Business Finance Lecture 9

Lecture 9: Net present value and other investment criteria Net present value Terms ! Net present value Ñ the difference between an investmentÕs market value and its cost. ! Discounted cash ßow valuation Ñ the process of valuing an investment by discounting its future cash ßows. ! Mutually exclusive investments Ñ a situation where taking one investment prevents taking the other. ! Lecture example 1 • • • • • • Cash revenues from a fertiliser business will be £20,000 per year ! Cash costs (including taxes) will be £14,000 per year ! We shall wind down the business in 8 years ! Plant, property and equipment will be worth £2,000 as salvage at that time ! The project costs £30,000 to launch ! We used 15% discount rate on new projects such as this one ! Step 1: Draw a timeline and add cash ßow data ! Step 2: Choose appropriate formula to discount the cash ßows ! Annuity for 8 years Final single cash flow £2   Step 3: Calculate present value and then NPV ! The total present value of future cash ßows is: ! PV annuity + PV single cash ßow: PV of an annuity (present value of future cash ßows) = C/r x [(1 Ñ (1/(1+r)^t] ! PV = FV/(1+r)^t! :. C/r x [(1 Ñ (1/(1+r)^t] + FV/(1+r)^t! £6,000 x [1 Ñ (1/1.158)]/0.15 + (2,000/1.158) ! = (£6,000 x 4.4873) + (2,000/1.158)! = £26,924 + 654! = £27,578! When we compare this to the £30,000 estimated cost, we see that the NPV is: ! NPV = Ñ£30,000 + £27,578! = Ñ£2,422 ! The NPV is negative, so you would have to REJECT the project. ! ! The NPV decision ! Accept Reject • NPV%is%greater% than%zero • NPV%is%less%than% zero Strengths of NPV ! • Uses cash ßows Ñ cash ßows are better than earnings. ! • Uses ALL cash ßows Ñ other approaches ignore cash ßows beyond a certain date. ! • Discount cash ßows Ñ fully incorporates the time value of money. ! The most important strength of NPV is that it gives you a Þgure for the value created for shareholders. This is important as businessesÕ main aim is to maximise shareholder value. ! The Payback Rule Payback periodÑ the amount of time required for an investment to generate cash ßows sufficient to recover its initial cost. ! The payback decision ! Accept Payback(period(is(less( than(benchmark Reject • Payback(period(is( greater(than(benchmark   In order to Þnd at what speciÞc time money is being paid back, you must do: Sum of all cash ßows until year it is being repaid/sum in year after repayment + number of years. ! Lecture example 2 A company only accepts projects with a payback period of 2 years or less. The company is evaluating a project which has the following cash ßows:! Initial investment (time 0): £62,000! Cash inßow year 1:) ) £30,000! Cash inßow year 2:) ) £20,000! Cash inßow year 3:) ) £10,000! Cash inßow year 4:) ) £5,000! a) Should this project be accepted based on the payback criteria?! b) Calculate the payback period for this project.! Remember: Unless told otherwise, cash ßows should be assumed to arise at the end of the year in all discounted cash ßow questions.! Step 1: Draw a timeline ! - £62,000 Answer: ! a) After 2 years, the project has only repaid £50,000 of the initial outlay of £62,000, so it has to be REJECTED. ! b) The payback period for this project is between 3 and 4 years. After 3 years, the amount outstanding is £2,000 (062K + 30K + 20K = Ñ2K). The next cash inßow in year 4 is £5,000. So the payback period is 3 years + £2,000/£5,000 = 3.4 years. ! Comparing projects using payback ! Payback decisions Accept the project(s) with the shortest payback, as long as the payback is within the companyÕs maximum payback limit. ! Lecture example 3 Evaluate the following projects using the payback period rule for a company that does not accept projects with a payback above 4 years.!   Accept project A as it has a playback period of 2.6 years. (2 years + 30/50 = 2.6 years).! Projects C and D have a longer payback period of 4 years. If the projects are mutually exclusive (meaning only one can be accepted), accept project A as it has a lower payback period. Projects B and E never repay the amount invested, so reject. ! Advantages and disadvantages of the payback period rule ! Advantages Disadvantages 1. Easy to understand ! 1. Ignores the time value money Ñ does not 2. Adjusts for uncertainty of later cash ßows Ñ i.e. consider discounted values! adjusts for the extra riskiness of later cash ßows 2. Requires an arbitrary cut-off point Ñ there is no (Ôwiggle roomÕ) ! guide to how to pick the cut off point, so it ends 3. Biased towards liquidity Ñ it favours up being arbitrarily chosen ! investments that free up cash for other uses 3. Ignores cash ßows beyond the cut-off point Ñ quickly there might be proÞtable long-term investments in a later period ! 4. Biased against long-term projects, such as research and development, and new projects The Discounted Payback DeÞnition ! Discounted payback Ñ the length of time required for an investmentÕs discounted cash ßows to equal its initial cost. ! The discounted payback method is a variation of the payback period, and was developed to Þx the problem of time-value which is ignored in the normal payback calculation. ! Discount payback rule ! Accept Reject • Discounted,payback, period,is,less,than, benchmark • Discounted,payback, period,is,greater,than, benchmark Lecture example 4 Project 2 has an initial outlay of $300,000. It is expected to generate the following cash ßows: ! Year 1 $150,000! Year 2 $120,000! Year 3)$80,000! Year 4)$40,000! Year 5)$30,000! Year 6)$20,000!   Required: Evaluate the project using discounted payback. The company uses a cut-off point of 4 years and has a cost of capital of 10%. ! In order to Þnd the discounted net cash ßows and then the present values, you must divide the net cash ßow by the discount factor. ! Answer: under discounted payback, the funds are repaid in year 3, so ACCEPT. The discounted payback period is 2.86 years (2 + 64.46 / 75.13 = 2.86). ! Advantages and disadvantages of discounted payback rule ! Advantages 1. Includes time value of money (i.e. discounted values) ! 2. Easy to understand ! 3. Does not accept negative estimated NPV investments ! 4. Biased towards liquidity Ñ it favours investments that free up cash for other uses quickly Disadvantages 1. My reject positive NPV investments ! 2. Requires an arbitrary cut-off point Ñ there is no guide to how to pick the cut off point, so it ends up being arbitrarily chosen ! 3. Ignores cash ßows beyond the cut-off point Ñ there might be proÞtable long-term investments in a later period ! 4. Biased against long-term projects, such as research and development, and new projects The Average Accounting Return Average Accounting Return Ñ an investmentÕs average net income divided by its average book value. ! There are a number of different deÞnitions used for average accounting return (ARR). ! AAR is always: Some measure of average accounting proÞt ! Some measuring of average accounting value ! AAR = Average net income ! Average book value ! Lecture example 5 Decision on whether or not to open a new store. The required investment in improvements is £500,000. Other relevant information: !   • The store has a 5 year life, reverts to mall owners after this ! • The required investment would be 100% depreciated (straight-line) over 5 years: = £500,000/5 = £100,000 per year ! • The tax rate is 25%! • The projected revenues and expenses are speciÞed in the table below ! Average book value will be the initial cost of the investment (500,000) + the value at the end of period (0). Hence, the answer for this as shown above, will be £250,000. As long as we use straight-line depreciation, the average investment will always be one-half of the initial investment. ! ' From the table, we can also see that net income is £100 in year 1, £150,000 in year 2, £50,000 in year 3, 0 in year 4 and Ñ£50,000 in year 5. Hence: ! [£100,000+£150,000+£50,000+0Ñ£50,000]/5! = £50,000! Answer: AAR = Average net income = £50,000 = 20%! ) ) Average book value £250,000! AAR decision rule ! Accept • Average(accounting( return(is(greater(than( target(return Reject • Average(accounting( return(is(less(than( target(return   Advantages and disadvantages of AAR ! Advantages Disadvantages 1. Easy to calculate ! 2. Needed information will usually be available 1. Not a true rate of return; time value of money is ignored (i.e. discounted values when calculating the average net income) ! 2. Uses an arbitrary benchmark cut-off rate ! 3. Based on accounting (book) values, not cash ßows and market values The Internal Rate of Return DeÞnition ! Internal rate of return Ñ the discount rate that makes the NPV of an investment zero.! With the IRR, we try to Þnd a single rate of return that summarises the merits of a project. Furthermore, we want this rate to be an ÔinternalÕ rate in the sense that it depends only on the cash ßows of a particular investment, not on rates offered elsewhere. Using this method allows businesses to have some ßexibility as it leaves some wiggle room. ! Unknown discount values ! For these types of calculations, it will often be the case that the discount rate is unknown. This presents a problem, but we can still ask how high the discount rate would have to be before this project was deemed unacceptable. We know that we are indifferent between taking and not taking this investment when its NPV is just equal to zero. In other words, the investment is economically a break-even proposition when the NPV is zero, because value is neither created nor destroyed. To Þnd the break-even discount rate, we set NPV equal to zero and solve for R. ! ! Decision rules for internal rate of return (IRR) ! Accept Reject • Internal)rate)of) return)is)greater)than) discount)rate • Internal)rate)of) return)is)less)than) discount)rate Lecture example 6 An investment costs £100 and has a cash ßow of £60 per year for 2 years. What is the investmentÕs internal rate of return? ! Find the discount rate ÔIRRÕ where the NPV is zero. That is, solve for ÔIRRÕ in the equation below: ! NPV = Ñ£100 + [60/(1+IRR)] + [60/(1+IRR)2]! 0 = Ñ£100 + [60/(1+IRR) + [60/(1+IRR)2]!   ! Answer: IRR is between 10% and 15% (hint: try 13% and 14% next and choose the answer where NPV is closest to zero). ! ! Alternatively: solve for IRR using a Þnancial calculator: ! Multiple rates of return (non-conventional cash ßows) ! Multiple rates of return Ñ the possibility that more than one discount rate will make the NPV of an investment zero. ! Rule of thumb Ñ the maximum number of IRRs there can be is equal to the number of times that the cash ßows change sign from positive to negative and/or negative to positive.! ! Example ! Suppose we have a strip mining project that requires a €60 investment. Our cash ßow in the Þrst year will be €155. In the second year the mine will be depleted, but we shall have to spend €100 to restore the terrain. This means that both the Þrst and third cash ßows are negative.! To Þnd the IRR, we van calculate the NPV at various rates: !   As seen in the diagram here, the NPV appears to be behaving in a peculiar fashion. The NPV is zero when the discount rate is 25% and also when it is 33.3%. Both or neither answers are correct in this case, as there is no unambiguously correct answer. This denotes the multiple rates of return issue. ! Mutually exclusive investments ! Mutually exclusive investment decisions Ñ a situation in which taking one investment prevents the taking of another. ! Even if there is a single IRR, another problem can arise concerning mutually exclusive investment decisions. If two investments, X and Y, are mutually exclusive, then taking one of them means that we cannot take the other. Two projects that are not mutually exclusive are said to be independent. For example, if we own one corner lot, then we can build a petrol staton or an apartment building, but not both. These are mutually exclusive alternatives. ! Lecture example 7 Which of these projects should a company accept assuming that the projects are mutually exclusive? Consider IRR and NPV results when arriving at your answer.! The IRR for A is 24% ad the IRR for B is 21%. Because these investments are mutually exclusive, we can take only one of them. Simple intuition suggests that investment A is better because of its higher return. Unfortunately, this is not always correct. ! One must always consider NPV Þrst! NPV results at different discount rates are shown below: Next consider IRR! Use trial and error or a Þnancial calculator to calculate IRR. A graphical approach can also help. The IRR for a (24%) is larger than the IRR for B (21%). However, if you compare the NPVs, youÕll see that which investment has the higher NPV depends on our required return. B has greater total cash ßow, but it pays back more slowly than A. As a result, it has a higher NPV at lower discount rates. !   In our example, the NPV and IRR rankings conßict for some discount rates. If our required return is 10%, for instance, then B has the higher NPV and is thus better of the two. If the required return is 15%, then there is no ranking conßict: A is better. NPV results show that project B is favourable at a discount rate of 0% to 10% and that project A is favourable at a discount rate of 15% and above. We need to do further calculations to determine the most attractive project for discount rates between 10% and 20%. ! In this case, the IRR for A is 24%, and the IRR for B is 21%. Because the investments are mutually exclusive, we can take only one of them, so the IRR rule says that we should choose project A. This is a different answer than when we used the NPV rule. What is going on here? • Project B is preferable for a discount rate above 11.1%! • Project A is preferable for a discount rate below 11.1%! The conßict between the IRR and NPV for mutually exclusive investments can be illustrated by plotting the investmentÕs NPV proÞles: ! This example illustrates that when we have mutually exclusive projects, we shouldnÕt rank them based on their returns. More generally, whenever we are comparing investments to determine which is best, looking at IRRs can be misleading. Instead, we need to look at the relative NPVs to avoid the possibility of choosing incorrectly. Remember, weÕre ultimately interested in creating value for shareholders, so the option with the higher NPV is preferred, regardless of the relative returns. Hence, we can say: ! Where IRR and NPV give conßicting results, use the NPV rule. NPV ad IRR in Þnancing decisions Ñ mirror images ! Below, project B is an investment decision and project A is a Þnancing decision. !   In this case, the NPV and IRR decision rules disagree. The Þgure shows the NPV proÞle for each project Ñ the NPV proÞle for B is upward sloping. This means that the project should be accepted if the required return is greater than 30%.! When a project has cash ßows like investment BÕs, the IRR is really a rate that you are paying, not receiving. For this reason, we say that the project has Þnancing-type cash ßows, whereas investment A has investing-type cash ßows. You should take a project with Þnancing-type cash ßows only if it is an inexpensive source of Þnancing, meaning that its IRR is lower than your required return. ! Advantage and disadvantages of IRR ! Advantages Disadvantages 1. Closely related to NPV, often leading to identical 1. May result in multiple answers, or not deal with decisions ! non-conventual cash ßows ! 2. Easy to understand and communicate Ñ 2. May lead to incorrect decisions in comparisons especially because it is calculated as a of mutually exclusive investments percentage as opposed to a value The ProÞtability Index DeÞnition ! The ProÞtability Index (PI) Ñ the present value of an investmentÕs future cash ßows divided by its initial cost. It can also be called the beneÞt-cost ratio. ! The proÞtability index thus measures the value created per cash unit invested. For this reason, it is often proposed as a measure of performance for government or other not-forproÞt investments. Also, when capital is scarce, it may make sense to allocate it to projects with the highest PIs. ! ! Using PI ! Accept • PI$>$1 Reject • PI$<$1 Lecture example 8 Evaluate the following potential project using PI: ! • Initial investment: $100 ! • Cash inßows: $80 a year for three years ! Answer ! PI = present value of future cash ßows ! initial cost ! ! PI > 1, therefore accept the project !   Advantages and disadvantages of PI ! Advantages 1. Closely related to NPV, generally leading to identical decisions ! 2. Easy to understand and communicate! 3. May be useful when available investment funds are limited ! 4. PI is used in capital rationing situations, where capital is limited Disadvantages 1. May lead to incorrect decisions in comparisons of mutually exclusive investments The practice of capital budgeting Importance of capital budgeting ! • Long-term effect Ñ capital, or long-term funds, raised by the Þrms are used to invest in assets that enable the Þrm to generate revenues several years into the future! • Timing of a decision is important Ñ decisions impact the Þrm for several years ! Good decision criteria ! • Provide information on whether we are creating value for the Þrm ! • Adjust for the time value of money ! • Take risk in account (e.g. how quickly the investment is repaid) ! An international perspective !  