ACCA F9 课件 part D investment appraisal

1、Part D Investment Appraisal,DCF methods and valuation criteria,Capital Investment Appraisal,Interest 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 rec

2、eived or disbursed) The financial market and the supply of savings and the demand for loans in the economy determine interest rate level.,Interest,The interest rate is the opportunity cost of what the money invested could earn in the best alternative of the same risk class Since $100 today does NOT

3、equal $100 in one year, we need a method to compare money across different time periods.,Simple Interest(I= Pi) is when only the original amount invested earns interest. Compound Interest is when the subsequently accrued interest earns interest too(not just the original amount).,Compounding computes

4、 the future value of cash flows from the past. Future value of a lump sum: Compound-interest factor=,Discounting computes the present value of future cash flows. Present value of a lump sum: Discount factor=,an annuity is series of equal, fixed cash payment to be paid or received at a regular period

5、s.,Perpetuities,The Determinants of Interest Rates,The interest rate on a particular security is determined by four main factors: 1. Current investment opportunities and consumers preferences (short-term risk free interest rate or real interest rate) 2. Investor time preferences and future investmen

6、t opportunities (the term structure of interest rates) 3. Expected inflation (nominal versus real interest rate) 4. Risk level of the security (premium for risk),1. Short-term, risk-free, real interest rate,Is the price of money at which the demand for investment is equal to the supply of capital. T

7、his is the equilibrium market rate (supply=demand). “Loanable funds” theory: framework for interest rate determination.,“Loanable Funds”,“Loanable Funds”,The supply of capital is upward sloping. Savers are willing to save more as interest rates increase. Greater supply of funds available at higher i

8、nterest rates. The demand for investment is downward sloping. At lower interest rates, investors can afford to borrow and make more profits. 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 ra

9、te.,2. The term structure of interest rates,The term structure defines the relationship between the annualized interest rates on securities with different maturities. (1+kn) = (1+r1) (1+r2) . (1+rn), Where kn = current interest rate on a loan with n years to maturity.,n,On average, long-term interes

10、t rates are short-term interest rates. Savers 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. Borrowers have a greater demand to borrow lon

11、g-term to reduce uncertainty in their financing. Savers supply more money for short-terms and borrowers demand more funds for long-terms. Interest rate is set at the equilibrium point where the supply of funds equals the demand of funds.,Longer-term bonds are more sensitive to changes in market inte

12、rest 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.,Class example 1:,Interest rate is 10% for this year and 20% for nex

13、t year. If you invest $1 today, a) what is your rate of return at 2 years? b) What is the annual interest rate? Timeline: yr 0 yr 1 r1=10% yr 2 r2 = 20 % l l l today $1.10 $1.32,a) (1+kn) = (1+r1) (1+r2) (1+k2) = (1+0.10)(1+0.20) = b) Recall r = (1+i) 1 =,n,2,n,a) (1+kn) = (1+r1) (1+r2) (1+k2) = (1+

14、0.10)(1+0.20) =1.32 b) Recall r = (1+i) 1 =14.89% Proof: $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. Why do we annualize interest rates?,n,2,n,Class Example 2:,The interest rate on a 1-year bond is 6% and on a 2-year bond is 10%. Assuming you are indiff

15、erent 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? 1st What is the question asking? Indifferent means you would receive the same return. So we want to know what is r2? Form

16、ula: (1+kn) = (1+r1) (1+r2),n,Sentence: 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.,3. Expected inflation,Is the rate of change in prices of a representative “basket” of commodities (a c

17、ommon 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 + i,4. Risk,The interest rate that a firm must commit to on their debt increases with the risk of default as perceived by investors.

18、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.,Class example 4:,A firm borrows

19、$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? 1st What is the interest required? $1,000 x 9% Interest required = Probability (interest): 0.95 (I) + .05(0) = $90; Out of 100 loans, 95 will earn $94.74 and 5 will e

20、arn $0. Thus averaging $90 Proof: (95 x $94.74)/100 = $90.,2nd To get interest of $94.74 on $1,000 original investment, Interest rate = interest / original investment = $94.74/$1,000 =9.474%,Basic Principles Required and Tested,Simple V compound interest Nominal V effective interest rates-D/05 Compo

21、unding and discounting PV r = 10%; n = 12 years (30-18); Formula method: 100,000 = A (1 - (1+0.1)-12)/0.1 A = 100,000/6.8137 = $14,676.31 Sentence: The son can take out $14,676.33 at the end of each year.,b) What are we trying to determine? At end so ordinary annuity and we want to determine the tim

22、e, n. In this case, the $100,000 is the FV. Formula method: 100,000 = A (1+0.1)18 - 1)/0.1 A = 100,000/45.5992 = $2,193.02 Sentence: The parents would have invested $2,193.02 at the end of each year. back,The cost of capital is the minimum after-tax rate of return the firm must earn on new investmen

23、t (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. back,Investment,Investment is any expenditure in the expectation of future benefits -capital expenditure Incur to acquire and improve earning capacity of

24、a non-current asset. -revenue expenditure For the purpose of the trade of the business or to maintain the existing earning capacity of the non-current assets,The capital budgeting decision process,The process of Identifying Analysing Selecting investment projects The capital budgeting entails decisi

25、ons on how to allocate funds across potential new capital assets (ex: new products, plants, equipment).,The investment decision-making process,Origination of proposals Project screening Analysis and acceptance Monitoring and review,Relevant cash flows to evaluate in capital budgeting,Four Rules when

26、 estimating project cash flows: 1. 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 divid

27、ends and investments,2. 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),3. Nominal cash flo

28、ws : 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 inflation,4. After-tax cash flows : Shareholders ca

29、n 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 rat

30、e (avoid double counting),Capital budgeting evaluation criteria,1.Net Present Value (NPV): NPV is a discount cash flow method. It meets two critical requirements for any capital budgeting rule: 1. Accounts for the time value of money 2. Considers all relevant cash flows,NPV is the sum of all discoun

31、ted 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.,Accepted positive NPV project,The objective of a financial executive is to maximize shareholder wealth/share price. Given this objective, the financial exec

32、utive 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. Thus, NPV rule (accept positive NPV projects, subject to capital rationing constraints) is the correct capital budgeting criterion sinc

33、e it coincides with the objective of maximizing shareholder wealth.,Class 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? Recall perpetu

34、al formula: PV = return/interest = $500/0.05 = $10,000. Thus the NPV = 9,500 (cost) + 10,000 (PV of future cash flow) = 500,Note : as a DCF method, it is the NPV at some level of discount rate (market interest rate, cost of capital, etc.),2. The Internal Rate of Return (IRR) is another discount cash

35、 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.,The IRR criterion is to accept a project if the IRR the pr

36、ojected risk adjusted discount rate, k. IRR is the interest rate at which NPV equals zero.,In equation form, IRR is the rate at which where C is the cost of the project t is the time frame k is the interest rate = IRR,Usually NPV and IRR criteria are consistent. Advantage: easy to understand a perce

37、ntage return.,Two 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 0 using 13%, thus project is rejected so IRR rule failed. This occurs when there is a change in direction of futu

38、re cash flows (net loss, net income, net loss, etc.),2. Crossing NPV profiles 2 mutually exclusive projects, choose one with highest IRR but NPV higher with project with lower IRR, IRR misleading. Occurs when the PV profiles of 2 projects cross over at some rate beyond or to the right of the k .,Rel

39、iance on the IRR approach implies that funds released from any project can be reinvested at that particular projects IRR The NPV method, implies that flows released from any project are reinvested at the discount rate that was used in calculating its NPV. The conflicts may occur because of a differe

40、nce in scale between projects , as the NPV as an absolute measure of investment worth varies with the size of the investment whereas the IRR as a relative measure remains unaffected.,3. The payback period,The payback period (PBP) measures the length of time that is required for expected after-tax ca

41、sh inflows to recover the initial cost of the project.,Ex: Project A generates $2,000/yr for 6 yrs and then $500/yr for the next 4 years. Project B generates $1,000/yr for 5 yrs, and then $6,000/yr for the next 5 yrs. Initial cost of each project is $10,000. Which project will you pick if the paybac

42、k period is 5yrs?,Payback: Cost = 10,000 therefore, determine when each project makes the $10,000 by. Project A: 2,000 +2,000 + 2,000 + 2,000 + 2,000 = 10,000 Thus 5 years. Project B: (1,000 x 5 years) + 6,000 = 11,000. Reach 10,000 between 5 and 6th year. Thus choose Project A as will reach $10,000

43、 sooner.,Disadvantages: - does not consider the time value of money - do not discount cash flows (no present values) - ignores all cash flows beyond the payback period - no standard to determine how many years is acceptable for payback period (1, 5, 10 years?),Advantages: - easy to understand how lo

44、ng before the project is in the black.,The profitability index (PI),The profitability index (PI) or benefit-cost ratio is the total present value of future cash flows divided by the initial investment in the project (GPV/cost). Project is acceptable if the PI 1, rejected if PI 1. PI will accept/reje

45、ct the same projects as NPV rule.,Disadvantage: provides no help in selecting projects under capital rationing conditions Advantages: PI rule is intuitive PI is the dollar-to-dollar return you obtain on a project,Capital Rationing,General method used to select projects when there is a constraint on

46、the amount of capital the firm can spend on new projects.,Capital rationing exists when the firm has generated more positive NPV projects than it can adopt due to a shortage of funds. Under capital rationing, how should you choose the best projects? - First try to sell the idea or form a joint ventu

47、re. - If cannot, use the PI method to rank projects, go down list until you exhaust your investable funds.,Problem: still have funds left but next projects initial investment exceeds total budget. Not utilizing full investment budget Solution: Use brute force method up to capital spending ceiling, a

48、ccepting the basket of projects that yields the highest combined NPV.,Class example,Four potential projects, Capital budget is $200: Project Initial. Invest. GPV NPV PI A $60 90 30 1.50 B 110 145 35 1.32 C 95 115 20 1.21 D 25 30 5 1.20 PI method: no rule to determine where to go next,Brute Force met

49、hod: -List all combinations/packages - Calculate required initial investment, if exceeds budget, throw out. -Pick the package with the highest NPVs:,Packages: A $60/30, B $110/35, C $95/20, D $25/5, AB $170/65, AC $155/50, AD $85/35, BD $135/40, CD $120/25, ABD $195/70, ACD $180/55 Note packages BC,

50、 ABC, BCD, ABCD costs $200 thus throw out.,The return on capital employed,The pilot paper states the ROCE should be based on the average investment Page 189,Advantages: Quick and simple Percentage return, easy to understand Looks at the entire project life Disadvantages: Based on accounting profits

51、,not cash flows Relative measure Take no account of time, so Ignore time value of the money,DCF method,The cost of capital A firms cost of capital is the cost of raising additional investment capital, in terms of required payments to investments.,Two viewpoints:,from the viewpoint of the financing f

52、irms 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.,from the viewpoint of the investors the cost of capital is an opportunity c

53、ost. 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.,The cost of capital is the required return on a dollar contributed today, thus, it reflects current market costs and values. The cos

54、t 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.,Summary The cost of capital is the minimum after-tax rate of return the firm must earn on new investment (i

55、n its own risk class) to just compensate the firms investors with their required rates of return. The cost of capital is an opportunity cost.,Project Appraisal Allowing for Inflation and Taxation,The real rate of return, is the return in constant price level term In inflating environment, use the mo

56、ney rate of return (nominal rate of return) Ex. Invest 1000 for one year, required rate of return is 20%, the inflation is expected to be 10% Then 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 go

57、t (1+money rate)=(1+real rate)(1+inflation rate),(1+money rate)=(1+real rate)(1+inflation rate) Equals to Money rate = real rate + inflation rate +real rateinflation rate,Which rate is used for cash flows?,The rules as follows: -The cash flows expressed in terms of the actual number of dollars on fu

58、ture dates, use nominal rate -The cash flows expressed in terms of the value of dollars at time 0( in constant price level terms), use real rate,Capital Allowances,What are capital allowances? Are used to reduce taxable profits, results in the reduction of tax payment, so it should be treated as a c

59、ash saving when accept the project. Depreciation in accounting, allowance(WDA) in taxation When the asset is sold Sale price reducing balance= taxable profit (balancing charge) Sale price reducing balance=tax allowable loss (balancing allowance),How do capital allowances affect cash flows? - Capital allowances reduce tax payment, considered as cash flow in. Do NOT