講義成果學校homework5.1lecture risk and project

1、Strategic Corporate financeWeek 4 Risk and project appraisalAdjust for risk by varying the discount ratePresent a sensitivity graph and discuss break even NPVUndertake scenario analysisMake use of probability analysisLearning esCertainty There is only one e and there is no doubt it will occurUncerta

2、inty there are different es but the probability of each cannot be determinedRisk - there are different es and the probability of each can be estimatedWhat is risk?Objective probabilitiesCan be established mathematically or from historic dataSubjective probabilitiesNo past information. Probabilities

3、must be estimatedWhat is risk?This states that investors require a higher return for accepting greater riskA business can add percentage points to a risk free rateExample: Sunflower plc has a risk free rate of 9% and adjusts for projects that have low, medium and high riskAdjusting the discount rate

4、Sunflower plcRisk premiumRisk adjusted 3%12%6%15%Level of riskLowMediumHighRisk free rate9%9%9%10%19%Sunflower plcYear012Cash flow-1005570Calculate the net present value for this project assuming low, medium and high risk.Sunflower plc has a project with the following cash flows:Sunflower plcLevel o

5、f riskNet present value DecisionLow4.91AcceptMedium0.76AcceptHigh-4.35RejectRisk perception and judgement are subjectiveDrawbacks of risk adjusted discount rateWhat if.Sales were 10% higher than expected?Labour costs were 5% lower?What level of change results in an NPV of Zero? (Break even NPV)Sensi

6、tivity analysisAllows management to:identify the most sensitive variablesFocus more attention on these variables Make them more accurate or,Understand the uncertainties betterSensitivity analysisAcmart plc has a new product line called the Mart. Likely demand is 1,000,000 per year, at a price of 1Pr

7、oject has a four year life Initial investment will be 800,000The discount rate is 15%Relevant cash flows per unit are:Sensitivity example: Acmart Cash flow per unitSale price1.00Costs Labour0.20 Materials0.40Relevant overhead0.100.700.30Sensitivity example: Acmart Required:Calculate the net present

8、value (NPV)Examine the sensitivity of the NPV to each of the variablesCalculate the break even value for each variable using Goal seekAcmartAcmartAcmart: Net present valueYearCash flowDisc facPV0-800,0001.000-800,0001300,0000.870260,8702300,0000.756226,8433300,0000.658197,2554300,0000.572171,526NPV5

9、6,494AmcartplcSensitivity AnalysisLowMedium HighBreak even-10%No change+10%Investment ()720,000800,000880,000856,494NPV ()136,49456,494-23,506NilQuantity demanded900,0001,000,0001,100,000934,041NPV ()-29,15656,494142,143NilAmcartplcSensitivity AnalysisLowMedium HighBreak even-10%No change10%Sale pri

10、ce ()0.911.10.98NPV ()-229,00456,494341,991NilLabour ()0.180.20.220.22NPV ()113,59356,494-606NilMaterials ()0.360.40.440.42NPV ()170,69356,494-57,706NilOverhead ()0.090.10.110.12NPV()85,04356,49427,944NilDiscount Rate13.50%15%16.50%18.50%NPV ()83,15056,49431,144NilMost sensitive variables:SalesMater

11、ialsQuantity demandedInvestmentAdverse changes to overheads and discount rates will lead to negative NPV Least sensitive variables: Adverse changes to overheads and discount rates will not lead to negative NPV Acmart conclusionsExcel worksheet Acmart (on Moodle)Deals with sensitivity at 10% and 5%A

12、scenario allows you to see the effect of changes to a number of variables i.e. Sales +10%, Costs +5%Scenarios using ExcelE.g. Increase sales to 1,050,000, reduce selling price to 99p and reduce labour costs to 19pExcel can manage this easilyData, What-If analysis, Scenario manager Scenarios manager

13、(excel)Expected return for a projectIdentify a range of possible esIdentify the probability of each esWeight the es by their probabilitySum the resultIf there is more than one project, choose the project with the highest expected returnNo guarantee expected return will be actual returnProbability an

14、alysisData as belowExpected value of project A e NPV KProbNPV xProb e 1200.408 e 2300.4012 e 3400.20828Data as belowExpected value of project B e NPV KProbNPV xProb e 1100.404 e 2300.4012 e 3600.201228Expected return of A and B is the sameProject B is more volatileVolatility is RiskMeasure risk usin

15、g standard deviationComparison of Project A and BProject AB e 12010 e 24030 e 34060Exp value2828Project A Standard deviationProject AReturnProbExpreturnMean returnDevDev22Devx prob e 1200.40828-86425.60 e 2300.401228241.60 e 3400.208281214428.8028Var56.00StdDev7.48Project B Standard deviationProject

16、 BReturnProbExpreturnMean returnDevDev22Devx prob e 1100.40428-18324129.60 e 2300.401228241.60 e 3600.201228321024204.8028Var336.00StdDev18.33Which project would you accept and why?Summary of projects A and BReturn (NPV)Risk (SD)Project A287.48Project B2818.33Risk and utilityUtility- satisfaction, w

17、ell beingDiminishing marginal utilityCan be used to show that people are normally risk averseTherefore, for the same return choose the lower riskChoose project AProbability analysisToo much faith in subjective probabilitiesToo complicatedProjects may be viewed in isolationProbabilities can be assign

18、ed to each variableProblems in using probability analysisPentagon plc has to decide between 5 mutually exclusive projects. You are given information about the return (NPV) and the probability of that return for each projectRequired: Calculate the expected return and the standard deviation of the ret

19、urns for each projectPlot the return and standard deviation on a chartWhich project should Pentagon undertake? Give reasons. Probability analysis: PentagonRet 000ProbExpreturnMean returnDevDev2Dev2x probxipixi x pimxi -m(xi -m)2(xi -m)2x pi Project1161.001616000.00Variance0.00Std Dev0.00Project 2201.002020000.00Variance0.00Std Dev0.00Project 3Recession-160.25-4-421,764441.00Growth360.50181010050.00Boom480.251226262622484121.0026Variance612.00StdDev24.74Ret 000ProbExpreturnMean returnDevDev2Dev2x probxipixi x pimxi -m(xi -m)2(xi -m)2x pi Project 4