ACCA F9 课件 part D investment appraisal

By Azurelai2Capital Investment Appraisal nInterest is the price that the borrower pays to the lender for the temporary use of money- therefore money has a time value(i.e. the economic value of a given amount of money depends on when the money was received or disbursed)n The financial market and the supply of savings and the demand for loans in the economy determine interest rate level.By Azurelai3Interestn The interest rate is the opportunity cost of what the money invested could earn in the best alternative of the same risk classn Since $100 today does NOT equal $100 in one year, we need a method to compare money across different time periods.By Azurelai4n Simple Interest(I= Pi) is when only the original amount invested earns interest.nCompound Interest is when the subsequently accrued interest earns interest too(not just the original amount).By Azurelai5nCompounding computes the future value of cash flows from the past.Future value of a lump sum:Compound-interest factor=nnrPVFV)1 ( nr)1( By Azurelai6nDiscounting computes the present value of future cash flows.Present value of a lump sum:Discount factor=nr)(1nFVPVnr)1 (By Azurelai7n an annuity is series of equal, fixed cash payment to be paid or received at a regular periods.1)1 (rrAFVn)1 (1rrAPVnBy Azurelai8nPerpetuitiesrAPV/By Azurelai9The Determinants of Interest RatesnThe interest rate on a particular security is determined by four main factors:n1. Current investment opportunities and consumers preferences (short-term risk free interest rate or real interest rate)n2. Investor time preferences and future investment opportunities (the term structure of interest rates)n3. Expected inflation (nominal versus real interest rate)n4. Risk level of the security (premium for risk)By Azurelai101. Short-term, risk-free, real interest ratenIs the price of money at which the demand for investment is equal to the supply of capital. This is the equilibrium market rate (supply=demand).n“Loanable funds” theory: framework for interest rate determination.By Azurelai11“Loanable Funds”By Azurelai12“Loanable Funds”nThe supply of capital is upward sloping. Savers are willing to save more as interest rates increase. Greater supply of funds available at higher interest rates.nThe demand for investment is downward sloping. At lower interest rates, investors can afford to borrow and make more profits.n where the supply slope and demand slope meet, is the point where the demand for investment is equal to the supply of capital. This is the equilibrium market rate. By Azurelai132. The term structure of interest ratesnThe term structure defines the relationship between the annualized interest rates on securities with different maturities.n(1+kn) = (1+r1) (1+r2) . (1+rn), nWhere kn = current interest rate on a loan with n years to maturity.nBy Azurelai14nOn average, long-term interest rates are short-term interest rates.nSavers supply less funds for long-term loans because they prefer short-term loans so they can cash in sooner (i.E. Liquidity preference). Thus a higher interest rate is needed to get savers to lend for longer terms.n Borrowers have a greater demand to borrow long-term to reduce uncertainty in their financing.n Savers supply more money for short-terms and borrowers demand more funds for long-terms.n Interest rate is set at the equilibrium point where the supply of funds equals the demand of funds.By Azurelai15nLonger-term bonds are more sensitive to changes in market interest rates than shorter-term bonds (PV concept). The longer it is to maturity, the lower the present value. Recall we use the market interest rate to calculate the present value, thus it has a direct effect on the price of the bond.By Azurelai16Class example 1:nInterest rate is 10% for this year and 20% for next year. If you invest $1 today, a) what is your rate of return at 2 years? b) What is the annual interest rate?nTimeline:nyr 0 yr 1 r1=10% yr 2 r2 = 20 %nl l lntoday $1.10 $1.32By Azurelai17na) (1+kn) = (1+r1) (1+r2)n(1+k2) = (1+0.10)(1+0.20) =nb) Recall r = (1+i) 1 =n2nBy Azurelai18na) (1+kn) = (1+r1) (1+r2)n(1+k2) = (1+0.10)(1+0.20) =1.32nb) Recall r = (1+i) 1 =14.89%nProof: $1 x 1.1489 = $1.1489 at the end of year 1. $1.1489 x 1.1489 = $1.32 at the end of year 2.nWhy do we annualize interest rates?n2nBy Azurelai19Class Example 2:nThe interest rate on a 1-year bond is 6% and on a 2-year bond is 10%. Assuming you are indifferent between investing in the 2-year bond or investing in the 1-year bond and reinvesting at the end of one year for another year. What is the expected interest rate for year 2?n1st What is the question asking? Indifferent means you would receive the same return. So we want to know what is r2?nFormula: (1+kn) = (1+r1) (1+r2)nBy Azurelai20nSentence: If interest rate is 14.15% in year 2, we would be indifferent to invest in the 1-year or 2-year bond, as the return at the end of year 2, $1.21, is the same.By Azurelai213. Expected inflationn Is the rate of change in prices of a representative “basket” of commodities(a common yardstick is the change in Consumer Price Index) Nominal interest rate, k, is composed of real risk-free interest rate, r, plus an inflation component, i; k = r + iBy Azurelai224. RisknThe interest rate that a firm must commit to on their debt increases with the risk of default as perceived by investors.n Risk of default has 2 effects: 1. In order to receive a given expected return, the nominal interest rate must be the expected return to adjust for the possibility of non-payment. 2. Since investors are risk-averse, they will demand a risk premium on risky securities.By Azurelai23Class example 4:nA firm borrows $1,000 for one year and the lender requires a 9% return. There is a 5% chance of default. What interest rate will the lender require?n1st What is the interest required? $1,000 x 9%n Interest required = Probability (interest): 0.95 (I) + .05(0) = $90; Out of 100 loans, 95 will earn $94.74 and 5 will earn $0. Thus averaging $90Proof: (95 x $94.74)/100 = $90.By Azurelai24n2nd To get interest of $94.74 on $1,000 original investment, Interest rate = interest / original investment = $94.74/$1,000 =9.474%By Azurelai25Basic Principles Required and TestednSimple V compound interestnNominal V effective interest rates-D/05 nCompounding and discounting PV & FVnUse of annuities and perpetuitiesnImportance of time value of moneynRole of cost of capital in appraisal investmentBy Azurelai26Stated & Effective Interest Rate for Varying Compound IntervalsnInterest rates are, by convention, quoted in annual terms. However, the compounding interval can vary. By convention, an account that pays 10% (stated) interest but is compounded quarterly is treated as follows:n10% annually is 10 4 = 2.5% per quarternand cash in the account is compounded quarterly:n$1 after 1 quarter= 1(1.025)= $1.0250n$1 after 2 quarters= 1(1.025)2= $1.0506n$1 after 3 quarters= 1(1.025)3= $1.0769n$1 after 1 year= 1(1.025)4= $1.1038nNote that after one year the balance is $1.1038, for an effective return of 10.38% (more than the stated 10% rate). By Azurelai27nShorter compounding intervals raise the effective annual interest rate nEXAMPLE nYou can earn an effective annual interest rate of 7%. What is the present value of three $10 payments to be received in 3, 6, and 9 months?n By Azurelai28nTo calculate the present value, it is necessary to determine the effective interest rate for a three-month interval (quarter). To do this, define q as the effective quarterly interest rate. In other words, if you earn at rate q for four quarters, you would earn 7% for the year:n(1 + q)4=1.07nq=(1.07)1/4 1nq=0.0171, or 1.71%n nThus, earning an effective quarterly interest rate of 1.71% is equivalent to earning an effective annual interest rate of 7%. Then:By Azurelai29nPV =10 (1.0171) + 10 (1.0171)2 + 10 (1.0171)3n=9.83 + 9.67 + 9.50n=$29.00nYou can therefore always convert from our annual opportunity cost of funds to any periodic effective interest rate.nbackBy Azurelai30Annuity and perpetuity nAn annuity is a fixed cash payment received at regular intervals for some limited length of time. ordinary annuities, is defined as an annuity paid or received at the end of the interest compounding period. By Azurelai31nupposer = 5%, then:n1 (1 + r) + 1 (1 + r)2 + 1 (1 + r)3= 0.9524 + 0.9070 + 0.8638n= 2.7232n nNote carefully the notation anr%. In this example, the notation is a35%, which translates to three years at 5%. By Azurelai32Example nOn your sons 18th birthday, you have saved $100,000 for his education. Interest rate is10% and your son plans to become a specialist in the field of medicine so he is expected to be 30 years old when he is done.na) What fixed amount of money can be taken out at the end of each year for his education?nb) How much did the parents have to save at the end of each year from their sons birth in order to accumulate $100,000 on their sons 18th birthday? Interest rate is still 10%.By Azurelai33nSoln:na) 1st Determine what type of annuity? Payment made at end so ordinary annuity.nWhat do we need to determine? The payments.nWhat information do we know: PV = $100,000; r = 10%; n = 12 years (30-18);nFormula method:n100,000 = A (1 - (1+0.1)-12)/0.1nA = 100,000/6.8137 = $14,676.31nSentence: The son can take out $14,676.33 at the end of each year.By Azurelai34nb) What are we trying to determine? At end so ordinary annuity and we want tondetermine the time, n. In this case, the $100,000 is the FV.nFormula method: n100,000 = A (1+0.1)18 - 1)/0.1nA = 100,000/45.5992 = $2,193.02nSentence: The parents would have invested $2,193.02 at the end of each year.nbackBy Azurelai35The cost of capital is the minimum after-tax rate of return the firm must earn on new investment (in its own risk class) to just compensate the firms investors with their required rates of return. The cost of capital is an opportunity cost.backBy Azurelai36InvestmentnInvestment is any expenditure in the expectation of future benefitsn-capital expenditureIncur to acquire and improve earning capacity of a non-current asset.n-revenue expenditureFor the purpose of the trade of the business or to maintain the existing earning capacity of the non-current assetsBy Azurelai37The capital budgeting decision processnThe process of nIdentifying nAnalysing nSelecting investment projectsnThe capital budgeting entails decisions on how to allocate funds across potential new capital assets (ex: new products, plants, equipment).By Azurelai38The investment decision-making process nOrigination of proposalsnProject screening nAnalysis and acceptancenMonitoring and reviewBy Azurelai39Relevant cash flows to evaluate in capital budgetingFour Rules when estimating project cash flows:n1. Actual cash flows, not accounting income : Accounting income includes non-cash expenses (ex: amortization) and includes allocated overhead cost (ignore if not incremental) : Shareholders only concerned with actual cash flow because that is what is used to pay dividends and investmentsBy Azurelai40n2. Incremental cash flows : Ignore sunk costs any expenditures made PRIOR to capital budgeting decision and can not be reclaimed : Include opportunity costs charge resources that sit idle and/or have alternative uses to the new project (lost opportunity cost)By Azurelai41n3. Nominal cash flows : Inflation must be incorporated in both the estimate of future cash flows generated from the project and the discount rate used to determine cost of capital for proper comparison : Thus, use nominal rates and market yields that reflect expected inflationBy Azurelai42n4. After-tax cash flows : Shareholders can only benefit from after-tax cash flows (dividends, capital gains) : Different projects have different tax exposures (ex: tax credits, Govt grants to encourage certain investments) : Do not include financial charges associated with financing of a project as they are incorporated in the discount rate (avoid double counting)By Azurelai43Capital budgeting evaluation criterian1.Net Present Value (NPV):nNPV is a discount cash flow method. It meets two critical requirements for any capital budgeting rule: n 1. Accounts for the time value of moneyn 2. Considers all relevant cash flowsBy Azurelai44nNPV is the sum of all discounted cash flows generated by a project. It represents the economic gain from the project and thus it measures the increase in value to the firm.ntttKC0)1(By Azurelai45Accepted positive NPV projectnThe objective of a financial executive is to maximize shareholder wealth/share price.n Given this objective, the financial executive should choose new investments that increase share price. Projects with positive NPVs translate into an increase in firms value equal to the amount of the NPV.n Thus, NPV rule (accept positive NPV projects, subject to capital rationing constraints) is the correct capital budgeting criterion since it coincides with the objective of maximizing shareholder wealth.By Azurelai46nClass example : A new project will pay a risk-free, perpetual after tax cash flow of $500/yr and the current cost of this project is $9,500. If firms value is $100,000 and risk-free rate is 5%, is this a good project?nRecall perpetual formula: PV = return/interest = $500/0.05 = $10,000.nThus the NPV = 9,500 (cost) + 10,000 (PV of future cash flow) = 500By Azurelai47nNote : as a DCF method, it is the NPV at some level of discount rate (market interest rate, cost of capital, etc.)By Azurelai48n2. The Internal Rate of Return (IRR)nis another discount cash flow method that calculates the break-even rate of return on the project such that the NPV = 0.In other words, by definition, the IRR is the rate of discount that when applied to the cash flows of an investment, will yield a net PV of ZERO.By Azurelai49nThe IRR criterion is to accept a project if the IRR the projected risk adjusted discount rate, k.nIRR is the interest rate at which NPV equals zero.By Azurelai50nIn equation form, IRR is the rate at whichnwhere C is the cost of the projectn t is the time framen k is the interest rate = IRRntttkC0)1 (By Azurelai51nUsually NPV and IRR criteria are consistent.nAdvantage: easy to understand a percentage return.By Azurelai52nTwo complications that occur when using IRR are: 1. Multiple IRRs which one do you use? Neither Ex: 2 IRRs: 15% & 50% both solve equation (NPV = 0), k = 13%, both k but NPV 1, rejected if PI $200 thus throw out.By Azurelai68The return on capital employednThe pilot paper states the ROCE should be based on the average investmentnPage 189%100investment itialaverage/in estimatedprofits talaverage/to estimatedROCEBy Azurelai69nAdvantages:nQuick and simplenPercentage return, easy to understandnLooks at the entire project lifenDisadvantages:nBased on accounting profits ,not cash flowsnRelative measurenTake no account of time, so Ignore time value of the moneyBy Azurelai70DCF methodThe cost of capital nA firms cost of capital is the cost of raising additional investment capital, in terms of required payments to investments.By Azurelai71Two viewpoints:nfrom the viewpoint of the financing firms the cost of capital is the cost in terms of required payments to investors of raising additional investment capital. That is, Management of the firm set the cost of capital to induce the investors to invest in the firm.By Azurelai72nfrom the viewpoint of the investorsthe cost of capital is an opportunity cost. That is investors determine what they could earn if they did not invest in the firm and demand at least the same return from the firm that they can get elsewhere.By Azurelai73nThe cost of capital is the required return on a dollar contributed today, thus, it reflects current market costs and values.nThe cost of capital is the after-tax cost, in terms of required payments to investors, of raising new funds. that the cost of capital is an appropriate hurdle rate for new capital budgeting projects.By Azurelai74nSummarynThe cost of capital is the minimum after-tax rate of return the firm must earn on new investment (in its own risk class) to just compensate the firms investors with their required rates of return. The cost of capital is an opportunity cost.By Azurelai75Project Appraisal Allowing for Inflation and TaxationnThe real rate of return, is the return in constant price level termnIn inflating environment, use the money rate of return (nominal rate of return)nEx. Invest 1000 for one year, required rate of return is 20%, the inflation is expected to be 10%nThen after one year, the initial investment must increase to 1200, in todays value term, equals to 1091(1200/1.10), so the real rate of return is 9.1%,weve got n(1+money rate)=(1+real rate)(1+inflation rate)By Azurelai76n(1+money rate)=(1+real rate)(1+inflation rate)nEquals to Money rate = real rate + inflation rate +real rateinflation rateBy Azurelai77Which rate is used for cash flows?nThe rules as follows:n-The cash flows expressed in terms of the actual number of dollars on future dates, use nominal raten-The cash flows expressed in terms of the value of dollars at time 0( in constant price level terms), use real rateBy Azurelai78Capital AllowancesnWhat are capital allowances?nAre used to reduce taxable profits, results in the reduction of tax payment, so it should be treated as a cash saving when accept the project.nDepreciation in accounting, allowance(WDA) in taxation nWhen the asset is soldnSale price reducing balance= taxable profit (balancing charge)nSale price reducing balance=tax allowable loss (balancing allowance) By Azurelai79nHow do capital allowances affect cash flows?n- Capital allowances reduce tax payment, considered as cash flow in.nDo NOTE that:nCapital allowance is not a cash flow in NPV calculation, it is the tax benefit of capital allowance included in NPV calculation.nCost savings will arise tax payment By Azurelai80nWhen taxation is ignored in DCF calculations ,the discount rate use PRE-tax rate of returnnWhen taxation is included in, use a POST-tax required rate of rateBy Azurelai81Project Appraisal Allowing for RisknRisk VS uncertainty-d/04n-TX p228nSystematic risk VS unsystematic riskn-Interest rate set by the central bank vs rate of return of each stock By Azurelai82Methods of dealing with decision-making under risk and uncertaintynSensitivity analysis- computation, strength and weakness J/03, D/04nProbabilities and expected values-advantages and limitationsnPrecise measure of risk- standard deviation and coefficient of variation nSimulation modelsBy Azurelai83Sensitivity AnalysisnUncertain independent variables:n-Selling pricen-Sales volumen-Cost of capital n-Initial costn-Operating costsn-benefitsnBefore NPV turn to negative, the extent of those variables may changeBy Azurelai84nSensitivity= NPV n present value of project variablenThe lower the percentage, the more sensitive is the NPV to the variable. (change small amount in this variable will make a great amount difference in NPV)By Azurelai85Probabilities and Expected Values AnalysisnStepsn1. Calculate an expected value of the NPVn2. Measure riskn-The worst possible outcome & its probabilityn-The probability of failing to achieve a positive NPVn-The standard deviation of the NPV2)(xxpsBy Azurelai86LeasingnOperating VS finance leasenOperating lease- lessor retains most of the risks and rewards of ownershipnFinance lease- transfer substantially all of the risks and rewards of ownership of an asset to the leasee. The agreement last for most or all of the assets expected useful life.By Azurelai87nApply DCF methods to projects involving buy or lease problemsnD/02, d/03, j/05nShould you borrow money to buy or to lease? -Cost of capital (investment decision) / cost of borrowing Lease period rent tax P1 0 22 1 33 2 44 3 5By Azurelai88Asset replacement decisionsnUse the equivalent annual cost methods to calculate an optimum replacement cyclenUse annuity PV formula By Azurelai89Sinking Funds nUsed for assets replacement n repay a loann repay mortgagen repay debtsnTh