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Consider how Kyler Valley Spring Park Lodge could use capital budgeting to decide whether the $13,000,000 Spring Park Lodge expansion would be a good investment. Assume Kyler Valley's managers developed the following estimates concerning the expansion. Under the assumption that the expansion would have a residual value of $950,000, the managers calculated the payback period to be 4.4 years, the ARR to be 20.89%,the average annual operating income to be $1,456,850, the average amount invested to be $6,975,000,and the average annual net cash inflow to be $2,963,100. Assume that Kyler Valley uses the straight-line depreciation method and now expects the lodge expansion to have zero residual value at the end of its eight-year life. Will the payback change? Explain your answer. Recalculate the payback if it changes. Round to one decimal place. Select the formula to calculate the payback period. Amount invested/Expected annual net cash flow = payback The payback will (select one of the two) \"continue to\" or \"now\" be _________ years. The residual value (select one of the two) \"affects\" or \"does not affect\" the computation of the payback and the payback method, (select one of the two) \"does not consider\" or \"consider\" cash flows that occur after the payback period. Fill in the blanks. See above The payback will ___________be___________. The residual value ______the computation of the payback of the payback and the payback method ________cash flows that occur after the payback period. ACCOUNTING - Tenth Edition Solutions Manual 1. Explain the difference between capital assets, capital investments, and capital budgeting. A capital asset is an operational asset used for a long period of time. A capital investment is the acquisition of a capital asset. Capital budgeting is the process of making capital investment decisions, planning to invest in long-term assets in a way that returns the most profitability to the company. 2. Describe the capital budgeting process. The capital budgeting process consists of the following: Step 2: Plan. o Substep 1: Identify potential capital investments. o Substep 2: Analyze potential capital investments. o Substep 3: Apply capital rationing. Step 3: Act. (Acquire and use approved capital investments.) Step 4: Control. (Perform post-audits, during and at the end of the investment's life.) 3. What is capital rationing? Capital rationing is the process of ranking and choosing among alternative capital investments based on the availability of funds. Managers must determine if and when to make specific capital investments, so capital rationing occurs when the company has limited cash available to invest in long-term assets. Chapter 26: Capital Investment Decisions Page 1 of 149 ACCOUNTING - Tenth Edition Solutions Manual 4. What are post-audits? When are they conducted? A post-audit is the comparison of actual results of capital investments to the projected results. The comparisons help companies determine whether the investments are going as planned and deserve continued support, or whether they should abandon the project and dispose of the assets. Post-audits should be routinely performed during the life of the project, not just at the end of the project life span. The intermediate post-audits allow managers to make adjustments to the projects during their lifetimes. Managers also use feedback from post-audits to better estimate projections for future projects. If managers expect routine post-audits, they will more likely submit realistic estimates with their capital investment proposals. 5. List some common cash inflows from capital investments. Cash inflows from a capital investment include cash revenue generated by the investment, cash savings in operating costs, and any future residual value of the investment (asset). 6. List some common cash outflows from capital investments. Cash outflows from a capital investment include the initial investment (acquisition cost), cash operating costs incurred, and cash paid for refurbishment, repairs, and maintenance. 7. What is the payback method of analyzing capital investments? The payback method is a capital investment analysis method that measures the length of time it takes to recover, in net cash inflows, the cost of the initial investment. Chapter 26: Capital Investment Decisions Page 2 of 149 ACCOUNTING - Tenth Edition Solutions Manual 8. How is payback calculated with equal net cash inflows? If net cash inflows are equal, the payback period (in years) of an investment is calculated with the following formula: Amount invested / Expected annual net cash inflow. 9. How is payback calculated with unequal net cash inflows? If net cash inflows are unequal, the payback period (in years) of an investment is calculated as follows: Add the accumulated net cash inflows for full years before complete recovery, then Number Payback = + Amount needed to complete recovery in next year of Full Net cash inflow in next year Years 10. What is the decision rule for payback? The decision rule for payback is: Investments with shorter payback periods are more desirable, all else being equal. 11. What are some criticisms of the payback method? The major criticisms of the payback method are that it ignores the time value of money, it focuses only on time to recover an investment, not on profitability, and it ignores any cash flows that occur after the payback period. Chapter 26: Capital Investment Decisions Page 3 of 149 ACCOUNTING - Tenth Edition Solutions Manual 12. What is the accounting rate of return? The accounting rate of return (ARR) is a capital investment analysis method that measures the profitability of an investment. 13. How is ARR calculated? The accounting rate of return (ARR) on an investment is calculated with the following formula: Average annual operating income / Average amount invested. 14. What is the decision rule for ARR? The decision rule for accounting rate of return is: If the expected accounting rate of return meets or exceeds the required rate of return, then invest. If it is less than the required rate of return, then do not invest. Chapter 26: Capital Investment Decisions Page 4 of 149 ACCOUNTING - Tenth Edition Solutions Manual 15. Why is it preferable to receive cash sooner rather than later? A dollar received today is worth more than a dollar to be received in the future because today's dollar can be invested to earn additional income over time. The fact that \\ invested cash earns income over time is called the time value of money and explains why it is preferable to receive cash sooner rather than later. 16. What is an annuity? How does it differ from a lump sum payment? An annuity is a stream of equal cash payments made at equal time intervals. In contrast, a lump sum payment is a one-time cash payment. 17. How does compound interest differ from simple interest? Simple interest means that interest is calculated only on the principal amount. In contrast, compound interest means that interest is calculated on the principal and on all previously earned interest. Compound interest assumes that all interest earned will remain invested and earn additional interest at the same interest rate. Over the life of a given investment, the total amount of compound interest is more than the total amount of simple interest. Chapter 26: Capital Investment Decisions Page 5 of 149 ACCOUNTING - Tenth Edition Solutions Manual 18. Explain the difference between the present value factor tablesPresent Value of $1 and Present Value of Annuity of $1. The Present Value of $1 table (Appendix B, Table B-1) is used to calculate the value today of one future amount (a lump sum). The Present Value of Annuity of $1 table (Appendix B, Table B-2) is used to calculate the value today of a series of equal future amounts (an annuity). 19. How is the present value of a lump sum determined? The present value (PV) of a lump sum is determined with the following formula: Future value PV factor (Appendix B, Table B-1) for the applicable interest rate i and period of time n. 20. How is the present value of an annuity determined? The present value (PV) of an annuity is determined with the following formula: Amount of each net cash inflow Annuity PV factor (Appendix B, Table B-2) for the applicable interest rate i and period of time n. Chapter 26: Capital Investment Decisions Page 6 of 149 ACCOUNTING - Tenth Edition Solutions Manual 21. Why are net present value and internal rate of return considered discounted cash flow methods? Net present value (NPV) and internal rate of return (IRR) are considered discounted cash flow methods because they incorporate compound interest (by assuming that future cash flows will be reinvested when they are received) and make comparisons by converting all cash flows to the same point in timenamely the present value. The NPV and IRR methods rely on present value calculations to compare the amount of an investment's initial cost with its expected net cash inflows. 22. What is net present value? Net present value (NPV) is a capital investment analysis method that incorporates the time value of money and measures the net difference between the present value of an investment's net cash inflows and the investment's initial cost. 23. What is the decision rule for NPV? The decision rule for net present value is: If the net present value is positive, then invest; if the net present value is negative, do not invest. Chapter 26: Capital Investment Decisions Page 7 of 149 ACCOUNTING - Tenth Edition Solutions Manual 24. What is the profitability index? When it is used? The profitability index is the number of dollars received for every dollar invested, with all calculations performed in present value dollars. It is calculated with the following formula: Present value of net cash inflows / Initial investment (cost). The profitability index is useful to rank investments that differ in initial cost. It allows comparison of alternative investments in present value terms (such as the net present value method), but it also considers differences in the investments' initial cost. 25. What is the internal rate of return? The internal rate of return (IRR) is a capital investment analysis method that incorporates the time value of money, where IRR is the rate of return, based on discounted cash flows, of a capital investment. It is the interest rate that makes the net present value of the investment equal to zero (makes the cost of the investment equal to the present value of the investment's net cash inflows). Chapter 26: Capital Investment Decisions Page 8 of 149 ACCOUNTING - Tenth Edition Solutions Manual 26. How is IRR calculated with equal net cash inflows? If net cash inflows are equal, the internal rate of return (IRR) on an investment can be calculated using present value (PV) tables as follows: Calculate the annuity PV factor using this equation: Annuity PV factor = Initial investment / (i = ?, n = given) Amount of each net cash inflow Use the PV of Annuity of $1 table (Appendix B, Table B-2) to find the calculated Annuity PV factor (on the row corresponding to the investment's expected life, n). The rate at the top of the column in which the factor appears is the IRR. However, if the exact factor isn't in the table, the two closest factors are identified and the estimated IRR is somewhere between the rates at the top of the two columns in which the factors appear. Alternatively, the IRR on an investment can be more easily and precisely found using a business calculator or computer spreadsheet software, such as Microsoft Excel. 27. How is IRR calculated with unequal net cash inflows? If net cash inflows are unequal, the internal rate of return on an investment can be estimated using trial-and-error. Start by calculating the net present value of the investment using the required rate of return as the discount rate. If the net present value is positive, the internal rate of return must be higher than the required rate. If the net present value is negative, the internal rate of return must be lower than the required rate. Continue the trial-and-error process using higher or lower discount rates until you find the rate that brings the net present value to as close to zero as possible. This rate is the estimated internal rate of return. Alternatively, the internal rate of return on an investment Chapter 26: Capital Investment Decisions Page 9 of 149 ACCOUNTING - Tenth Edition Solutions Manual can be more easily and precisely found using a business calculator or computer spreadsheet software, such as Microsoft Excel. 28. What is the decision rule for IRR? The decision rule for internal rate of return is: If the internal rate of return exceeds the required rate of return, then invest. If it is less than the required rate of return, then do not invest. 29. How can spreadsheet software, such as Excel, help with sensitivity analysis? Using computer spreadsheet software, such as Microsoft Excel, can be beneficial because it allows for easy manipulation of figures to perform sensitivity analysis. Sensitivity analysis is a \"what if\" technique that shows how results differ when underlying assumptions change. Capital budgeting decisions affect cash flows far into the future. A company's managers often want to know whether their decisions would be affected by any of their major assumptions. Examples include changing the discount rate, future net cash inflows, and/or future net cash outflows. After reviewing the basic information for net present value and internal rate of return analyses, managers can perform sensitivity analyses to recalculate and review the results. One method of setting up Excel spreadsheets is to have areas of the spreadsheet designated for inputs and outputs. Cells for entering the inputs are at the top of the spreadsheet. Cells with formulas to calculate the outputs are in a section below the inputs. All outputs are calculated by Excel based on the formulas entered, which reference the cells with the inputs. This method of setup allows the user to make changes to any input cell and have Excel automatically recalculate the outputs to complete a sensitivity analysis. Chapter 26: Capital Investment Decisions Page 10 of 149 ACCOUNTING - Tenth Edition Solutions Manual 30. Why should both quantitative and qualitative factors be considered in capital investment decisions? Most companies have limited resources and have to make hard decisions about which projects to pursue and which ones to delay or reject. These decisions are not just based on the quantitative factors of payback, accounting rate of return (ARR), net present value (NPV), profitability index, and internal rate of return (IRR). Qualitative factors must also be considered. For example, a company may choose manufacturing equipment with a lower NPV or IRR because it is more environmentally friendly or accept a project that is not profitable but adds value to the community. Companies should also consider the opportunity costs of rejecting certain projects and the possibility of lost business if there is negative public perception of the company's choices. 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However, if fied and the wo columns in ly found using a ment can be net present value ate. If the net the required rate. s until you find the his rate is the on an investment Chapter 26: Capital Investment Decisions Page 20 of 149 ACCOUNTING - Tenth Edition Solutions Manual n exceeds the return, then do not e beneficial r when underlying into the future. uld be affected ount rate, future asic information n perform preadsheet he top of the on below the r to make outputs to Chapter 26: Capital Investment Decisions Page 21 of 149 ACCOUNTING - Tenth Edition Solutions Manual apital investment ons about which re not just based net present value actors must also quipment with a t a project that is consider the business if there Chapter 26: Capital Investment Decisions Page 22 of 149 ACCOUNTING - Tenth Edition Solutions Manual S26-1 Place the activities in sequential order as they occur in the capital budgeting process. Solution: Order of activities: f. b. g. a. d. c. e. Chapter 26: Capital Investment Decisions Page 23 of 149 ACCOUNTING - Tenth Edition Solutions Manual S26-2 Use the decision rule for payback to rank the projects from most desirable to least desirable, all else being equal. Solution: The ranking of the projects from most desirable to least desirable (shortest payback to longest, all else being equal) is: Project C, Project A, Project B. Chapter 26: Capital Investment Decisions Page 24 of 149 ACCOUNTING - Tenth Edition Solutions Manual S26-3 Use the decision rule for ARR to rank the projects from most desirable to least desirable.Cortes Company's required rate of return is 8%. Solution: The ranking of the projects from most desirable to least desirable (highest accounting rate of return to lowest) is: Project Y, Project Z, Project X. However, Project X should be rejected because the ARR is less than the required rate of return. Chapter 26: Capital Investment Decisions Page 25 of 149 ACCOUNTING - Tenth Edition Solutions Manual S26-4 Requirements 1. Compute the average annual net cash inflow from the expansion. 2. Compute the average annual operating income from the expansion. Solution: Requirement 1 Average annual = Average cash spent cash inflow by each skier per day = $236 = $3,920,904 Additional skiers per day 117 Average annual = Average variable cost of Additional cash outflow serving each skier per day skiers per day = $76 117 = $1,262,664 Average annual = net cash inflow = = Average annual cash inflow $3,920,904 $2,658,240 Average days of skiing per year 142 Average days of skiing per year 142 Average annual cash outflow $1,262,664 Requirement 2 Total net cash inflows during operating life of expansion Chapter 26: Capital Investment Decisions = Average annual net cash inflow = $2,658,240 = $26,582,400 Operating life of expansion 10 years Page 26 of 149 ACCOUNTING - Tenth Edition Total depreciation during operating life of expansion Solutions Manual = = = Cost $13,500,000 $12,500,000 Total net cash inflows during operating life of expansion Less: Total depreciation during operating life of expansion Total operating income during operating life Divide by: Expansion's operating life in years Average annual operating income from expansion Chapter 26: Capital Investment Decisions Residual value $1,000,000 $ $ 26,582,400 12,500,000 14,082,400 10 years 1,408,240 Page 27 of 149 ACCOUNTING - Tenth Edition Solutions Manual S26-5 Compute the payback for the expansion project. Round to one decimal place. Solution: Payback = = = (a) Amount invested Expected annual net cash inflow $13,500,000 $2,658,240(a) 5.1 years (rounded) Calculated in S26-4, Requirement 1 Chapter 26: Capital Investment Decisions Page 28 of 149 ACCOUNTING - Tenth Edition Solutions Manual S26-6 Calculate the ARR. Round to two decimal places. Solution: Average amount invested = = = ARR = = = (a) Amount invested + Residual value 2 $13,500,000 + $1,000,000 2 $7,250,000 Average annual operating income Average amount invested $1,408,240(a) $7,250,000 19.42% (rounded) Calculated in S26-4, Requirement 2 Chapter 26: Capital Investment Decisions Page 29 of 149 ACCOUNTING - Tenth Edition Solutions Manual S26-7 Requirements 1. Will the payback change? Explain your answer. Recalculate the payback if it changes. Round to one decimal place. 2. Will the project's ARR change? Explain your answer. Recalculate ARR if it changes. Round to two decimal places. 3. Assume Smith Valley screens its potential capital investments using the following decision criteria: Maximum payback period 5.3 years Minimum accounting rate of return 16.55% Will Smith Valley consider this project further or reject it? Solution: Requirement 1 If the expansion has a residual value of zero, rather than $1,000,000, the payback period will not change because the payback method considers only those cash flows that occur during the payback period and ignores any cash flows that occur after the end of the payback period. The $1,000,000 residual value assumed in Short Exercises S26-4 and S26-5 occurs at the end of the expansion's 10-year operating life, which is after the payback period of 5.1 years calculated in Short Exercise S26-5. Thus, a change in the expansion's expected residual value doesn't affect the payback period. Chapter 26: Capital Investment Decisions Page 30 of 149 ACCOUNTING - Tenth Edition Solutions Manual Requirement 2 If the expansion has a residual value of zero, rather than $1,000,000, the accounting rate of return (ARR) will change because expected residual value is considered in the calculation of average annual operating income (numerator of the ARR) as well as the average amount invested (denominator of the ARR). If residual value is zero, rather than $1,000,000, (1) average annual operating income is lower because annual depreciation expense is higher and (2) the average amount invested is lower because book value at the end of the expansion's operating life is lower. Total depreciation during operating life of expansion = = = Average amount invested = = = Total net cash inflows during = operating life of expansion = = (a) Cost $13,500,000 $13,500,000 Residual value $0 Amount invested + Residual value 2 $13,500,000 + $0 2 $6,750,000 Average annual net cash inflow $ 2,658,240(a) $26,582,400 Operating life of expansion 10 years Calculated in S26-4, Requirement 1 Chapter 26: Capital Investment Decisions Page 31 of 149 ACCOUNTING - Tenth Edition Solutions Manual Total net cash inflows during operating life of expansion Less: Total depreciation during operating life of expansion Total operating income during operating life Divide by: Expansion's operating life in years Average annual operating income from expansion ARR = = = $ $ 26,582,400 13,500,000 13,082,400 10 years 1,308,240 Average annual operating income Average amount invested $1,308,240 $6,750,000 19.38% (rounded) If residual value is zero, rather than $1,000,000, the revised ARR for the expansion is 19.38% (rounded). Note that this is a decrease from the 19.42% ARR calculated in Short Exercise S26-6. Although the decrease in the average amount invested (denominator), by itself, would cause the ARR to increase, the decrease in average annual operating income (numerator) was higher as a percentage change and thus dominated the overall effect on ARR (a decrease). Requirement 3 Smith Valley will consider the expansion project further because the payback period of 5.1 years is less than the maximum of 5.3 years and the ARR of 19.38% is greater than the minimum of 16.55%. Chapter 26: Capital Investment Decisions Page 32 of 149 ACCOUNTING - Tenth Edition Solutions Manual S26-8 What are the expected annual net cash savings from the new software? Solution: Payback = Thus: Expected annual net cash savings = = = Chapter 26: Capital Investment Decisions Amount invested Expected annual net cash savings Amount invested Payback $28,575 3 years $9,525 Page 33 of 149 ACCOUNTING - Tenth Edition Solutions Manual S26-9 Requirements 1. What is the total present value of the cash flows received over the five-year period? 2. Could you characterize this stream of cash flows as an annuity? Why or why not? 3. Use the Present Value of Annuity of $1 table (Appendix B, Table B-2) to determine the present value of the same stream of cash flows. Compare your results to your answer to Requirement 1. 4. Explain your findings. Solution: Requirement 1 Time 1 2 3 4 5 Cash PV Factor Inflow (i = 8%) Present value of each year's $1 (n = 1) (n = 2) (n = 3) (n = 4) (n = 5) Total present value $1 1 1 1 1 0.926 0.857 0.794 0.735 0.681 Present Value $ $ 0.926 0.857 0.794 0.735 0.681 3.993 Requirement 2 The stream of cash flows is an annuity because it is a stream of equal cash payments made at equal time intervals. Chapter 26: Capital Investment Decisions Page 34 of 149 ACCOUNTING - Tenth Edition Solutions Manual Requirement 3 The total present value is $3.993, which is the same as in Requirement 1. Present value = Amount of Annuity PV Factor for i each cash inflow = 8%, n = 5 = $1 3.993 = $3.99 Requirement 4 The total present value of the stream of cash inflows ($3.993) is the same in Requirement 1 and Requirement 3 because the annuity table of present value factors (Table B-2) is derived from the lump sum table of present value factors (Table B-1). The present value factor for an annuity of $1 received at the end of each year for five years assuming an 8% interest rate (3.993 from Table B-2) is the sum of the present value factors of $1 received at the end of one year, two years, three years, four years, and five years assuming an 8% interest rate (the sum of 0.926, 0.857, 0.794, 0.735, and 0.681 from Table B-1 is 3.993). The annuity table enables a one-step calculation rather than separately calculating the present value of each annual cash inflow and then summing the individual present values. Chapter 26: Capital Investment Decisions Page 35 of 149 ACCOUNTING - Tenth Edition Solutions Manual S26-10 Requirements 1. Calculate the present value of each scenario using a 6% discount rate. Which scenario yields the highest present value? Round to nearest whole dollar. 2. Would your preference change if you used a 12% discount rate? Solution: Requirement 1 Scenario #1: Present value = = = Amount of = each cash inflow $8,750 = $48,843 (rounded) Annuity PV Factor for i = 6%, n = 7 5.582 Scenario #2: Present value is $50,050 (the net cash inflow) because it would be received now. Scenario #3: Present value = = = Scenario #1 #2 #3 Cash inflow $100,250 $66,666 (rounded) PV Factor for i = 6%, n = 7 0.665 Present Value (i = 6%, n = 7) $48,843 (rounded) $50,050 $66,666 (rounded) Scenario #3 yields the highest present value, thus is preferred. Chapter 26: Capital Investment Decisions Page 36 of 149 ACCOUNTING - Tenth Edition Solutions Manual Requirement 2 Scenario #1: Present value = = = Amount of each cash inflow $8,750 $39,935 Annuity PV Factor for i = 12%, n = 7 4.564 Scenario #2: Present value is $50,050 (the cash inflow) because it would be received now. Scenario #3: Present value = = = Scenario #1 #2 #3 Cash inflow $100,250 $45,313 PV Factor for i = 12%, n = 7 0.452 Present Value (i = 6%, n = 7) $39,935 $50,050 $45,313 If the discount rate is 12% (rather than 6%), Scenario #2 (rather than Scenario #3) is preferred because it yields the highest present value. Chapter 26: Capital Investment Decisions Page 37 of 149 ACCOUNTING - Tenth Edition Solutions Manual S26-11 What is the project's NPV (round to nearest dollar)? Is the investment attractive? Why or why not? Solution: Net Cash Inflow Time 1 - 10 years PV of annuity 10 PV of residual value Total PV of net cash inflows 0 Initial investment NPV of the project (a) 2658240(a) 1,000,000 Annuity PV Factor PV Factor (i = 10%, Present Value (i = 10%, n = 10) n = 10) 6.145 $ 16,334,885 0.386 386,000 16,720,885 (13,500,000) $ 3,220,885 Calculated in S26-4, Requirement 1 Chapter 26: Capital Investment Decisions Page 38 of 149 ACCOUNTING - Tenth Edition Solutions Manual The project's net present value (NPV) is $3,220,885. Based on NPV, the investment is attractive because the NPV is positive. Note: Decisions about which investments to pursue and which ones to delay or reject should not be based on quantitative factors only. Qualitative factors should also be considered. A project that is acceptable based on quantitative factors might be rejected after considering qualitative factors (and a project that would be rejected based on quantitative factors might be accepted after considering qualitative factors). Chapter 26: Capital Investment Decisions Page 39 of 149 ACCOUNTING - Tenth Edition Solutions Manual S26-12 What is the project's NPV (round to nearest dollar)? Is the investment attractive? Why or why not? Solution: Net Cash Inflow Time 1 - 10 years 0 PV of annuity Initial investment NPV of the project $ 2,658,240(a) (a) Calculated in S26-4, Requirement 1 Annuity PV Factor Present Value (i = 10%,n = 10) 6.145 $ 16,334,885 (13,500,000) $ 2,834,885 The project's net present value (NPV) is $2,834,885. Based on NPV, the investment is attractive because the NPV is positive. Note: Decisions about which investments to pursue and which ones to delay or reject should not be based on quantitative factors only. Qualitative factors should also be considered. A project that is acceptable based on quantitative factors might be rejected after considering qualitative factors (and a project that would be rejected based on quantitative factors might be accepted after considering qualitative factors). Chapter 26: Capital Investment Decisions Page 40 of 149 ACCOUNTING - Tenth Edition Solutions Manual S26-13 What is the project's IRR? Is the investment attractive? Why or why not? Solution: Annuity PV Factor = (i = ?%, n = 10) = = (a) Initial investment / Amount of each net cash inflow $13,500,000 5.079 (rounded) / $2,658,240(a) Calculated in S26-4, Requirement 1 Annuity PV Factor (i = 14%,n = 10) (i = 15%,n = 10) 5.216 5.019 Because 5.079 is between 5.019 and 5.216, the IRR is between 14% and 15%. Note: Using a business calculator or Microsoft Excel, the IRR is 14.69% (rounded). The project's internal rate of return (IRR) is between 14% and 15%. Based on IRR, the investment is attractive because the IRR is greater than the company's 10% required rate of return. Note: Decisions about which investments to pursue and which ones to delay or reject should not be based on quantitative factors only. Qualitative factors should also be considered. A project that is acceptable based on quantitative factors might be rejected after considering qualitative factors (and a project that would be rejected based on quantitative factors might be accepted after considering qualitative factors). Chapter 26: Capital Investment Decisions Page 41 of 149 ACCOUNTING - Tenth Edition Solutions Manual S26-14 Calculate the NPV of the investment. Should the company invest in the project? Why or why not? Solution: Time 1 2 3 0 PV of each year's net cash inflow (n = 1) (n = 2) (n = 3) Total present value of net cash inflows Initial investment Net present value of the investment Net Cash Inflow PV Factor (i = 12%) Present Value $ 225,000 150,000 100,000 0.893 0.797 0.712 $ 200,925 119,550 71,200 391,675 (350,000) $ 41,675 The investment's net present value (NPV) is $41,675. Based on NPV, the company should invest in the project because the NPV is positive. Note: Decisions about which investments to pursue and which ones to delay or reject should not be based on quantitative factors only. Qualitative factors should also be considered. A project that is acceptable based on quantitative factors might be rejected after considering qualitative factors (and a project that would be rejected based on quantitative factors might be accepted after considering qualitative factors). Chapter 26: Capital Investment Decisions Page 42 of 149 ACCOUNTING - Tenth Edition Solutions Manual E26-15 Match each definition with its capital budgeting method. Solution: Methods 1. 2. 3. 4. Definitions b. d. c. a. Chapter 26: Capital Investment Decisions Page 43 of 149 ACCOUNTING - Tenth Edition Solutions Manual E26-16 Fill in each statement with the appropriate capital investment analysis method. Solution: a. b. c. d. e. f. g. h. i. NPV and IRR Payback ARR IRR NPV Payback IRR Payback ARR Chapter 26: Capital Investment Decisions Page 44 of 149 ACCOUNTING - Tenth Edition Solutions Manual E26-17 Requirements 1. Determine the payback period of each project. Rank the projects from most desirable to least desirable based on payback. 2. Are there other factors that should be considered in addition to the payback period? Solution: Requirement 1 The payback period of each project, ranked from most desirable (shortest) to least desirable (longest) is: Project N M L Payback Period 2 years 3 years 4 years Chapter 26: Capital Investment Decisions Page 45 of 149 ACCOUNTING - Tenth Edition Solutions Manual Requirement 2 The company should also consider the cash inflows that occur after the payback period. For example, Project N has the shortest payback period, but does not generate any cash flows after that point. Therefore, the project only recoups the initial cash investment but does not provide any profits. Projects L and M have longer payback periods, but generate cash inflows after the payback period. Project M generates an additional $900,000 after the payback period and Project L generates an additional $600,000. Also, companies generally use more than one method to compare investments. In addition to the payback period, the accounting rate of return, net present value, profitability index, and internal rate of return should also be calculated for each project. The projects should then be ranked from most desirable to least desirable based on the results of each method. Additionally, decisions about which investments to pursue and which ones to delay or reject should not be based on quantitative factors only. Qualitative factors should also be considered (e.g. environmental considerations, impact on the community, lost business, and negative public perception of the company's choices). A project that is acceptable based on quantitative factors might be rejected after considering qualitative factors, and a project that would be rejected based on quantitative factors might be accepted after considering qualitative factors. Chapter 26: Capital Investment Decisions Page 46 of 149 ACCOUNTING - Tenth Edition Solutions Manual E26-18 Use the payback method to determine whether Preston should purchase this plant. Round to one decimal place. Solution: Payback = = = Amount invested Expected annual net cash inflow $1,100,000 $297,000 3.7 years (rounded) Based on payback, Preston should purchase the plant because the payback period of 3.7 years (rounded) is less than 6 years. Note: Decisions about which investments to pursue and which ones to delay or reject should not be based on quantitative factors only. Qualitative factors should also be considered. A project that is acceptable based on quantitative factors might be rejected after considering qualitative factors (and a project that would be rejected based on quantitative factors might be accepted after considering qualitative factors). Chapter 26: Capital Investment Decisions Page 47 of 149 ACCOUNTING - Tenth Edition Solutions Manual E26-19 Compute the payback period. Solution: Net Cash Outflows Amount Invested $1,454,000 Year 0 1 2 3 4 5 6 7 8 9 10 Annual $ Amount needed to complete recovery in Year 6 = = = Payback = 5 years + = 5 years + = 5 years + = 5.4 years Chapter 26: Capital Investment Decisions Net Cash Inflows Accumulated 300,000 270,000 260,000 260,000 260,000 260,000 260,000 260,000 260,000 260,000 Amount invested $1,454,000 $104,000 $ 300,000 570,000 830,000 1,090,000 1,350,000 1,610,000 1,870,000 2,130,000 2,390,000 2,650,000 Accumulated net cash inflows at the end of Year 5 $1,350,000 Amount needed to complete recovery in Year 6 Net cash inflow in Year 6 $104,000 $260,000 0.4 years Page 48 of 149 ACCOUNTING - Tenth Edition Solutions Manual E26-20 Compute the ARR for the investment. Round to two places. Solution: Total net cash inflows during = Sum of net cash inflows during operating operating life of project life of project = $300,000 Yr. 1 + $270,000 Yr. 2 + ($260,000 8 yrs.) = $2,650,000 Total depreciation during operating life of project = = = Cost $1,454,000 $1,454,000 Residual value $0 Total net cash inflows during operating life of project Less: Total depreciation during operating life of project Total operating income during operating life Divide by: Project's operating life in years Average annual operating income from project Average amount invested $ = Amount invested + Residual value 2 = $1,454,000 + $0 2 $727,000 = ARR $ = = Chapter 26: Capital Investment Decisions 2,650,000 1,454,000 1,196,000 10 years 119,600 Average annual operating income Average amount invested $119,600 $727,000 Page 49 of 149 ACCOUNTING - Tenth Edition Solutions Manual = 16.45% (rounded) Chapter 26: Capital Investment Decisions Page 50 of 149 ACCOUNTING - Tenth Edition Solutions Manual E26-21 Requirements 1. How much money does Janice need now to fund her travels? 2. After speaking with a number of banks, Janice learns she will only be able to invest her funds at 4%. How much does she need now to fund her travels? Solution: Requirement 1 Present value = = = Amount of each net cash inflow (cash needs) $28,000 $111,804 Annuity PV Factor for i = 8%, n = 5 3.993 Janice needs $111,804 now in order to fund her travels. Requirement 2 Present value = = = Amount of each net cash inflow $28,000 $124,656 Annuity PV Factor for i = 4%, n = 5 4.452 If the interest rate is 4% (rather than 8%), Janice needs $124,656 now in order to fund her travels. Chapter 26: Capital Investment Decisions Page 51 of 149 ACCOUNTING - Tenth Edition Solutions Manual E26-22 Assuming you can earn 8% on your funds, which option would you prefer? Solution: Option #1: Present value Option #2: Present value = = = Net cash inflow $15,000,000 $10,215,000 PV Factor for i = 8%, n = 5 0.681 = Amount of each net cash inflow Annuity PV Factor for i = 8%, n = 5 = = Option #3: Present value Option #1 #2 #3 = = = $2,150,000 $8,584,950 Net cash inflow $13,000,000 $10,322,000 x x 3.993 PV Factor for i = 8%, n = 3 0.794 Present Value $ 10,215,000 $ 8,584,950 $ 10,322,000 Option #3 is preferred because it yields the highest present value. Chapter 26: Capital Investment Decisions Page 52 of 149 ACCOUNTING - Tenth Edition Solutions Manual E26-23 Requirements 1. Compute this project's NPV using Sprocket's 16% hurdle rate. Should Sprocket invest in the equipment? 2. Sprocket could refurbish the equipment at the end of six years for $103,000. The refurbished equipment could be used one more year, providing $75,000 of net cash inflows in year 7. Additionally, the refurbished equipment would have a $54,000 residual value at the end of year 7. Should Sprocket invest in the equipment and refurbish it after six years? (Hint: In addition to your answer to Requirement 1, discount the additional cash outflow and inflows back to the present value.) Solution: Requirement 1 Time 1 2 3 4 5 6 0 Net Cash Inflow PV of each year's net cash inflow (n = 1) (n = 2) (n = 3) (n = 4) (n = 5) (n = 6) Total PV of net cash inflows Initial investment NPV of the equipment Chapter 26: Capital Investment Decisions $ 260,000 254,000 225,000 215,000 205,000 173,000 PV Factor Present (i = 16%) Value 0.862 0.743 0.641 0.552 0.476 0.410 $ 224,120 188,722 144,225 118,680 97,580 70,930 844,257 (905,000) $ (60,743) Page 53 of 149 ACCOUNTING - Tenth Edition Solutions Manual The net present value of the equipment is $(60,743). Based on net present value, Sprocket should not invest in the equipment because the net present value is negative. Note: Decisions about which investments to pursue and which ones to delay or reject should not be based on quantitative factors only. Qualitative factors should also be considered. A project that is acceptable based on quantitative factors might be rejected after considering qualitative factors (and a project that would be rejected based on quantitative factors might be accepted after considering qualitative factors). Requirement 2 Net Cash PV Factor Present Inflow (i = 16%) Value (Outflow) Time 7 7 6 PV of each year's net cash inflow (n = 7) (n = 7) Total PV of net cash inflows Cost to refurbish the equipment (n = 6) NPV of the refurbishment Net present value of the equipment with refurbishment = = = Chapter 26: Capital Investment Decisions Net present value of the equipment prior to refurbishment ($60,743) ($57,307) $ 75,000 54,000 0.354 0.354 (103,000) 0.410 + + $ 26,550 19,116 45,666 (42,230) $ 3,436 Net present value of the refurbishment $3,436 Page 54 of 149 ACCOUNTING - Tenth Edition Solutions Manual Based on net present value (NPV), Sprocket should not invest in the equipment and refurbish it after six years because the NPV of the equipment with refurbishment is negative $(57,307). Note: Decisions about which investments to pursue and which ones to delay or reject should not be based on quantitative factors only. Qualitative factors should also be considered. A project that is acceptable based on quantitative factors might be rejected after considering qualitative factors (and a project that would be rejected based on quantitative factors might be accepted after considering qualitative factors). Chapter 26: Capital Investment Decisions Page 55 of 149 ACCOUNTING - Tenth Edition Solutions Manual E26-24 Requirements 1. What is the NPV of each project? Assume neither project has a residual value. Round to two decimal places. 2. What is the maximum acceptable price to pay for each project? 3. What is the profitability index of each project? Round to two decimal places. Solution: Requirement 1 Time Net Cash Inflow Annuity Present PV Factor Value (i = 16%, (i = 14%, n = 7) n = 10) Project A: 1 - 7 years 0 PV of annuity Initial investment NPV of the project $ 57,000 1 - 10 years PV of annuity 0 Initial investment NPV of the project $ 75,000 4.039 $ 230,223 (260,000) $ (29,777) Project B: 5.216 $ 391,200 (375,000) $ 16,200 Requirement 2 The maximum acceptable price to pay is $230,223 for Project A and $391,200 for project B (the total present value of net cash inflows from each project, calculated in Requirement 1). Chapter 26: Capital Investment Decisions Page 56 of 149 ACCOUNTING - Tenth Edition Solutions Manual Requirement 3 / Initial investment = Profitability Index Project Present value of net cash inflows A $230,223 / $260,000 = 0.89 (rounded) B $391,200 / $375,000 = 1.04 (rounded) Chapter 26: Capital Investment Decisions Page 57 of 149 ACCOUNTING - Tenth Edition Solutions Manual E26-25 Compute the IRR of each project and use this information to identify the better Solution: Project A: Annuity PV Factor = (i = ?%, n = 7) = = Initial investment / Amount of each net cash inflow $260,000 / 4.561 (rounded) $57,000 Annuity PV Factor (i = 12%,n = 7) (i = 14%,n = 7) 4.564 4.288 Because 4.561 is between 4.288 and 4.564, the IRR is between 12% and 14%. Note: Using a business calculator or Microsoft Excel, the IRR is 12.02% (rounded). Project B: Annuity PV Factor = (i = ?%, n = 10) = = Initial investment / $375,000 5,000 / Amount of each net cash inflow $75,000 Annuity PV Factor (i = 15%,n = 10) (i = 16%,n = 10) 5.019 4.833 Chapter 26: Capital Investment Decisions Page 58 of 149 ACCOUNTING - Tenth Edition Solutions Manual Because 5.000 is between 4.833 and 5.019, the IRR is between 15% and 16%. Note: Using a business calculator or Microsoft Excel, the IRR is 15.10% (rounded). Project A's internal rate of return (IRR) is between 12% and 14%, which is less than the 16% required rate of return on projects like A. Project B's IRR is between 15% and 16%, which is greater than the 14% required rate of return on projects like B. Thus, based on IRR, Project B is the better investment. Note: Decisions about which investments to pursue and which ones to delay or reject should not be based on quantitative factors only. Qualitative factors should also be considered. A project that is acceptable based on quantitative factors might be rejected after considering qualitative factors (and a project that would be rejected based on quantitative factors might be accepted after considering qualitative factors). Chapter 26: Capital Investment Decisions Page 59 of 149 ACCOUNTING - Tenth Edition Solutions Manual E26-26 Which investment should Brighton pursue at this time? Why? Solution: Equipment A B C Present value of net cash inflows $1,735,915 $1,969,888 $2,207,765 Initial investment / / / / $1,563,887 $1,669,397 $1,886,979 = = = = Profitability Index 1.11 1.18 1.17 Because each of the three alternatives requires a different initial investment (cost), comparing the net present value of the three alternatives is not valid. The profitability index of an investment provides a measure of the number of dollars returned for every dollar invested, with all calculations performed in present value dollars. Thus, the profitability index allows valid comparison of alternatives with different initial investment amounts. The profitability index of each investment should be computed, and the investment with the highest profitability index should be pursued. The ranking of the investments based on the profitability index, from highest (most desirable) to lowest (least desirable), is Equipment B (1.18), Equipment C (1.17), and Equipment A (1.11). Because Brighton has funds available to pursue only one of the investments, based on the profitability index it should invest in Equipment B. Note: Decisions about which investments to pursue and which ones to delay or reject should not be based on quantitative factors only. Qualitative factors should also be considered. A project that is acceptable based on quantitative factors might be rejected after considering qualitative factors (and a project that would be rejected based on quantitative factors might be accepted after considering qualitative factors). Chapter 26: Capital Investment Decisions Page 60 of 149 ACCOUNTING - Tenth Edition Chapter 26: Capital Investment Decisions Solutions Manual Page 61 of 149 ACCOUNTING - Tenth Edition Solutions Manual E26-27 Determine if each investment is acceptable or should be rejected (ignore qualitative factors). Rank the acceptable investments in order from most desirable to least desirable. Solution: The acceptability of each project based on each criterion: Project A B C D E Payback Period (Acceptable if or = 12.5%) Acceptable Acceptable Reject Acceptable Acceptable Profitability Index (Acceptable if > or = 1.0) Acceptable Acceptable Reject Acceptable Acceptable The ranking (most desirable to least desirable) of each acceptable project based on each criterion: Ranking #1 #2 #3 #4 Payback Period The lower the payback period, the more desirable the project, all else being equal. NPV The higher the NPV, the more desirable the project (if the initial investment is the same for all projects). IRR The higher the IRR, the more desirable the project. Profitability Index The higher the profitability index, the more desirable the project. Project A Project D Project B Project E Project B Project D Project A Project E Project B Project D Project A Project E Project D Project B Project A Project E Chapter 26: Capital Investment Decisions Page 62 of 149 ACCOUNTING - Tenth Edition Solutions Manual P26-28A Requirements 1. How much money must you accumulate by retirement to make your plan work? (Hint: Find the present value of the $235,000 withdrawals.) 2. How does this amount compare to the total amount you will withdraw from the investment during retirement? How can these numbers be so different? Solution: Requirement 1 Present value = = = Amount of each net cash inflow (investment withdrawal) $235,000 $1,937,340 Annuity PV Factor for i = 12%, n = 40 8.244 You would need to accumulate $1,937,340 by retirement. Requirement 2 Total withdrawn during retirement = = = Amount withdrawn each year $235,000 $9,400,000 Total number of years 40 years The $9,400,000 total amount withdrawn from the investment during retirement is greater than the $1,937,340 investment (principal) at the beginning of retirement because only a portion of the principal is withdrawn each year and interest is earned on principal that is left invested each year. Chapter 26: Capital Investment Decisions Page 63 of 149 ACCOUNTING - Tenth Edition Solutions Manual P26-29A Requirements 1. Compute the payback, the ARR, the NPV, the IRR, and the profitability index of this investment. 2. Recommend whether the company should invest in this project. Solution: Requirement 1 Payback = Amount invested Expected annual net cash inflow = $1,870,000 $460,000 Total net cash inflows during = operating life of facility Average annual net cash inflow Operating life of facility $460,000 8 years = Chapter 26: Capital Investment Decisions = 4.1 years (rounded) = $3,680,000 Page 64 of 149 ACCOUNTING - Tenth Edition Solutions Manual Total depreciation during operating life of facility = = Cost Residual value $1,870,000 $0 = Total net cash inflows during operating life of facility Less: Total depreciation during operating life of facility Total operating income during operating life Divide by: Facility's operating life in years Average annual operating income from facility Average amount invested = = Chapter 26: Capital Investment Decisions $1,870,000 $ $ 3,680,000 1,870,000 1,810,000 8 years 226,250 Amount invested + Residual value 2 $1,870,000 + $0 2 = $935,000 Page 65 of 149 ACCOUNTING - Tenth Edition ARR = Solutions Manual Average annual operating income Average amount invested = $226,250 $935,000 Time 1 - 8 years 0 Annuity PV Factor (i = ?%, n = 8) = Net Cash Inflow PV of annuity Initial investment NPV of the facility = = Initial investment $1,870,000 Chapter 26: Capital Investment Decisions $ / / 24.20% (rounded) Present Annuity Value PV Factor (i = 10%,n = 8) 460,000 Amount of each net cash inflow $460,000 = 5.335 $ 2,454,100 (1,870,000) $ 584,100 4.065 (rounded) Page 66 of 149 ACCOUNTING - Tenth Edition Solutions Manual Annuity PV Factor (i = 18%,n = 8) (i = 20%,n = 8 4.078 3.837 Because 4.065 is between 3.837 and 4.078, the IRR is between 18% and 20%. Note: Using a business calculator or Microsoft Excel, the IRR is 18.10% (rounded). Profitability Index = Present value of net cash inflows = Chapter 26: Capital Investment Decisions / $2,454,100 / Initial investment $1,870,000 = 1.31 (rounded) Page 67 of 149 ACCOUNTING - Tenth Edition Solutions Manual Requirement 2 Based on the quantitative measures calculated in Requirement 1, the company should invest in the project because the payback period is less than the operating life, the net present value is positive, the profitability index is greater than one, and both the accounting rate of return and internal rate of return are greater than the company's required rate of return. Note: Decisions about which investments to pursue and which ones to delay or reject should not be based on quantitative factors only. Qualitative factors should also be considered. A project that is acceptable based on quantitative factors might be rejected after considering qualitative factors (and a project that would be rejected based on quantitative factors might be accepted after considering qualitative factors). Chapter 26: Capital Investment Decisions Page 68 of 149 ACCOUNTING - Tenth Edition Solutions Manual P26-30A Requirements 1. Compute the payback, the ARR, the NPV, and the profitability index of these two plans. 2. What are the strengths and weaknesses of these capital budgeting methods? 3. Which expansion plan should Leches choose? Why? 4. Estimate Plan A's IRR. How does the IRR compare with the company's required rate of return? Solution: Requirement 1 Payback = Amount invested Expected annual net cash inflow Plan A: = $8,400,000 $1,500,000 = 5.6 years Plan B: = $8,250,000 $1,080,000 = 7.6 years (rounded) Chapter 26: Capital Investment Decisions Page 69 of 149 ACCOUNTING - Tenth Edition Solutions Manual Average annual net cash inflow Total net cash inflows during operating life of property = Plan A: = $1,500,000 10 years = $15,000,000 Plan B: = $1,080,000 10 years = $10,800,000 Total depreciation during operating life of property = Cost Residual value Plan A: = $8,400,000 = $8,400,000 Plan B: = = $7,250,000 Total net cash inflows during operating life of property Less: Total depreciation during operating life of property Total operating income during operating life Divide by: Property's operating life in years Average annual operating income from plan Chapter 26: Capital Investment Decisions Operating life of property $0 $1,000,000 $ $ Plan A 15,000,000 8,400,000 6,600,000 10 years 660,000 Plan B $ $ 10,800,000 7,250,000 3,550,000 10 years 355,000 Page 70 of 149 ACCOUNTING - Tenth Edition Solutions Manual Average amount invested = Amount invested + Residual value 2 Plan A: = Plan B: = $8,400,000 + $0 2 $8,250,000 + $1,000,000 2 ARR = Plan A: = Plan B: = Chapter 26: Capital Investment Decisions Average annual operating income Average amount invested $660,000 $4,200,000 $355,000 $4,625,000 = $4,200,000 = $4,625,000 = 15.71% (rounded) = 7.68% (rounded) Page 71 of 149 ACCOUNTING - Tenth Edition Solutions Manual Time Plan A: 1 - 10 years 0 Plan B: 1 - 10 years 10 0 Plan A B Net Cash Inflow Annuity PV Factor (i = 10%, n = 10) PV Factor (i = 10%, n = 10) Present Value PV of annuity Initial investment NPV of Plan A $1,500,000 6.145 $ PV of annuity PV of residual value Total PV of net cash inflows Initial investment NPV of Plan B $1,080,000 1,000,000 6.145 $ Present value of net cash inflows $9,217,500 $7,022,600 Chapter 26: Capital Investment Decisions / / / Initial investment = $8,400,000 $8,250,000 = = 9,217,500 (8,400,000) $ 817,500 0.386 6,636,600 386,000 7,022,600 (8,250,000) $ (1,227,400) Profitability Index 1.10 (rounded) 0.85 (rounded) Page 72 of 149 ACCOUNTING - Tenth Edition Solutions Manual Requirement 2 Payback Focus The time it takes to recover the initial cash investment. Accounting Rate of Return (ARR) How the investment affect operating income. Net Present Value (NPV) The difference between the present value of the net cash inflows and the initial cash investment The only method that uses accrual uses accrual accounting figures. accounting figures. the Measures profitability ofof the profitability the asset over its entire asset over its life. entire life. Incorporates the time value of money. Considers the asset's net cash flows over its net cash flows over entire life. its entire entire life.life. Indicates whether the asset will earn the company's minimum required rate of return. Simple to compute. Strengths Highlights risks of investments with with longer cash recovery periods. Chapter 26: Capital Investment Decisions Profitability Index The number of dollars returned for every dollar invested, with all calculations in present value dollars. Incorporates the time value of money. Considers the asset's net cash flows over its entire life. Indicates whether the asset will earn the company's minimum required rate of return. No additional steps needed for capital rationing Page 73 of 149 ACCOUNTING - Tenth Edition Solutions Manual decisions when assets require different initial investments. Ignores the time Ignores the time value of money. value of money. Ignores any cash Weaknesses flows occurring after the payback period, including any value. The profitability index Doesn't show the should be computed absolute total capital rationing dollar amounts for decisions when the present value assets require of net cash inflows different initial and the initial investments. investment. Requirement 3 Based on the quantitative measures calculated in Requirement 1, Leches should choose Plan A, rather than Plan B. Plan A has a positive net present value (NPV), whereas Plan B has a negative NPV. Plan A also has the lower payback period and the higher accounting rate of return and profitability index. Note: Decisions about which investments to pursue and which ones to delay or reject should not be based on quantitative factors only. Qualitative factors should also be considered. A project that is acceptable based on quantitative factors might be rejected after considering qualitative factors (and a project that would be rejected based on quantitative factors might be accepted after considering qualitative factors). Chapter 26: Capital Investment Decisions Page 74 of 149 ACCOUNTING - Tenth Edition Solutions Manual Requirement 4 Annuity PV = Factor (i = ?%, n = 10) = = Initial investment / $8,400,000 $6 / Amount of each net cash inflow $1,500,000 Annuity PV Factor (i = 12%, n = 10) (i = 14%, n = 10) 5.65 5.216 Because 5.600 is between 5.216 and 5.650, the IRR is between 12% and 14%. Plan A's internal rate of return (IRR) is between 12% and 14%, which is greater than the company's 10% required rate of return. Chapter 26: Capital Investment Decisions Page 75 of 149 ACCOUNTING - Tenth Edition Chapter 26: Capital Investment Decisions Solutions Manual Page 76 of 149 ACCOUNTING - Tenth Edition Solutions Manual P26-31A Requirements 1. Compute the payback, the ARR, the NPV, and the profitability index of these two options. 2. Which option should Metz choose? Why? Solution: Requirement 1 Refurbish Current Machine: Net Cash Outflows Year Amount Invested 0 $1,000,000 1 $ 2 3 4 5 6 7 8 Chapter 26: Capital Investment Decisions Net Cash Inflows Annual Accumulated 500,000 400,000 300,000 200,000 100,000 100,000 100,000 100,000 $ 500,000 900,000 1,200,000 1,400,000 1,500,000 1,600,000 1,700,000 1,800,000 Page 77 of 149 ACCOUNTING - Tenth Edition Amount needed to complete recovery in Year 3 Solutions Manual = Amount invested = = Payback $1,000,000 $100,000 Accumulated net cash inflows at the end of Year 2 $900,000 = 2 years + = 2 years + = = 2 years 2.3 years (rounded) + Amount needed to complete recovery in Year 3 Net cash inflow in Year 3 $100,000 $300,000 0.3 years (rounded) Purchase New Machine: Year 0 1 2 3 4 5 6 7 8 Net Cash Outflows Amount Invested $2,000,000 Chapter 26: Capital Investment Decisions Net Cash Inflows Annual Accumulated $ 700,000 600,000 500,000 400,000 300,000 300,000 300,000 300,000 $ 700,000 1,300,000 1,800,000 2,200,000 2,500,000 2,800,000 3,100,000 3,400,000 Page 78 of 149 ACCOUNTING - Tenth Edition Solutions Manual 9 10 Amount needed to complete recovery in Year 4 300,000 300,000 = = = Payback $2,000,000 $200,000 Accumulated net cash inflows at the end of Year 3 $1,800,000 = 3 years + = 3 years + = = 3 years 3.5 years (rounded) + Amount needed to complete recovery in Year 4 Net cash inflow in Year 4 $200,000 $300,000 0.5 years (rounded) Residual value Total depreciation during operating life of machine = Refurbish Current Machine: Purchase New Machine: = = Chapter 26: Capital Investment Decisions Amount invested 3,700,000 4,000,000 Cost $1,000,000 $2,000,000 $0 $0 = = $1,000,000 $2,000,000 Page 79 of 149 ACCOUNTING - Tenth Edition Solutions Manual Average amount invested = Amount invested + Residual value 2 Refurbish Current Machine: = $1,000,000 + $0 2 = $500,000 Purchase New Machine: = $2,000,000 + $0 2 = $1,000,000 Total net cash inflows during operating life of machine Less: Total depreciation during operating life of machine Total operating income during operating life Divide by: Machine's operating life in years Average annual operating income from machine Chapter 26: Capital Investment Decisions Refurbish Current Purchase New Machine Machine $ 1,800,000 $ 4,000,000 1,000,000 $ 4,000,000 800,000 2,000,000 8 years 10 years $ 100,000 $ 200,000 Page 80 of 149 ACCOUNTING - Tenth Edition ARR Solutions Manual = Average annual operating income Average amount invested Refurbish Current Machine: = $100,000 $500,000 = 20% Purchase New Machine: = $200,000 $1,000,000 = 20% Refurbish Current Machine: Time 1 2 3 4 5 6 7 PV of each year's net cash inflow (n = 1) (n = 2) (n = 3) (n = 4) (n = 5) (n = 6) (n = 7) Chapter 26: Capital Investment Decisions Net Cash Inflow $ 500,000 400,000 300,000 200,000 100,000 100,000 100,000 PV Factor (i = 10%) 0.909 0.826 0.751 0.683 0.621 0.564 0.513 Present Value $ 454,500 330,400 225,300 136,600 62,100 56,400 51,300 Page 81 of 149 ACCOUNTING - Tenth Edition 8 0 Solutions Manual (n = 8) Total PV of net cash inflows Initial investment NPV of refurbishing current machine 100,000 $ Purchase New Machine: Time 1 2 3 4 5 6 7 8 9 10 0 Net Cash Inflow PV of each year's net cash inflow (n = 1) (n = 2) (n = 3) (n = 4) (n = 5) (n = 6) (n = 7) (n = 8) (n = 9) (n = 10) Total PV of net cash inflows Initial investment NPV of purchasing new machine Option Refurbish Present value of net cash inflows $1,363,300 Chapter 26: Capital Investment Decisions 0.467 $ 700,000 600,000 500,000 400,000 300,000 300,000 300,000 300,000 300,000 300,000 PV Factor (i = 10%) 0.909 0.826 0.751 0.683 0.621 0.564 0.513 0.467 0.424 0.386 Present Value $ $ / / Initial investment $1,000,000 46,700 1,363,300 (1,000,000) 363,300 636,300 495,600 375,500 273,200 186,300 169,200 153,900 140,100 127,200 115,800 2,673,100 (2,000,000) 673,100 = Profitability Index = 1.36 (rounded) Page 82 of 149 ACCOUNTING - Tenth Edition Solutions Manual Current Machine Purchase New Machine $2,673,100 / $2,000,000 = 1.34 (rounded) Requirement 2 Payback period: Accounting rate of return (ARR): Net present value (NPV): Profitability index: Refurbish Current Machine 2.3 years (rounded) 20% $363,300 1.36 (rounded) Purchase New Machine 3.5 years 20% $673,100 1.34 (rounded) Based on payback Metz should choose to refurbish the current machine (the option with the shorter payback period). Because the accounting rate of return (ARR) of the two options is the same, ARR doesn't help choose between the two options. Because each of the two options requires a different initial investment (cost), comparing the net present value (NPV) of the two options is not valid. The profitability index of an investment provides a measure of the number of dollars returned for every dollar invested, with all calculations performed in present value dollars. Thus, the profitability index allows valid comparison of alternatives with different initial investment amounts. Based on the profitability index, Metz should choose to refurbish the current machine (the option with the higher profitability index). Chapter 26: Capital Investment Decisions Page 83 of 149 ACCOUNTING - Tenth Edition Solutions Manual Thus, based on both the payback period and profitability index, Metz should choose to refurbish the current machine. Note: Decisions about which investments to pursue and which ones to delay or reject should not be based on quantitative factors only. Qualitative factors should also be considered. A project that is acceptable based on quantitative factors might be rejected after considering qualitative factors (and a project that would be rejected based on quantitative factors might be accepted after considering qualitative factors). Chapter 26: Capital Investment Decisions Page 84 of 149 ACCOUNTING - Tenth Edition Solutions Manual P26-32A Requirements 1. Use Excel to compute the NPV and IRR of the two plans. Which plan, if any, should the company pursue? 2. Explain the relationship between NPV and IRR. Based on this relationship and the company's required rate of return, are your answers as expected in Requirement 1? Why or why not? 3. After further negotiating, the company can now invest with an initial cost of $5,500,000. Recalculate the NPV and IRR. Which plan, if any, should the company pursue? Solution: Requirement 1 Microsoft Excel Results: Chapter 26: Capital Investment Decisions Page 85 of 149 ACCOUNTING - Tenth Edition Solutions Manual Microsoft Excel Formulas: Plan Alpha Net present value (NPV): $(349,777) (rounded) Internal rate of return (IRR): 10.56% (rounded) Plan Beta $306,286 (rounded) 13.51% (rounded) Based on the foregoing