【正文】 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。3. Sign Effect of NCFs on NPV and IRR(1) Conflict——Which One is Applicable? We one discussed a classification of cash flows: conventional NCF and nonconventional NCF, the rational behind this classification is to identify applicability of capital budgeting techniques, particularly for NPV and IRR. If a project’s stream of estimated NCFs changes sign more than once, the stream of NCFs is nonconventional. In this case, IRR is not applicable because it can result in multiple rates of return! Why? A simple answer to this question is that if the stream of NCFs changes sign more than one time, mathematically, solving the equation of IRR will results in more than one solutions——Multiple Rates of Returns. 廈門大學(xué)吳世農(nóng) Geometrically, the multiple rates of return can be shown in the following graph. NPV0 K Some Studies show that cash flows of investment projects were highly associated with economic environment, market petition, management ability and many others. In practice, it is mon that NCF changes sign many times during its entire life as the influential factors change. Thus, IRR is ineffective to the case of nonconventional cash flows.Advanced Topics in Capital Budgeting(2) Solution Oilwell Pump Investment is a typical case in capital budgeting to show the problem of multiple rates of return if IRR is employed to evaluate this project’s IRR. A oil pany is trying to decide whether or not to install a highspeed pump on an oilwell which is already in operation. The pump will cost $1,600 to install. The pump will, for the first year, generate $10,000 more oil than the pump used now, but for the second year the new pump will generate $10,000 less oil because the well has been depleted. Should the oil pany install the highspeed pimp? We summarize the estimated incremental cash flows and present them in the following table. Year 0 1 2 NCF 1,600 10,000 10,000 (a) Confusing Solution Resulted from IRR 1600=[10000/(1+IRR)1 ]+[10000/(1+IRR)2 ] [1600/(1+IRR)]+[10000/(1+IRR)1 ]+[10000/(1+IRR)2 ]=0 廈門大學(xué)吳世農(nóng) Because this equation shows that NCF change its sign from “+” to “” one time, the solution to this equation produces two alternative results: IRR=25% IRR=400% Obviously, the results are confusing and hard to interpreted. NPV IRR=25% IRR=400%1000500 100 200 300 400 500 K(%)50010001500Advanced Topics in Capital Budgeting (b) Alternative Solution Offered by Teichrow (1964) Teichrow thought the Oilwell Pump Investment in a different way——add the cash flows of two adjacent periods (period 0 and period 1) together by a logically economic way to make NCF’s sign change to conventional. Assume put money into the investment twice: $1600 at the time of the initial investment, and $10000 in the second time period. The project can be thought of as lending +$10000 at 10% (cost of capital) to the firm in the first time period. So, the first, the firm invests $1600 now and expects to earn the IRR at the end of the first period, that is 1600(1+IRR)廈門大學(xué)吳世農(nóng) In the second period, the difference between this result 1600(1+IRR) and the amount of money (+10000), which the project lends to the firm at 10%, is the amount borrowed at 10%, the future value of this difference at the end of the second time period is [100001600(1+IRR)](1+10%) Thus, we can establish an new equation to solve IRR [100001600(1+IRR)](1+10%) = $10000 IRR=% This answer suggests that he project must be rejected. (c) Simple Solution Resulted from NPV NPV=[10000/(1+10%)1 ]+[10000/(1+10%)2 ] 1600 = =$ This solution provided by NPV suggests that this project must be rejected, this 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