【文章內(nèi)容簡(jiǎn)介】 is is consistent with the conclusion by Teichrow’s. Advanced Topics in Capital BudgetingIII. Capital Budgeting with Inflation1. Inflation Effect on Cost of Capital Inflation must considered in capital budgeting since investors will incorporated expectation about inflation into their required rate of return. In fact, Nominal Rate of Return, which we usually see, consists of real rate of return and inflation rate. Nominal Rate of Return (Kn) is a real rate of return (K) plus inflation rate (f), but we can not simply add these two ponents together, nominal rate of return is lager than a result from an addition of K and i. More precisely, (1+Kn ) = (1+K)(1+f) Kn = K+f+K?f 2. Capital Budgeting by NPV under Inflation (1) Cash Inflows and Outflows Grow with the Same Inflation Rate NPV= [? NCFi(1+f)i /(1+K)i(1+f)i ]I0 ? [? NCFi /(1+K+f)i ]I0廈門(mén)大學(xué)吳世農(nóng)Thus, if the inflation is reflected in both the cash flows and in the required rate of return, the resulting NPV will be free of inflation bias.(2) Different Inflation on Cash Inflows and Outflows [CIFi (1+f1 )i COFi (1+f2 )i ](1T) + Depreciation?T NPV= ? I0 [(1+K)i (1+f )i ] where CIF=cash inflows。 COF=cash outflows。 f1 and f2 = inflation rates for CIF and COF, respectively。 f= average inflation rate。 T= tax rate. Advanced Topics in Capital BudgetingIV. Capital Budgeting for Projects with Unequal Lives1. Mutually Exclusive Projects with Different Lives(1) Problem Raised from the Assumption on Equal Life Usually, capital budgeting assumes that all mutually exclusive projects have the same life (and scale). In practice, this assumption many not be hold. Given that a set of mutually exclusive projects have different lives, how to evaluate and paring their NPVs? Suppose that there are two mutually exclusive projects, A and B, K=10% and their NCFs are presented in the following table. Year 0 1 2 3 n NPV(K=10%) Project A 1000 600 600 2 41 Project B 1000 400 400 475 3 50 By calculation, NPVA = 41。 NPVB = 50. Will be project B better than project A? No, In fact, they are not parable!廈門(mén)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。 (b) Use the IRR rule。 (c) Use NPV rule with constant scale replication. 廈門(mén)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。 To determine NPV under uncertainty, it is necessary to identify whether NCFs in each period are independent or dependent. (a) Independent NCFi If NCF in each Period is independent to each others, then, then the expected NCF in each period will be equal an averaged NCF, and the expected NPV of a project will be equal to a cumulative sum from the average of discounted expecte