【正文】 given that state 2 in the first period happens, it is possible for the project to have either NCF=$2023 with 50% probability or NCF=$1000 with 50% probability. The questions is that under such a uncertainty, what is expected NPV and its risk (standard deviation)? Period State NCF Probability Period State NCF Probability 1 10000 70% 1 7000 90% 2 9000 30% 1 2 1 2023 50% 2 2023 10% 2 1000 50%廈門大學(xué)吳世農(nóng)(a) Find possible binations of NCFs Combination of NCFs Probability for Combination $7000, $10000 (90%)(70%)=63% $7000, $9000 (90%)(30%)=27% $2023, $2023 (10%)(50%)=5% $2023, $1000 (10%)(50%)=5% Total 100%(b) Determine possible NPV for each bination State NPVj Probability 1 1000+7000()+10000()=4624 2 1000+7000()+ 9000()=3797 3 1000+2023()+ 2023()=6530 4 1000+2023()+ 1000()=7356 Total (c) Compute Expected NPV and Variance E(NPV)=4623(63%)+3797(27%)+(6530)(5%)+(7356)(5%)=$3242 S(NPV)=[? (NPVj 3242)2 ?Probability]1/2 =$3254 Advanced Topics in Capital BudgetingVI. Project Abandonment1. Why to Abandon a Project?(1) Economic Environment (2) Market Competition(3) ProductConsumption Cycle (4) Technological Changes(5) Management Team(6) Wrong Estimation in Capital BudgetingSales Test Growth Mature Decline t 廈門大學(xué)吳世農(nóng)2. When to Abandon a Project? (1) Project Abandonment Under Certainty Suppose that a firm invests $10000 in a project, K=10%, n=5. The following table contains the project’s data for making the accept/reject decision and the abandonment decision. Year 1 2 3 4 5 NCF 5000 4000 3000 2023 1000 Salvage(F) 7000 5000 3000 1000 0(a) Is the project acceptable? NPV= 5000()+4000()+3000()+2023()+1000() 10000 = $2089 0, so the project should be accepted!(b) Should be the project be abandoned after its operation? Yes, because the project’s NCFs rend to decline year by year! (c) When to abandon the project? The firm should abandon the project when the NPV is maximized! The following Calculation show Max(NPV) appears when n=3. Why? Advanced Topics in Capital Budgeting(c1) NPV for 5year Operation: NPV= 5000()+4000()+3000()+2023()+1000() 10000 = $2089 (c2) NPV for 4year Operation: NPV= 5000()+4000()+3000()+2023()+1000() 10000 = $2157 (c3) NPV for 3year Operation: NPV= 5000()+4000()+3000()+3000()10000 = $2355=Max(NPV) (c4) NPV for 2year Operation: NPV= 5000()+4000()+5000()10000 = $1979 (c5) NPV for 1year Operation: NPV= 5000()+7000()10000 = $908廈門大學(xué)吳世農(nóng)(2) Project Abandonment Under Uncertainty Suppose that a firm considers a project which initial outlay is $10000, K=10%, n=2, and its NCFs and associated probabilities were shown in the previous section (see IV). If the firm expected that salvage value(F) by the end of period 1 is $3000 while nothing left by the end of period 2, will this project is acceptable? If yes, should be it abandoned after operation? (a) Is the project acceptable? By putation from Section IV, E(NPV)0, so the project must be accepted! E(NPV)=4623(63%)+3797(27%)+(6530)(5%)+(7356)(5%)=$3242 S(NPV)=[? (NPVj 3242)2 ?Probability]1/2 =$3254 (b) When to Abandon the Project? Year1 or Year2? (b1): If the project is abandoned at the end of year 2, then E(NPV)=$3242 S(NPV)=$3254 Advanced Topics in Capital Budgeting(b2): If the project is abandoned at the end of year 1, then E(NPV)=4623(63%)+3797(27%)+(5455)(5%)+(5455)(5%)=$3392 S(NPV)=[? (NPVj 3392)2 ?Probability]1/2 =$2971 The results above e from the following table: State NPVj Probability 1 1000+7000()+10000()=4624 2 1000+7000()+ 9000()=3797 3 1000+(2023+3000)() =5455 4 1000+(2023+3000)() =5455 Total (b3) Decisions The first, the results suggest that abandoning the project at the end of year 1 shows a larger NPV and less standard deviation by a parison to NPV and standard deviation resulted fr