1、Lecture1 Capital BudgetingContents:Time value of money introduction Compounding Discounting Annuities Perpetuities Capital Budgeting Techniques:Net Present Value Internal Rate of Return The Payback Method The Accounting Rate of Return1Criterion for Shareholders Wealth Maximisation All cash flows sho
2、uld be considered.The cash flows should be discounted at the opportunity cost of funds.The technique should select from a set of mutually exclusive projects the one that maximizes shareholders wealth.Management should be able to consider one project independently from all others(this is known as the
3、 value-additivity principle).2Why Use Cash Flows Rather Than Profits?Cash is what ultimately matters profits are simply a guide to the availability of cash Profit measurement is subjective Cash is used to pay dividends The ultimate method of transferring wealth to equity holders 3Time Value of Money
4、 Introduction The interaction of lenders with borrowers sets an equilibrium rate of interest.Borrowing is only worthwhile if the return on the loan exceeds the cost of the borrowed funds Lending is only worthwhile if the return is at least equal to that which can be obtained from alternative opportu
5、nities in the same risk class.4Time Value of Money Introduction cntd.The interest rate received by the lender is made up of:The time value of money:the receipt of money is preferred sooner rather than later.Money can be used to earn more money.The risk of the capital sum not being repaid.Inflation:m
6、oney may lose its purchasing power over time.5Future Value(FV)The general formula for computing Future Value is as follows:FVn=Vo(l+r)nwhere Vo=the initial sum investedr=the interest raten=the number of periods for which the investment is to receive interest.6Future Value of Annuity(FVA)7)(1)1()1(,1
7、ninnttnnFVIFAPMTiiPMTiPMTFVAFuture Value of Annuity(FVA)Example8Calculate future value at the end of three years if at the end of each of the following three years 100 is paid into a bank account that earns 5%interest rate.FVA3=PMT*FVIFA0.05,3FVA3=100*3.1525=315.25Present Value of Annuity(PVA)9)(111
8、)1(1,1nintntnPVIFAPMTiiPMTiPMTPVAPresent Value of Annuity(PVA)Example10Calculate the present value if at the end of each of the following three years 100 is paid into a bank account that earns 5%interest rate.PVA=PMT(PVIFAi,n)=100(2.7232)=272.32Future Value cntd.Self Assessment Question(SAQ)i)What i
9、s the future value of 100 invested at 10%per year at the end of 1 year?ii)What is the future value of 100 invested at 10%per year at the end of 5 years?11Present Value(PV)We can derive the Present Value(PV)by using the FV formula:FVn=Vo(I+r)n By denoting Vo by PV we obtain:FVn=PV(I+r)n by dividing b
10、oth sides of the formula by(I+r)n we derive:PV=FVn/(I+r)n 12Present Value(PV)cntd.Self Assessment Question(SAQ)i)What is the present value of 110 at the end of one year if interest rate is 10%per year?ii)What is the PV of 161 at the end of 5 years if interest rate is 10%per year?13Net Present Value(
11、NPV)14TtttTtrCINPVrCrCrCrCINPV10332210)1()1(.)1()1()1(Net Present Value(NPV)Cntd.where:Ct=the net cash receipt at the end of year tIo=the initial investment outlayr=the discount rate/the required minimum rate of return on investmentt=the project/investments duration in years.Decision rule:If NPV is
12、positive(+):accept the project If NPV is negative(-):reject the project15Net Present Value(NPV)Cntd.Self Assessment Question:A firm intends to invest 1,200 in a project that is expected to generate net receipts of 850,950 and 700 at the end of the first,second and third years respectively.Should the
13、 firm go ahead with the project if the discount rate is 12%?16AnnuityA set of cash flows that are equal in each and every period is called an annuity.PV=PVAF X ACFPVAF=Present Value of Annuity Factor(use table)ACF=Annuity cash flow17Annuity Cntd.Self Assessment QuestionA project requires an initial
14、investment of 125,000.It is expected to generate a net receipt of 17,500 at the end of each year during the 12 years life of the project.Calculate the NPV of the project with a discount rate of 12%.18PerpetuityA perpetuity is an annuity with an infinite life.It is an equal sum of money to be paid in
15、 each period forever.where:C=the sum to be received per periodr=the discount rate19rCPVPerpetuity Cntd.Self Assessment QuestionCalculate the PV of 25000 to be received at the end of every year for indefinite period of time if the discount rate is 15%.20Perpetuity with Growth21rategrowthgflowcashperp
16、etuitycWheregrgCPV:)1(Perpetuity with Growth Cntd.Self Assessment QuestionCalculate the PV of 25000 with an annual growth rate of 5%to be received at the end of every year for indefinite period of time if the discount rate is 15%.22Basic DataExpected Net Cash Flow(m)Year0123Project M(100)106080Proje
17、ct T(100)70502023Example-NET PRESENT VALUE Project L:r=10%0 1 2 3100.00 10 60 809.0949.59 60.11NPVM=18.79NPVT=19.98If the projects are independent,accept both.If the projects are mutually exclusive,accept Project T since NPVT NPVM.Note:NPV declines as r increases,and NPV rises as r decreases.24Inter
18、nal Rate of Return(IRR)The IRR is the discount rate at which the NPV for a project equals zero.This rate means that the present value of the cash inflows for the project would equal the present value of its outflows.The IRR is the break-even discount rate.The IRR is found by trial and error.25Intern
19、al Rate of Return(IRR)Cntd.26NPVIRRCIRRTttt0)1(0Example-Internal Rate of Return(IRR)rNPVMNPVT0%5040533 291019 20157 1220(4)527Example-Internal Rate of Return(IRR)Cntd.r=18.1%0 1 2 3100 10 60 80 8.4743.0248.570.06 0IRRM=18.1%IRRT=23.6%If the projects are independent,accept both:IRR r.Note:IRR is inde
20、pendent of the cost of capital.28Example-Internal Rate of Return(IRR)Cntd.29IRRM=18.1%IRRT=23.6%Crossover Point =8.7%Discount Rate(%)NPV(m)Comparison of NPV with IRR-Reinvestment rate assumption The NPV rule considers the market-determined opportunity cost of capital IRR assumes that investors can r
21、einvest their money at the IRR for each project.The implicit IRR assumption for reinvestment is hence weak.The IRR does not discount the cash flows at the opportunity cost of capital.30Comparison of NPV with IRR Multiple Rates of Return IRR can result in a multiple rates of return if the estimated c
22、ash flows change sign more than once.Example of an oil pump incremental cash flows year0=(1600);year1=10,000;year2=(10,000).Determine IRR.Descartes rule of signs:every time the cash flows change signs,there may be a new(positive,real)root to the problem solution.Solving the quadratic equation:IRR=25
23、%or 400%31210)1(000,10)1(000,10)1(16000IRRIRRIRRNPVThe Payback Method The number of years it takes to recover the initial cash outlay on a project Project is accepted if it pays back on or before the companys cut off payback period The payback method fails to take all project cash flows into account
24、 It also fails to consider the time value of money this shortcoming is overcome by applying the discounted payback method32The Payback Method cntd.Self Assessment Question:Determine the payback periods for the following two projects and provide a brief comment on your answer.Year012345C/flow(X)-1000
25、 100 900 100 -100 -400C/flow(Y)-1000 100 200 300 400 125033The Accounting Rate of Return(ARR)The ARR is the average after-tax profit divided by the initial cash outlay The project with a higher ARR is considered superior to a project with a lower ARR The ARR uses the accounting profit rather than ca
26、sh flows and ignores the time value of money.34The Accounting Rate of Return(ARR)cntdSelf Assessment Question:The following profits(losses)are reported for projects X and Y.Determine the ARR and provide a brief comment on your answer.Year012345Profit(X)-1000 100 900 100 -100 -400Profit(Y)-1000 100 2
27、00 300 400 125035Taxation in Investment Appraisal Project cash flows give rise to taxation which has an impact on project appraisal Capital allowances reduce the amount of tax organizations are required to pay and hence has to be considered in project appraisal The discount rate used for project app
28、raisal is effectively an after tax figure and the actual interest payment on a borrowing is ignored(since it is already provided for in calculating the cost of capital)Where a tax loss arises in a project,it is assumed that there are sufficient tax profits elsewhere in the organisation to reduce the
29、 tax paid36Inflation and Project Evaluation Real cash flows are discounted by a real discount rate Nominal cash flows are discounted by a nominal discount rate The following relationship is applied:(1+r)=(1+m)/(1+i)where r=real discount rate;m=money interest rate and i=rate of inflation.Money intere
30、st rates and cash flows include the effect of inflation Real interest rates and cash flows exclude the effects of inflation37Project Appraisal and TaxationExample:Monarch Ltd is considering manufacturing a new product.This requires machinery costing 20,000 with a life of four years and terminal valu
31、e of 5,000.profits from depreciation from the project will be 8000 per annum.An investment of working capital of 2,000 will be required for the duration of the project.Tax allowances on the machine are at 25%per annum reducing balance.At the end of the project life,a balancing charge or allowance wi
32、ll arise equal to the difference between the scrap proceeds and the tax written down value.Tax is payable at a rate of 35%.Tax cash flows on profits occur in the same year as the profits giving rise to the tax charge.The cost of capital is 15%.Should the project be accepted?38Project Appraisal and T
33、axation SolutionSteps:Calculate the effects on cash flows of the capital allowances Establish the project cash flows for each year Calculate the NPV of the project from these cash flows39Project Appraisal and Taxation SolutionCapital allowances():YearWritten down25%Capital 35%Tax value at startallow
34、ancesaving120,0005,0001,750215,0003,7501,313311,2502,81398548,4372,10973856,3284(sale value)5,000Balancing allowance=1,3284651,20340Project Appraisal and Taxation SolutionNet cash flows():Year01234Machine(20,000)Working capital (2,000)2,000Project profit8,0008,0008,0008,000Tax on profit(2,800)(2,800
35、)(2,800)(2,800)Tax saved C/All1,7501,313 9851,203Net cash flow(22,000)6,9506,513 6,18515,40341Lecture1 Capital BudgetingNPV calculation():YearNet cashDiscount Presentflow factor 15%value0(22,000)1.000(22,000)16,9500.8706,04726,5130.7564,92436,1850.6584,070415,4030.5728,811NPV 1,852Project is worthwh
36、ile.42Project Evaluation Incorporating Inflation-ExampleA project has the following anticipated cash flows before allowing for inflation(in current terms/in todays prices):YearCash flow0(750)133022423532These are not,therefore,the flows expected if all figures grow in line with inflation.The cost of
37、 capital has been calculated at 15.5%to include an allowance for inflation.The rate of inflation is expected to remain constant at 5%.You are required to evaluate the project in terms of:(a)real cash flows and discount rates;(b)money cash flows and discount rates.43Project Evaluation Incorporating I
38、nflation-Example(a)Real discount rates and cash flows:15.5%discount rate includes 5%expected inflationTo calculate real discount rate(r):(1+r)=(1+m)/(1+i)where m=money interest rate and i=rate of inflation.r=(1.155)/(1.05)1=10%.Discounting the cash flows()as per the question:YearCash flowPV factorPr
39、esent value0(750)1.000(750)1 3300.90930022420.82620035320.751400NPV15044Project Evaluation Incorporating Inflation-ExampleMoney discount rates and cash flows():Money discount rate=15.5%Increase cash flows at 5%compounded each year to allow for inflationYear0123Real cash flow(750)330242532Inflation f
40、actor11.05(1.05)2(1.05)3Money cash flow*(750)346267616Discount factor1.0000.8660.7500.649Present value(750)300200400NPV150i.e.,actual cash flowDiscount real cash flows using real discount rateDiscount money cash flow using money discount ratesIf a constant rate of inflation does not apply to all fac
41、tors,the best approach is to use money cash flows and money discount rates45Incremental Cash Flows Use relevant cash flows in project appraisal Incremental cash flows that arise as a result of accepting a project are relevant cash flows Ignore cash flows that could arise whether a project is accepte
42、d or not should be ignored Ignore sunk costs i.e.costs that are incurred before investment decision is made e.g.Research and development cost46Incremental Cash FlowsRelevant Costs Include:Direct cash outflows arising from the projectInfrastructure costs,such as the necessary cabling of new net work
43、connections required by the IT department to monitor the projectMarketing costs arising from carrying out the project,that would not have been incurred if the project had not been carried outHuman resources development needs,such as the training costs that have to be incurred to enable the workforce
44、 to work effectively on the projectRelevant Benefits:Direct cash inflows arising from the projectCash savings arising on other activities as a result of carrying out this project(e.g.Opportunity costs)47Opportunity Costs in Project Appraisal If there are scarce resources that would be required for a
45、 project(e.g.Labour,materials,machineries),their relevant cost should be their opportunity cost The variable cost of the resource plus the contribution foregone by not being able to use the resources in their next-most profitable way For example,skilled labour needed on a new project might have to b
46、e withdrawn from normal production causing a loss in contribution:Relevant cost in this case would be wage of the labour plus the contribution that would be lost on normal production48Opportunity Costs in Project AppraisalSelf Assessment Question 1:A new project requires the use of 50 tons of metal
47、ZX81.This metal is used regularly on all of the firms projects.There are 100 tons of ZX81 in inventory at the moment,which were bought for 200 per ton.The current purchase price is 210 per ton,and the metal could be disposed of for net scrap proceeds of 150 per ton.a)With what cost should the new co
48、ntract be charged for the ZX81?b)If the organisation has no use for the ZX81 in inventory,what is the relevant cost of using it on the new contract?49Opportunity Costs in Project AppraisalSelf Assessment Question 2:A mining operation uses skilled labour costing 4 per hour,which generates a contribut
49、ion,after deducting these labour costs,of 3 per hour.A new project is being considered which requires 5,000 hours of skilled labour.There is a shortage of the required labour.Any used on the new project must be transferred from normal working.What is the relevant cost of using the skilled labour on the project?50
