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【正文】 (b) Use the IRR rule。 graph 2 states for the earlier periods A’s NCFs are larger than B’s NCFs, thus NPVA NPVB, but for the later periods (after K*) A’s NCFs are smaller than B’s NCFs, thus NPVANPVB. NPV Graph 1 NPV Graph 2 B A NPVA NPV B B A NPVA NPV B NPVA =NPV B K NPVA NPV B K k IRRB IRRA k* IRRAIRRB 廈門大學(xué)吳世農(nóng) For graph 1, project A will be chosen for investment while project be will be given up. The decision is clear. For graph 2, it is hard to say which one is better. The question can not be answered until we do a further study. (2) Solution To illustrate the case shown in graph 2, the following table contains necessary information for making the accept/reject decision. Project I0 NCF1 NCF2 NPV(K=10%) IRR NPV(K=20%) A 1000 1000 310 % B 1000 200 1200 20% 0 To answer the question for the case of graph 2, we has to create a differential project (BA), we regard the difference of B’s NCF and A’NCF in the first year (NCF1B NCF1A) as I1, which is a negative value (or cash outflow). Also we treated the difference of B’s NCF and A’NCF in the second year (NCF2B NCF1A) as NCF1, which is a positive value (or cash inflow). Thus the differential project’s NPV and IRR can be shown as follows:Advanced Topics in Capital Budgeting NPV(BA) = [890/(1+10%)] 800 = $ [890/(1+IRR(BA))] 800。 IRR(BA) = % By the calculations above, it suggests that project B is better than project A。 (c) Use NPV rule with constant scale replication. 廈門大學(xué)吳世農(nóng) For the same problem, you may find that the solutions from the three approaches will yield different answers. However, a key to achieving the correct answer is to maximize NPV of a stream of projects replicated at constant scale. Advanced Topics in Capital BudgetingV. Capital Budgeting Under Uncertainty 1. Expected NPV and Variance of NPV(1) NCFi with probability Distribution In many cases in practice, a firm is faced with an investment project which NCFs are uncertain, for each period of n periods, there may be more than one possible values of NCF associated with probabilities。 NPVB = 50. Will be project B better than project A? No, In fact, they are not parable!廈門大學(xué)吳世農(nóng)(2) Solution To make project A and project B parable, it is reasonable to assume that project A and project Bcan be replicated at a constant scale. Thus, project A should be superior to project B because it recovers cash flows faster. How? In order to pare projects with unequal lives, we need to assume that the projects can be replicated at constant scale and pute the NPV of infinite stream of constant replications. By doing so, we finally have the following formula to pute NPV for project A and project B, assuming that both A and B are replicated at constant scale forever. (1+K)n NPV( n, ? ) = NPN(n) (1+K)n 1 By employing the formula above to project A and project B, we find that NPVA ( n, ? ) = $ 236 NPVB ( n, ? ) = $ 202 The results suggest that project A is superior to project B, thus, the firm must accept project A instead of project B! Advanced Topics in Capital Budgeting2. Important Notices(1) Reasonable Judgement on Replication Simple NPV rule, if misused, also can lead to wrong decision. For mutually exclusive projects with unequal lives, correct usage of simple NPV depends on whether or not the projects can be reasonably assumed to be replicable. (2) Implication of NPV with Infinite Replication at Constant Scale Infinite Replication at Constant Scale implies that the projects will be repeated at a constant scale every n years. Such an implication is applicable to some cases in practice such as forestry operation, X’mas tree planting and harvesting, raising pigs or chickens, and so on. (3) A Problem Remained Unsolved——Duration We may try to find out an optimal life——duration of a project. This optimal problem can be solved with different criteria: (a) Use the simple NPV rule。 by IRR (or PVI) B is over A. This case is typical as a conflict raised from decision criteria by NPV or by IRR? 廈門大學(xué)吳世農(nóng)(2) Solution Since K=10% is assumed to be fixed, we can solve this conflict by creating a differential project (BA), if the differential project yields a positive NPV, it is obvious that B is better than A because not only a part of B will create a NPV equal to NPVA, but also create a positive NPV for the differential project (BA). Thus, we create a differential project (BA), and then calculate its NPV and IRR NPV(BA) = [(750008000)/(1+10%)](500005000)=$15909 [(750008000)/(1+IRR(BA) )]=(500005000), IRR(BA) =% No doubt, the results above suggests that the investors of the firm will be better off if project B is accepted. Advanced Topics in Capital Budgeting2. Trend Effect of NCF on NPV and IRR (1) Conflict——Which One is a Sounding Decision Rule?
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