. 5 Seddet International a Project A At 20%: –−5,266 + 2,500 2.1065 = 0, therefore IRR = 20% Project B At 7%: −–8,000 + 10,000 0.8163 = +163 At 8%: −–8,000 + 10,000 0.7938 = –62 Project C At 22%: −–2,100 + 200 0.8197 + 2,900 0.6719 = +12.45 At 23%: −–2,100 + 200 0.8130 + 2,900 0.6610 = –20.5 Project D At 16%: −–1,975 + 1,600 0.8621 + 800 0.7432 = −–1 Therefore, IRR is slightly under 16%. The IRR exceeds the hurdle rate of 16% per cent in the case of A and C. Therefore, if all projects can be accepted these two should be undertaken. b Ranking under IRR: IRR Project C 22.4% best project Project A 20% Project D 16% Project B 7.7% c Project A −–5,266 + 2,500 2.2459 = 349 Project B −–8,000 + 10,000 0.6407 = –1,593 Project C −–2,100 + 200 + 0.8621 + 2,900 0.7432 = 228 Project D −–1,975 + 1,600 0.8621 + 800 0.7432 = –1 Ranking NPV Project A 349 best project Project C 228 Project D –−1 Project B −1,593 Project A ranks higher than project C using NPV because it generates a larger surplus (value) over the required rate of return. NPV measures in absolute amounts of money and because project A is twice the size of project C it creates a greater NPV despite a lower IRR. d This report should comment on the meaning of a positive or negative NPV expressed in everyday language. It should mention the time value of money and opportunity cost of capital and explain their meanings. Also the drawbacks of IRR should be discussed: multiple solutions;ranking problem – link with the contrast of a percentage-based measure and an absolute money-based measure;additivity not possible;the reinvestment assumption is flawed.

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