CHAPTER 6PRJECT ANALYSIS UNDER CERTAINTY ANSWERS TO REVIEW QUESTIONS QUESTIONS 6.1 Explain and define the terms: net present value, internal rate of return, modified internal rate of return, accounting rate of return, and payback period. 6.2 Explain the role of ‘certainty’ in project evaluation decisions. 6.3 Assume that Anvil Inc. has estimated the following annual data for the introduction of a new product, Ranch Hand: EOY 0 Cash Flows -14,250 Accounting Income EOY 1 EOY 2 EOY 3 EOY 4 EOY 5 3,700 2,980 6,540 7,810 6,320 2,870 2,540 5,890 6,720 5,780 Required rate of return: 14%pa. Reinvestment rate of return: 12% pa. (a) For Ranch Hand calculate NPV, IRR, MIRR, ARR, and payback period. (b) Based on the calculations in part (a), make a recommendation to Anvil’s management about the introduction of Ranch Hand. 6.4 With respect to investment decisions, explain the terms: mutual exclusivity, replacement decisions, retirement decisions. 6.5 Discuss the difference in the usage of the terms ‘ asset replacement’ and ‘asset replication’. 6.6 The formula to arrive at an NPV for asset replication in perpetuity is: NPV p NPVr NPVn 1 r 1 n (1 r ) n or NPVr n (1 r ) 1 Explain how this formula works, and show how it can be set up as a generic calculation within an Excel spreadsheet. 6.7 Assume that White Knuckle Airlines Inc. operates a regional fifty-seat jet aircraft fleet. White Knuckle expects that there will be a constant demand for this type of flight service, and that the model of aircraft employed will remain in production for the foreseeable future. White Knuckle has predicted the set of operational cash flows shown in Table 6.11 for each aircraft. $143.600.000. ANSWERS Answer to Q 6.000 per year for the next three years with the new machine.000. in perpetuity.115 1. and accounts payable by $15. The machine currently in use was originally purchased two years ago for $65. For a simplified case where there is only one capital outlay which occurs at the beginning of the first year of the project.3 12.956 2. the investments in accounts receivable is expected to increase by $9. (a) (b) (c) (d) (e) (f) Calculate the initial investment associated with the proposed replacement decision.000. the inventory by $13.000. See Chapter 1. What is the proposed investment’s IRR? Use the computed IRR and NPV results and discuss the project accept / reject decision. Calculate the incremental operating cash flows of the proposed replacement decision.00 (cost) 4.8 If White Knuckle Inc. The beforetax net operating cash flow is estimated as $120. The expected resale value of the old and new machines in three years’ time would be $4.000. Calculate the terminal cash flows associated with the proposed replacement decision. Operational cash flows Year 0 1 2 3 4 5 Annual Net Cash Flows $M 23. Taxallowable depreciation is $13.0 18. 6. the net present value (NPV) is calculated by subtracting this capital outlay from the present value of the annual net operating cash flows and the net terminal cash flow. The corporate tax rate is 30%.000 per year for the first two years.7 16. Tax-allowable depreciation is $70.875 2. ‘shareholder wealth maximization and net present value’ section for more details . The current market value of this machine is $23. The economic life of the machine is estimated as three years.Table 6. Compute the NPV of the replacement project assuming a discount rate of 6% per annum.000 per year for the next three years with the old machine and.000 shipping cost and $2. respectively.11. and require $4.875 Salvage Value $M 21.000.000 and $6. determine the optimum aircraft replacement cycle time. The new machine being considered would cost $140.865 3. If the new machine is acquired.1 Net present value: This is the net increase in the firm’s current wealth that will result from undertaking an investment.8 Kandy Corporation is considering a replacement investment. has a required rate of return of 12% per annum.000 installation costs.1 14.000 per year for five years. One of the underlying assumptions of the IRR method is that received cash flows can be re-invested at the IRR. For a calculation example. For example. where a specified re-investment rate of return is applied to the received cash flows. If the IRR is greater than or equal to the required rate of return. The calculated ratio is compared with the required rate in the same way as is the IRR. which.including a simple calculation example. The IRR is sometimes not suitable an investment decision criterion for the following reasons: (1) it may have zero or multiple solutions. Accounting rate of return: This measure is a ratio of the average annual accounting income to the dollar amount of the investment. The MIRR outcome is compared against the required rate of return. This change of sign normally occurs between the negative initial outlay. The dollar amount of the investment can be calculated in several ways. there must be at least one change of sign in the cash flows for a solution to be possible. and the first. under certainty. Under Descarte’s rule of sign. with the added disadvantage of requiring an extra prediction for a future re-investment rate. Some of these are: the amount of the initial investment. The ARR is not a recommended project evaluation measure for the following reasons: . Internal rate of return: This is the rate of discount which will equate all the future net cash flows to the initial outlay. The present value is calculated by discounting the future values. In many cases. will equal the risk free rate. the average of the initial investment and the closing book value. In other words. The discount rate represents the firm’s required rate of return. which contains a capital outlay at a later year of the project (in addition to the initial capital investment at the beginning of the project). then the re-investment rate is applied and the MIRR calculated. (2) it can cause conflict in ranking mutually exclusive projects. and the average of annual successive written down book values. the firm should accept the project. an upgrade to the plant and machinery may occur in a later year. the firm will be indifferent towards the project. or subsequent net operating cash flows. see Delta project example in this chapter. the project should be rejected. and the decision is made in the same way as that for the IRR. the project should be rejected. Modified internal rate of return: This method re-calculates the IRR. This re-investment rate is a rate predicted by management at which cash flows can be re-invested as they come to hand. the capital outlays can occur not only at the beginning of the first year of the project but at other times later during the project’s progress as well. The MIRR has the same drawbacks as does the IRR. If management feels that this is not likely. the firm should accept the project. (which has continued from Chapter 2). (3) it does not relate directly to the firm’s goal of wealth maximisation. In such cases the present value of those capital outlays need to be calculated by discounting the future capital outlays and then the present value of the total capital outlays need to be subtracted from the present value of net operating and terminal cash flows. If the IRR is less than the required rate of return. If a calculated NPV is positive. Other values are also possible. (4) its calculation implicitly assumes that cash flows as received can be re-invested at the required rate of return and this assumption may not be tenable. If the NPV is zero. it is the discount rate at which the NPV is equal to zero. and if the NPV is negative. Product Ranch Hand: NPV IRR MIRR ARR Pay Back Period $3.49% 33. It does not account for the time value of money. it is not an objective measure as is annual cash flow. These assumptions allow the essential elements of decision-making to be studied. Sophisticated risk analyses could then be applied to this basic certainty model. IRR. Operating cash flows occurring after the payback period are ignored. The rate of return calculated is not a time value of money rate of return.3 (a) Calculation of NPV. it is an accounting ratio. The assumption of perfect certainty is usually employed in the initial stages of project analysis so that an NPV model can be established. Answer to Q 6.50 22. In practice. There are several variants of the ARR measure. . Since this is positive at $3.71% 18. Payback period: This is a measure of the time taken for the accumulated annual operating cash flows to become equal to the initial outlay.166. The Payback Period is not a recommended as a stand-alone project evaluation decision support criterion for the following reasons: It does not account for the time value of money.xls’ The results are summarised below. (b) Recommendations: The NPV is the primary decision parameter.2 In order to develop conceptual models for financial decision-making. Answer to Q 6. it would be sensible to analyse most projects initially under the assumption of certainty. so that the necessary cash flow relationships and discounting processes could be established.3 Excel Solution. There is no objective measure of an acceptable payback period. The definition of accounting ‘income’ is situation specific. whilst other lesser influences are controlled and held over for later analysis.40% 4 Years. ARR. all of which are ‘correct’. the new product Ranch Hand should be introduced.609. The calculated accounting ratio does not relate to the firm’s goal of wealth maximisation. The calculated payback period does not relate to the firm’s goal of wealth maximisation. These are: perfect certainty. PP: These have been calculated on the Excel work sheet titled ‘Q 6. Some of these may have a negative impact on the project’s viability. MIRR. perfect capital markets and rational investors. three assumptions are usually invoked. The relevant cash flows in this case are the current cash flows from the asset in place. a trucking company should review its truck fleet periodically. For example. For example. thus supporting the NPV finding that Ranch Hand should be introduced. it will essentially provide the same services. The firm can build either a two storey. The point of mutual exclusivity is that the NPV rule should always be used in evaluating the competing investments. Whilst a new truck may represent some improvement in performance and safety. In this case. assume a firm owns a parcel of land. current book values. four storey or seven storey building on this land. but at 22. Each one of theses projects excludes the others. but as the payback measure is an unreliable parameter. if the firm replaced a current truck with one of markedly increased capacity. The Payback Period of 4 years may support the proposal. and the present value of the cash from sale. then new forecasts of future cash flows would have to be made. The projects are mutually exclusive. The relevant cash flows in the replacement decision will be the future changeable flows. The relevant cash flows will be concerned with the earning power of the asset in place. then the asset review decision will be an asset replacement decision. Past cash flows. In this case. the investment decision is an ‘upgrade’ decision. However. assets currently held by the firm must be reviewed periodically to determine whether they are still viable.49% also supports the introduction of the new product. Anvil should not rely on this figure for project acceptance. A firm should evaluate assets to see whether the future benefits warrant the continuation of the asset. its value and interpretation are open to question. If the firm will continue to produce the same output at the same level and in the same style. albeit at a lesser cost. The ARR result of 33. against the earning power of a similar replacement asset. and would have to be viewed as new investment to replace the existing investment.56% appears to support the proposal.4 Mutual exclusivity: this occurs where two or more assets compete for acceptance within the constraint of limiting physical resources. existing forecasts of revenues and costs can be used. The IRR rule may give misleading and conflicting results. and past cash spent on the asset will not be relevant. The MIRR at 18.71% it is above the required rate of 14%. Replacement decisions: As part of ongoing efficient management. However. Retirement decisions: These decisions are part of the asset review process. . so Anvil should not rely on this measure as a decision parameter. or whether the cash released by the sale of the asset could be better employed elsewhere. The IRR is not as reliable or definitive a measure as the NPV. Answer to Q 6. NPV p NPVn 1 r 1 n = The NPV at the present time of all the NPVs in the replicating stream to perpetuity.Answer to Q 6. NPVr = The NPV of the initial replication NPVn = The NPV of each replication at year n. For convenience.1 = 1. If the competing assets have different life spans. let us denote this as ‘k’. but it can be alternatively cast out in perpetuity.07) 5 . being replaced every 5 years. This formula is simply that for a perpetuity. The choice rests on the comparative NPVs. The word ‘replication’ is used to emphasise this infinite replacement chain. would have present NPV of $1. 1 r n 1 = The periodic interest rate for each replication length.456. .5 Asset replacement looks at comparing the asset in post with a similar asset that could perform the same duties. being discounted at the periodic rate k. then the NPV evaluation of each needs to be computed over a common time horizon. an asset having an NPV of $418 . Answer to Q 6.6 The formula for the present value of an infinite replacement chain is: NPV p NPVr where. Asset replacement becomes problematical when two or more assets compete to replace the present asset. having a cash flow of NPVn . rather than the more limited word ‘replacement’ which might imply only a ‘once-off’ decision. plus the NPV of the first asset in the cycle. with an annual rate of 7%.1 (1 . This term implies that the asset will be replaced in exactly the same style and size over the same cycle length in perpetuity. If the life span is infinite. This time horizon is usually the lowest common multiple number of years of the asset lifetimes. as follows: k (1 i ) 5 .2552% per five years. It can therefore be viewed as the formula for a ‘perpetuity due’. the term used to describe the periodic asset replacement is ‘replication’.37 for the infinite chain.402552 -1 = 40. For example. 7 For each replacement cycle time.595/ 0.12) + ($3.750 This means that White Knuckle Airlines should replace its jet fleet at the end of every year in perpetuity.933 -$6. For example: Hold 1 Year: NPV = ($4.456.12)2 –1 = 25. NPV p $418 $418 . The final results are given below.927 -$8.Then.595 with a 2 year cycle. we compute the NPV from the expected yearly cash inflows and the salvage value to be received at the end of the cycle.297 -$8. However.37 This application can be made generic via the use of parameters in an Excel spreadsheet.$23 = -$0.09375 NPVinf = $0.865+ $21) /(1.402552 = $1.6 Excel Solutions.$23 = $0.956+ $18. k = (1.7)/((1. These individual cycle length NPVs are then converted at their cycle lengths into the equivalent current NPVs for infinite replication chains.12) = $0.44% NPVinf = -$0.) . the full solution is shown to give a template for other investment projects.875 Hold 2 Years: NPV = $4.xls’.595 + (-$0.12) . Answer to Q 6. This is done on Excel file titled ‘Q 6.2544) = -$2.933 These calculations are extended for all cycles up to the 5-year cycle on the Excel spreadsheet titled ‘Q 6.12)2) .865/(1.xls’.875 -$2. Replication Cycle Length 1 Year 2 Years 3 Years 4 Years 5 Years Present Overall NPV $0. (The solution is obvious in this particular case.09375 +($0.7 Excel Solutions. since the one year cycle is the only one with a positive NPV.09375/. Answer to Q 6.000 2) = 39. This layout is: Initial Investment: + Cost of new asset + Installation costs .000 –15.Proceeds from sale of old asset .000 (depreciable outlay) 23.Proceeds from sale of old asset + Taxes on sale of old asset + Initial investment in working capital = Initial investment Incremental Operating Cash Flows: Operating cash flow new machine .000) .we can use the same argument and layout as for Repco Corportaion in Chapter 2.200 Taxes on sale of old machine = (Sale Proceeds – Book Value ) x tax rate = (23.800 (tax benefit) 7.000 – 39.000) Initial investment $140.proceeds from sale of old machine + taxes on sale of old machine + change in net working capital (9.4.30 = .000 (depreciable outlay) 4.800 (tax saving) Book Value = cost – tax allowable accumulated depreciation = 65.000 (depreciable outlay) 2.8 For this solution .Operating cash flow old machine = Incremental cash flow of the proposed replacement project Terminal Cash Flow: + Proceeds from sale of new asset .Taxes on sale of new asset + Taxes on sale of old asset + recovery of working capital = Terminal cash flow (a) Initial Investment for the Proposed Replacement Investment: cost of new machine + shipping + installation .000 – (13.000 + 13.000 125.000 (current market value) -4.000 . 900 33. Income after tax 6.000 32.900 87.000 180 1.30 = 1. Operating cash inflows ( 5 + 2) 120. Old machine 3.000 13.000 x 2) = 6000 Taxes on sale of old machine = (Sale Proceeds – Book Value ) X tax rate = (4.100 100.200 12.900 51.200 (c ) Kandy Coraption -Terminal cash flow for the proposed replacement investment Proceeds from sale of new machine .000 107.000 107.100 32. Operating cash inflows ( 5 + 2) Year 1 Year 2 Year 3 143. Tax @ 30% 5.000 – (70.900 74. Income after tax 6. New machine 2.100 121.100 Old machine 1.900 51. Depreciation 3.000 70.000 120.900 87.000 21. Operating income 2.000 21. Income before tax 4.900 Incremental 1.100 74.000 – (13.000 0 73.620 Taxes on sale of new machine = (Sale Proceeds – Book Value ) x tax rate = (6.000 107.900 87.000 x 5) = 0 .000 – 0) X .000 70.taxes on sale of new machine + taxes on sale of old machine + recovery of working capital $6.3 = 180 Book Value = cost – tax allowable accumulated depreciation = 146.000 10.000 13.100 100. 100 100.100 143.900 33.200 Book Value = cost – tax allowable accumulated depreciation = 65.200 121.100 74.000 143.600 4.000 143. Depreciation 3.000 32.900 120. Income before tax 4.900 87.900 42.600 –6.100 87.000) x .proceeds from sale of old machine . Proposal’s incremental cash inflows (1 – 2) 121.(b) Incremental Operating Cash Flows for Proposed Replacement Investment New machine 1.000 73.100 121. Tax @ 30% 5. Operating Income 2.200 7.000 13.100 87. 820 (1. If the replacement project commenced (at the beginning of year 2001).06) 3 = -$45. Why then should we include the $4.04%.000 salvage value of the old machine at the end of year 2003 as a terminal cash outflow of the proposed replacement investment? The answer lies in the opportunity cost principle. that amount is attributed as a cash outflow for the proposed replacement project. The reason why we subtract the proceeds from the sale of old machine in arriving at the terminal cash flow of the proposed replacement investment is now explained. This was treated as an inflow of capital in calculating the initial investment of the proposed replacement investment project.200 Operating flows: Terminal cash flow: EOY 1 EOY 2 EOY3 +$33.06) 2 (1. Therefore. and the IRR may even be negative.200 +$12. The proceeds from the sale of old machine at that time was $23. . That is why the initial investment was reduced by that amount.200 22.xls’. is now lost ‘with’ the proposed project. and the IRR is less than the required rate of 6.000 (which would have been a terminal cash inflow ‘without’ the proposed project). The rationale for the inclusion of cash inflow from the sale of new asset is obvious. All calculations are shown in the Excel file titled ‘Q 6. as the NPV is negative.8 Excel Solution.200 33.000.171. the old asset would have been sold at that time.200 +$10.For replacement projects.620 Using a required rate of return of 6.00%. the Net Present Value is: NPV 125. It is easier to read the IRR result from the spreadsheet solution.00% ( the required rate). The resultant IRR is -16.25 (e) IRR calculation for Kandy Corporation’s proposed investment Using trial and error as a manual calculation for the IRR will be difficult here. the replacement project should NOT be undertaken.06)1 (1.00% for these cash flows. This results means that the IRR will be less than 6. (f) IRR and NPV and project accept / reject decision Since the NPV is negative. (d) NPV computation for Kandy Corporation The cash flow layout for the proposed replacement is: Time: EOY 0 Initial outlay: -$125. we need to include proceeds from both the new asset and the old asset.200 33. The old machine’s sale proceeds of $4.200 +$33.