Solution manual cost accounting by carter 14e ch23

CHAPTER 23 DISCUSSION QUESTIONS Q23-1 The weighted average cost of capital is computed by the following steps: (a) Calculate each component of capital as a percentage of total capital (b) Calculate the after-tax cost of each individual capital component (c) For each capital component, multiply (a) by (b) and sum the results Q23-2 Using the cost of a specific source of funds may lead to faulty decisions For example, when debt is used, low-return projects would be acceptable while better investments would have to be ruled out in a following period, when common stock shares are sold to obtain funds Q23-3 There are two problem areas associated with estimating the firm’s weighted average cost of capital—the proportions of each source of funds and the cost of each source of funds The proportions that are expected over the investment horizon should be used Since these amounts are typically unknown, the proportions desired by management in the long run are usually used With respect to costs, the market prices of each source of funds should be used Since the market price varies over time as creditor and investor expectations change, current market prices adjusted for changes expected by management are commonly used CGA-Canada (adapted) Reprint with permission Q23-4 The payback (or payout) period method measures the length of time required by a project to recover the initial investment outlay Q23-5 In computing the accounting rate of return on original investment, the denominator is the original investment, whereas in computing the accounting rate of return on average investment, the denominator is the average investment Q23-6 The present value concept states that a dollar received today is worth more than a dollar to be received at a future date because of the earnings the “today” dollar can generate in the interim It is important in capital budgeting because of the relatively long periods between the investment of funds and the return of those funds as earnings (i.e., dollars returned a long time in the future are worth considerably less than those invested today) Q23-7 The basic difference between the payback method and the net present value method concerns the recognition of the time value of money The payback method, which ignores the time value of money and all cash flows beyond the payback period for the project, is the measure of the time it will take to recover the initial capital investment in net cash inflows The net present value method does consider the time value of money This method involves comparing the present value of all future cash inflows and outflows of a given project, using some minimum desired rate of return A positive result implies that the project’s rate of return exceeds this minimum rate, whereas a negative result indicates that the project’s rate of return is less than this minimum rate Q23-8 In the net present value method, the discount rate is known; whereas, in the internal rate of return method, the discount rate is not known In the internal rate of return method, the discount rate is the one that will result in a net present value of zero Q23-9 The net present value method assumes that earnings are reinvested at a rate of return equal to the firm’s cost of capital, whereas the internal rate of return method assumes that earnings are reinvested at the rate of return of the particular project being considered The firm’s cost of capital rate is more realistic If an investment proposal is predicted to be extremely profitable (e.g., having an internal rate of return of 50%), it is unlikely that similar proposals are available However, a firm should ordinarily have several investment opportunities at or near the rate of its cost of capital CGA-Canada (adapted) Reprint with permission 23-1 23-2 Q23-10 Setting the discount rate at something in excess of the cost of capital in order to compensate for risk and uncertainty associated with a capital expenditure proposal is conceptually unsound, because the reinvestment potential of cash flows is overstated Cash received in early periods has more value than cash received in later periods, because only the cash received in the early periods can be reinvested As a consequence, the use of a rate in excess of the reinvestment rate in the net present value method will result in an Chapter 23 overstatement of the value of cash received early in the life of the capital expenditure project A better approach would be to compute the terminal value of the cash flows using the reinvestment rate (i.e., compute the value of all cash flows at the end of the life of the project), and then discount the total to present value at a risk-adjusted discount rate An even better approach is to explicitly consider uncertainty by using probability analysis, as discussed in Chapter 24 Chapter 23 23-3 EXERCISES E23-1 Proportion After-Tax Weighted Funds—Source of Funds Cost Cost Bonds (10% × (1 – 45% tax rate)) 30% 5.5% 1.65% Preferred stock 10% 12.5% * 1.25% Common stock and retained earnings 60% 15.0% ** 9.00% 100% 11.90% *(12% × $100 par value for preferred stock) ÷ $96 market value **($75,000 ÷ 50,000 shares of common stock) ÷ $10 market price per share E23-2 Weighted average cost of capital before bond retirement and sale-leaseback transaction: (1) Capital Component Bonds Preferred stock Common stock and retained earnings (2) (3) (4) Amount $ 5,000,000 1,000,000 Percent of Total 50% 10% Pretax Cost 8.0% 9.0% After-Tax Cost 4.8% 9.0% 4,000,000 $10,000,000 40% 100% 12.5% 12.5% (5) Weighted Cost (2) × (4) 2.4% 9% 5.0% 8.3% Weighted average cost of capital after bond retirement and sale-leaseback transaction: (1) Capital Component Lease Bonds Preferred stock Common stock and retained earnings (2) 3) (4) Amount $ 1,000,000 4,000,000 1,000,000 Percent of Total 10% 40% 10% Pretax Cost 10.0% 8.0% 9.0% After-Tax Cost 6.0% 4.8% 9.0% 4,000,000 $10,000,000 40% 100% 12.5% 12.5% (5) Weighted Cost (2) × (4) 60% 1.92% 90% 5.00% 8.42% 23-4 Chapter 23 E23-3 (1) Annual cash inflow before income tax $15,000 Less depreciation (the same for financial accounting and income tax purposes ($40,000 cost ÷ years)) 5,000 Annual taxable income $10,000 Annual income tax ($10,000 taxable income × 40%) 4,000 Annual income after taxes $ 6,000 $15,000 Annual after-tax cash inflow $11,000 4,000 $40,000 initial cash outflow = 3.636 years to payback $11,000 annual cash inflow (2) $6,000 average annual income = 15 or 15% rate of return $40,000 original investment on original investment E23-4 (1) $33,000 initial cash outflow $10,000 annual cash inflow (2) Present value of annual cash inflows for six years ($10,000 annual cash inflow × 3.784) Less initial cash outflow to acquire investment (3) = 3.3 years to payback $37,840 33,000 Net present value of investment 4,840 Cash desired at end of six years Present value of $1 compounded annually at 15% $33,000 × 432 Investment required $14,256 E23-5 (1) (2) Present value of annual cash inflows for 10 years ($20,000 annual cash inflow × 5.216) Present value of salvage value at end of 10-year life ($10,000 cash inflow from salvage × 270) $104,320 2,700 Present value of all cash inflows Less initial cash outflow to purchase press $107,020 (99,000) Net present value of investment $ Present = value index $8,020 net present value $99,000 initial investment = 08101 or 8.1% 8,020 Chapter 23 23-5 E23-6 (1) Year (2) MACRS StraightRecovery Line Rate Rate 0.200 0.320 0.192 0.115 0.115 0.058 0.100 0.200 0.200 0.200 0.200 0.100 (3) (4) (5) (6) Cost Recovery Under MACRS StraightLine Depreciation Difference (3) – (4) $ 20,000 32,000 19,200 11,500 11,500 5,800 $ 10,000 20,000 20,000 20,000 20,000 10,000 $10,000 12,000 (800) (8,500) (8,500) (4,200) $100,000 $100,000 (7) Income Tax Present Savings Value of (5) × 40% $1 @ 14% $4,000 4,800 (320) (3,400) (3,400) (1,680) 0 0.877 0.769 0.675 0.592 0.519 0.456 (8) Present Value of Tax Savings (6) × (7) $3,508 3,691 (216) (2,013) (1,765) (766) $2,439 E23-7 (1) Year Unadjusted Estimate of Cash Inflows $20,000 18,000 16,000 10,000 10,000 $74,000 Inflation Adjustment 1.10000* 1.21000 1.33100 1.46410 1.61051 Inflation Adjusted Estimate of Cash Inflows $22,000.00 21,780.00 21,296.00 14,641.00 16,105.10 $95,822.10 *(1 + 10)n where n = number of periods (2) Unadjusted Adjusted PV of $1 Year Cash Flows Cash Flows @ 15% $(60,000) $(60,000) 1.000 20,000 22,000 870 18,000 21,780 756 16,000 21,296 658 10,000 14,641 572 10,000 16,105 497 Net present value of investment PV of Unadjusted Cash Flows $(60,000) 17,400 13,608 10,528 5,720 4,970 $ (7,774) PV of Adjusted Cash Flows $(60,000) 19,140 16,466 14,013 8,375 8,004 $ 5,998 23-6 Chapter 23 E23-8 Year (1) Year 10 Annual Pretax Cash Inflows (1) (2) Tax Basis of New Airplane $500,000 500,000 500,000 500,000 500,000 500,000 500,000 500,000 7-Year Property Recovery Rate 0.143 0.245 0.175 0.125 0.089 0.089 0.089 0.045 (2) (3) Increase (Decrease) Tax in DepreTaxable ciation Income Deduction (1) – (2) $130,000 $ 71,500 130,000 122,500 130,000 87,500 130,000 62,500 130,000 44,500 130,000 44,500 130,000 44,500 130,000 22,500 130,000 130,000 $ 58,500 7,500 42,500 67,500 85,500 85,500 85,500 107,500 130,000 130,000 (4) Income Tax Rate 40% 40% 40% 40% 40% 40% 40% 40% 40% 40% (5) Increase (Decrease) in Income Tax (3) × (4) $23,400 3,000 17,000 27,000 34,200 34,200 34,200 43,000 52,000 52,000 (3) Tax Depreciation on New Airplane (1) × (2) $ 71,500 122,500 87,500 62,500 44,500 44,500 44,500 22,500 $500,000 (6) (7) After-Tax Cash Inflows (1) – (5) Present Value of $1 @ 15% $106,000 127,000 113,000 103,000 95,800 95,800 95,800 87,000 78,000 78,000 0.870 0.756 0.658 0.572 0.497 0.432 0.376 0.327 0.284 0.247 (8) Present Value of After-Tax Cash Inflows (6) × (7) $ 92,742 96,012 74,354 58,916 47,613 41,386 36,021 28,449 22,152 19,266 Present value of periodic after-tax cash inflows Plus present value of after-tax salvage ($100,000 × (1 – 40%) × 247) $516,911 14,820 Present value of cash inflows over useful life of new airplane Less initial cash outflow (cost of new airplane) $531,731 500,000 Net present value of investment $ 31,731 Chapter 23 23-7 E23-9 Cost of new machine Trade-in allowance for old machine Net cash outflow at beginning of project Tax basis of old machine traded in Tax basis of new machine $38,000 18,000 $20,000 16,000 $36,000 Annual cost of operating old machine Annual cost of operating new machine Annual cost savings with new machine $40,000 34,000 $6,000 Year (1) Original Tax Basis of Old Machine $20,000 20,000 20,000 20,000 20,000 (2) 5-Year Property Recovery Rate 0.320 * 0.192 0.115 0.115 0.058 (3) Tax Depreciation on Old Machine (1) × (2) $ 6,400 3,840 2,300 2,300 1,160 $16,000 *Note that year is actually the second year the old property is depreciated Therefore, the recovery rate for the second year is used to compute the amount of depreciation on the old property in the first year of the capital expenditure proposal Year (1) Original Tax Basis of New Machine $36,000 36,000 36,000 36,000 36,000 36,000 (2) 5-Year Property Recovery Rate 0.200 0.320 0.192 0.115 0.115 0.058 (3) Tax Depreciation on New Machine (1) × (2) $ 7,200 11,520 6,912 4,140 4,140 2,088 $36,000 23-8 Chapter 23 E23-9 (Concluded) (1) (2) Allowable Tax Depreciation New Old Year Machine Machine $ 7,200 11,520 6,912 4,140 4,140 2,088 $6,400 3,840 2,300 2,300 1,160 (3) Additional Tax Depreciation with New Machine (1) – (2) $ 800 7,680 4,612 1,840 2,980 2,088 (4) (5) Annual Cost Savings With New Machine Increase (Decrease) in Taxable Income (4) – (3) $6,000 6,000 6,000 6,000 6,000 6,000 $ 5,200 (1,680) 1,388 4,160 3,020 3,912 (6) (7) Increase (Decrease) in Income Income Tax Tax Rate (5) × (6) 40% 40% 40% 40% 40% 40% $2,080 (672) 555 1,664 1,208 1,565 (8) Net Cash Inflow (4) – (7) $ 3,920 6,672 5,445 4,336 4,792 4,435 Total increase in periodic cash inflow Less initial cash outlay for new machine $29,600 20,000 Increase in cash inflows over initial cash outlay for new machine $ 9,600 Year (1) (2) Net After-Tax Cash Inflow (Outflow) $(20,000) 3,920 6,672 5,445 4,336 4,792 4,435 Present Value of $1 @ 12% 1.000 0.893 0.797 0.712 0.636 0.567 0.507 (3) Present Value of Cash Flows @ 12% (1) × (2) $(20,000) 3,501 5,318 3,877 2,758 2,717 2,249 $ 420 (4) Present Value of $1 @ 14% 1.000 0.877 0.769 0.675 0.592 0.519 0.456 (5) Present Value of Cash Flows @14% (1) × (4) $(20,000) 3,438 5,131 3,675 2,567 2,487 2,022 $ (680) ⎛ ⎛ ⎞⎞ $420 Internal rate of return = 12% +⎜ 2% ×⎜ ⎟⎟= 12.76% ⎝ $420 + $680 ⎠⎠ ⎝ Recommendation: The investment may be acceptable because the internal rate of return exceeds the company’s cost of capital; however, the internal rate of return on this project should be compared with the internal rate of return for other projects to determine if this is the best use of available funds Chapter 23 23-9 E23-10 (1) Project A Cash Inflow PV of $1 Year (Outflow) @15% $(15,000) 1.000 1-5 5,000 3.352 Net present value PV of Cash Flow $(15,000) 16,760 $ 1,760 Project B Cash Inflow PV of $1 Year (Outflow) @15% $(15,000) 1.000 35,000 497 Net present value (2) Project A Year 1-5 Cash Inflow (Outflow) $(15,000) 5,000 PV of $1 @18% 1.000 3.127 PV of Cash Flow $(15,000) 15,635 $635 PV of $1 @20% 1.000 2.991 PV of Cash Flow $(15,000) 17,395 $ 2,395 PV of Cash Flow $(15,000) 14,955 $ (45) ⎛ ⎞⎞ $635 Internal rate = 18% +⎜ 2% ×⎛ ⎜ ⎟⎟= 18% + (2% × 934 ) = 19.87% of return ⎝ $635 + $45 ⎠⎠ ⎝ Project B Year Cash Inflow (Outflow) $(15,000) 35,000 PV of $1 @18% 1.000 437 PV of Cash Flow $(15,000) 15,295 $295 PV of $1 @20% 1.000 402 PV of Cash Flow $(15,000) 14,070 $(930) ⎛ ⎞⎞ $295 Internal rate = 18% +⎜ 2% ×⎛ ⎜ ⎟⎟= 18% + (2% × 241) = 18.48% of return ⎝ $295 + $930 ⎠⎠ ⎝ (3) Using the internal rate of return method, Project A is superior to Project B Using the net present value method, Project B is more attractive than A The decision hinges on assumptions made about reinvestment of cash inflow Theory suggests resorting to the net present value method because the cost of capital reinvestment assumption implicit in this method is considered more realistic than the internal rate of return method, where a reinvestment at the project’s internal rate is assumed 23-10 Chapter 23 PROBLEMS P23-1 (1) Alternative Plan (a) (b) Weighted Average Cost 7.20% Source of Financing Debt Portion of After-Tax Cost Total Required 12% × (1 – 40% tax rate) $10,000,000 $10,000,000 Debt 12% × (1 – 40% tax rate) $5,000,000 $10,000,000 3.60% 9% (1 – 4% issue cost) $5,000,000 $10,000,000 4.69% Preferred stock 8.29% (c) (2) Source of Financing Debt Preferred stock Common stock Common stock $2.10 earnings per share $10,000,000 11.05% ($20 × (1 – 5% issue cost)) $10,000,000 Portion of Current Total $20,000,000 $90,000,000 9% $10,000,000 $90,000,000 $2.10 earnings per share $60,000,000* $20 market price per share $90,000,000 After-Tax Cost 10% × (1 – 40% tax rate) Weighted Average Cost 1.33% 1.00% 7.00% 9.33% *3,000,000 shares outstanding × $20 market price per share Chapter 23 23-21 P23-7 Year 10 Recovery Year (1) (2) Periodic Net Cash Inflows $ 20,000 25,000 30,000 30,000 30,000 30,000 25,000 20,000 15,000 10,000 $235,000 Annual 7% Price-Level Adjustment (1 + 07) = 1.070 (1 + 07)2 = 1.145 (1 + 07)3 = 1.225 (1 + 07)4 = 1.311 (1 + 07)5 = 1.403 (1 + 07)6 = 1.501 (1 + 07)7 = 1.606 (1 + 07)8 = 1.718 (1 + 07)9 = 1.838 (1 + 07)10 = 1.967 (1) (2) 7-Year Property Recovery Percentage 0.143 0.245 0.175 0.125 0.089 0.089 0.089 0.045 Depreciable Basis of Machine $100,000 100,000 100,000 100,000 100,000 100,000 100,000 100,000 (3) Adjusted Estimate of Net Cash Inflows (1) × (2) $ 21,400 28,625 36,750 39,330 42,090 45,030 40,150 34,360 27,570 19,670 $334,975 (3) Tax Depreciation (1) × (2) $ 14,300 24,500 17,500 12,500 8,900 8,900 8,900 4,500 $100,000 23-22 Chapter 23 P23-7 (Continued) (1) (4) (5) (6) Federal Income Net Adjusted Taxable and Tax After-Tax Estimate of Tax Income State Payment Cash Net Cash Deprec(Loss) Income (Reduction) Inflows Year Inflows iation (1) – (2) Tax Rate (3) × (4) (1) – (5) $21,400 $14,300 $ 7,100 40% $ 2,840 $ 18,560 28,625 24,500 4,125 40% 1,650 26,975 36,750 17,500 19,250 40% 7,700 29,050 39,330 12,500 26,830 40% 10,732 28,598 42,090 8,900 33,190 40% 13,276 28,814 45,030 8,900 36,130 40% 14,452 30,578 40,150 8,900 31,250 40% 12,500 27,650 34,360 4,500 29,860 40% 11,944 22,416 27,570 27,570 40% 11,028 16,542 10 19,670 19,670 40% 7,868 11,802 Total inflation-adjusted after-tax cash inflows $240,985 (1) (2) (3) Payback period: Recovery of Initial Cash Outlay Net After-Tax Year Cash Inflow Needed Balance $18,560 $100,000 $81,440 26,975 81,440 54,465 29,050 54,465 25,415 28,598 25,415 Total payback period in years (2) Accounting rate of return on original investment: Total inflation-adjusted after-tax cash inflow Less financial accounting depreciation Net income over economic life of project Average annual return Years Required Until Payback 1.0 1.0 1.0 0.9 3.9 $240,985 100,000 $140,985 = Net income = $140,985 = $14,099 Economic life 10 years Accounting rate of return on original = Average annual return = $14,099 = 1410 or 14.10% investment Original investment $100,000 Chapter 23 23-23 P23-7 (Continued) (3) Accounting rate of return on average investment: Accounting rate of return on average = Average annual return = $14,099 = 2820 or 28.20% investment Original investment ÷ $50,000 (4) Net present value and net present value index: (1) (2) Net After-Tax Present Cash Value (Outflow) of $1 Year Inflow @ 15% $(100,000) 1.000 18,560 0.870 26,975 0.756 29,050 0.658 28,598 0.572 28,814 0.497 30,578 0.432 27,650 0.376 22,416 0.327 16,542 0.284 10 11,802 0.247 Net present value Net present = value index (5) (3) Present Value of Net Cash Flow (1) × (2) $(100,000) 16,147 20,393 19,115 16,358 14,321 13,210 10,396 7,330 4,698 2,915 $ 24,883 Net present value = $24,883 = 249 Required investment $100,000 Present value payback in years: Recovery of Present Initial Cash Outlay Value of After-Tax Year Cash Inflow Needed Balance $16,147 $100,000 $83,853 20,393 83,853 63,460 19,115 63,460 44,345 16,358 44,345 27,987 14,321 27,987 13,666 13,210 13,666 456 10,396 456 Total payback period in years Years Required for Present Value Payback 1.00 1.00 1.00 1.00 1.00 1.00 0.04 6.04 23-24 Chapter 23 P23-7 (Concluded) (6) Internal rate of return: (1) Year 10 Net After-Tax Cash (Outflow) Inflow $(100,000) 18,560 26,975 29,050 28,598 28,814 30,578 27,650 22,416 16,542 11,802 (2) Present Value of $1 @ 20% 1.000 0.833 0.694 0.579 0.482 0.402 0.335 0.279 0.233 0.194 0.162 (3) (4) Present Value of Cash Flow Present Discounted Value @20% of $1 (1) × (2) @ 22% $(100,000) 1.000 15,460 0.820 18,721 0.672 16,820 0.551 13,784 0.451 11,583 0.370 10,244 0.303 7,714 0.249 5,223 0.204 3,209 0.167 1,912 0.137 $ 4,670 (5) Present Value of Cash Flow Discounted @ 22% (1) × (4) $(100,000) 15,219 18,127 16,007 12,898 10,661 9,265 6,885 4,573 2,763 1,617 $ (1,985) ⎛ Internal rate ⎛ ⎞⎞ $4, 670 of return = 20% +⎜ 2% ×⎜ $4, 670 + $1, 985 ⎟⎟= 2140 or 21.4% ⎝ ⎠⎠ ⎝ P23-8 (1) (1) (2) Reduced Reduced Labor Machine Year Cost Setup Time $15,000 25,000 30,000 30,000 30,000 30,000 $40,000 50,000 60,000 60,000 60,000 60,000 (3) Reduced Inventory Carrying Cost $25,000 35,000 40,000 40,000 40,000 40,000 (4) (5) Total Lost Periodic Contribution Savings from Margin CIM System Avoided (1) + (2) + (3) + (4) $200,000 300,000 400,000 500,000 600,000 700,000 $280,000 410,000 530,000 630,000 730,000 830,000 (6) (7) Net Periodic Additional Savings Maintenance with CIM Cost with System CIM System (5) – (6) $25,000 25,000 25,000 25,000 25,000 25,000 $255,000 385,000 505,000 605,000 705,000 805,000 Chapter 23 23-25 P23-8 (Continued) (7) (8) Year Net Periodic Savings with CIM Tax Depreciation and Amortization* $255,000 385,000 505,000 605,000 705,000 805,000 $440,000 680,000 424,000 270,000 270,000 116,000 (9) (10) Taxable Income (Loss) (7) – (8) Effective Tax Rate $(185,000) (295,000) 81,000 335,000 435,000 689,000 40% 40% 40% 40% 40% 40% (11) (12) (13) Tax Liability (Refund) (9) × (10) Periodic Net After-Tax Cash Inflows (7) – (11) Index for Anticipated 8% Rate of Inflation (14) InflationAdjusted Periodic Net AfterTax Cash Inflows (12) × (13) $ (74,000) (118,000) 32,400 134,000 174,000 275,600 $329,000 503,000 472,600 471,000 531,000 529,400 1.080 1.166 1.260 1.360 1.469 1.587 $ 355,320 586,498 595,476 640,560 780,039 840,158 Total annual inflation-adjusted after-tax savings from investment in CIM system Cash inflow from salvage of equipment and machinery ($100,000 salvage × 1.587 adj × (1 – 40% tax rate)) $3,798,051 Total inflation-adjusted after-tax cash inflows from investment in CIM system Less initial investment ($2,000,000 in equipment plus $200,000 in software) $3,893,271 2,200,000 Excess of inflation-adjusted after-tax savings over cost of CIM system $1,693,271 * (1) Year (2) (3) Rate for Recovery MACRS Property 5-year Tax Basis Property $2,000,000 2,000,000 2,000,000 2,000,000 2,000,000 2,000,000 0.200 0.320 0.192 0.115 0.115 0.058 Tax Depreciation (1) × (2) $ 400,000 640,000 384,000 230,000 230,000 116,000 $2,000,000 (4) (5) (6) 5-year Tax Straight-Line AmortiSoftware Amortization zation Tax Basis Rate (4) × (5) $200,000 200,000 200,000 200,000 200,000 200,000 0.200 0.200 0.200 0.200 0.200 0.000 95,220 (7) Total Tax Amortization and Depreciation (3) + (6) $ 40,000 40,000 40,000 40,000 40,000 $ 440,000 680,000 424,000 270,000 270,000 116,000 $200,000 $2,200,000 23-26 Chapter 23 P23-8 (Concluded) (2) Inflation Adjusted Periodic Net After-Tax Year Cash Inflows Needed Balance $355,320 $2,200,000 $1,844,680 586,498 1,844,680 1,258,182 595,476 1,258,182 662,706 640,560 662,706 22,146 780,039 22,146 Total payback in years Payback Years Required 1.00 1.00 1.00 1.00 0.03 4.03 (3) InflationAdjusted Present Periodic Net Value After-Tax of $1 Year Cash Inflows @14% $(2,200,000) 1.000 355,320 0.877 586,498 0.769 595,476 0.675 640,560 0.592 780,039 0.519 935,378* 0.456 Net present value of investment Present Value of Cash Inflows $(2,200,000) 311,616 451,017 401,946 379,212 404,840 426,532 $ 175,163 *$840,158 after-tax cash inflow for year plus $95,220 after-tax salvage value at the end of year Chapter 23 23-27 P23-9 Purchase alternative: Year 10 11 12 13 14 15 (1) (2) (3) (4) Cash Inflows MACRS Depreciation Rate Income Tax Depreciation* $600,000 600,000 600,000 600,000 600,000 600,000 600,000 600,000 600,000 600,000 600,000 600,000 600,000 600,000 600,000 143 245 175 125 089 089 089 045 000 000 000 000 000 000 000 $286,000 490,000 350,000 250,000 178,000 178,000 178,000 90,000 0 0 0 (5) (6) Increase in Taxable Income (1) – (3) Income Tax Rate Increase in Income Tax (4) × (5) $314,000 110,000 250,000 350,000 422,000 422,000 422,000 510,000 600,000 600,000 600,000 600,000 600,000 600,000 600,000 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 $125,600 44,000 100,000 140,000 168,800 168,800 168,800 204,000 240,000 240,000 240,000 240,000 240,000 240,000 240,000 (7) Net After-Tax Cash Inflows (1) – (6) $ 474,400 556,000 500,000 460,000 431,200 431,200 431,200 396,000 360,000 360,000 360,000 360,000 360,000 360,000 360,000 After-tax cash inflow from salvage at end of economic life $6,200,000 120,000 ** Total after-tax cash inflow from the purchase alternative Less initial cash outflow $6,320,000 2,000,000 Total after-tax cash inflow over economic life of project $4,320,000 *The depreciation is determined by multiplying the depreciable basis of $2,000,000 by the MACRS cost recovery percentages provided in Exhibit 22-4 of the text for seven-year property ** The salvage received at the end of the economic life of the asset would be fully taxable because the tax basis of the property would be zero The after-tax cash inflow would be $120,000, i.e., ($200,000 salvage value × (1 – 40 tax rate)) 23-28 Chapter 23 P23-9 (Concluded) Year 10 11 12 13 14 15 Net Net After-Tax PV of $1 Cash Flow @ 14% $(2,000,000) 1.000 474,400 877 556,000 769 500,000 675 460,000 592 431,200 519 431,200 456 431,200 400 396,000 351 360,000 308 360,000 270 360,000 237 360,000 208 360,000 182 360,000 160 360,000 140 present value PV of Cash Flow $(2,000,000) 416,049 427,564 337,500 272,320 223,793 196,627 172,480 138,996 110,880 97,200 85,320 74,880 65,520 57,600 50,400 $ 727,129 Lease alternative: Annual Annual Annual Annual Annual Year 1-15 cash inflow before lease payment lease payment pretax cash inflow and increase in taxable income increase in income tax expense ($280,000 × 40%) after-tax cash inflow from lease alternative Cash Inflow $168,000 PV of Annuity $1 @ 14% 6.142 $600,000 320,000 $280,000 112,000 $168,000 PV of Cash Flows $1,031,856 The lease alternative appears to be preferable because the net present value of the estimated after-tax cash flows is greater than for the purchase alternative ($1,031,856 versus $727,129) Chapter 23 23-29 P23-10 (1) General-Purpose SelfEquipment Constructed Lease Purchase Equipment Recurring cash flows from operations: Estimated sales volume in units Unit contribution margin Estimated total contribution margin 40,000 $ 1.55 $62,000 40,000 $ 1.55 $62,000 40,000 $ 1.90 $76,000 Less fixed costs: Supervision Property taxes and insurance Maintenance Total fixed cost Annual cash inflows before tax $16,000 0 $16,000 $46,000 $16,000 3,000 3,000 $22,000 $40,000 $17,000 5,000 2,000 $24,000 $52,000 Lease equipment alternative: Annual cash inflow before tax Annual lease payment Annual increase in taxable income Annual increase in income tax ($6,000 × 40%) Annual after-tax cash inflow PV of $1 received annually for years @ 14% Net present value of lease alternative $46,000 40,000 $ 6,000 2,400 $ 3,600 × 3.889 $14,000 23-30 Chapter 23 P23-10 (Continued) Purchase equipment alternative: (1) (2) (3) Year Pretax Cash Inflows Income Tax Depreciation* $40,000 40,000 40,000 40,000 40,000 80,000** $25,000 40,000 24,000 14,375 14,375 7,250 Taxable Income (1) – (2) (4) Income Tax at 40% Tax Rate (3) × 40% (5) Net After-Tax Cash Inflows (1) – (4) (6) PV of $1 @ 14% (7) PV of Net After-Tax Cash Inflows (5) × (6) $15,000 16,000 25,625 25,625 72,750 $ 6,000 6,400 10,250 10,250 29,100 $34,000 40,000 33,600 29,750 29,750 50,900 877 769 675 592 519 456 $ 29,818 30,760 22,680 17,612 15,440 23,210 Present value of net cash inflows Less initial cash outflow $139,520** 125,000 Net present value of purchase alternative $ 14,520 *Tax depreciation is determined by multiplying the depreciable basis of the equipment under the purchase alternative ($125,000) by the MACRS depreciation rates provided in Exhibit 22-4 of the text **Includes salvage value of $40,000, all of which would be taxable, since the equipment would be fully depreciated for income tax purposes at the end of the sixth year.The total after-tax cash flow from operations of $50,900 shown in column (5) is composed of after-tax cash inflow from operations of $26,900 ($40,000 – (($40,000 – $7,250) × 40 tax rate)) and the after-tax cash flow from salvage of $24,000 ($40,000 × (1 – 40 tax rate)) Chapter 23 23-31 P23-10 (Continued) Self-constructed equipment alternative: (1) (2) (3) Year Pretax Cash Inflows Income Tax Depreclation* $52,000 52,000 52,000 52,000 52,000 82,000** $36,000 57,600 34,560 20,700 20,700 10,440 Taxable Income (1) – (2) (4) Income Tax at 40% Tax Rate (3) × 40% (5) Net After-Tax Cash Inflows (1) – (4) (6) PV of $1 @ 14% $16,000 (5,600) 17,440 31,300 31,300 71,560 $ 6,400 (2,240) 6,976 12,520 12,520 28,624 $45,600 54,240 45,024 39,480 39,480 53,376 877 769 675 592 519 456 (7) PV of Net After-Tax Cash Inflows (5) × (6) $ 39,991 41,711 30,391 23,372 20,490 24,339 Present value of net cash inflows Less initial cash outflow $180,294 165,000*** Net present value of purchase alternative $ 15,294 * Tax depreciation is determined by multiplying the depreciable basis of the equipment under the self-construction alternative ($180,000, which is the full construction cost including allocated fixed cost) by the MACRS depreciation rates provided in Exhibit 22-4 of the text **Includes salvage value of $30,000, all of which would be taxable, since the equipment would be fully depreciated for income tax purposes at the end of the sixth year.The total after-tax cash flow from operations of $53,376 shown in column (5) is composed of after-tax cash inflow from operations of $35,376 ($52,000 – (($52,000 – $10,440) × 40 tax rate)) and the after-tax cash flow from salvage of $18,000 ($30,000 × (1 – 40 tax rate)) ***Because Egelston Corporation is operating at normal capacity and the construction of the new equipment will not interfere with regular activities, the company should not incur any additional fixed factory overhead Therefore, the $15,000 of fixed factory overhead is not included in the differential cost of the self-constructed asset The initial cash outlay would be $180,000 full cost less $15,000 of allocated fixed factory overhead, or $165,000 23-32 Chapter 23 P23-10 (Concluded) (2) Egelston Corporation should consider any proposal that is expected to have an earnings rate in excess of the firm’s cost of capital If a proposal has a positive net present value, that proposal’s expected earnings will yield a rate of return that exceeds the firm’s cost of capital In this case, the purchase of general-purpose equipment, the construction of special-purpose equipment, and the lease of general-purpose equipment are all acceptable to Egelston Corporation, because the net present value of all three proposals is positive Egelston Corporation should attempt to maximize the earnings that can be obtained from the funds available for capital investments When comparing a set of mutually exclusive alternatives, the alternative with the largest net present value will result in a maximization of stockholder wealth Accordingly, construction of special-purpose equipment appears to be the most attractive alternative However, the net present value should be related to any required investment by calculating a net present value index as follows: Construction of special-purpose equipment: Net present value = Required investment $15,294 = 0927 $165,000 Purchase of special-purpose equipment: Net present value = Required investment $14,520 $125,000 = 1162 Purchase of general-purpose equipment promises a larger net present value index and would be preferable, provided that the investment difference of $40,000 ($165,000 – $125,000) can be used to earn a net present value greater than $774 ($15,294 – $14,520) Chapter 23 23-33 CASES C23-1 (1) (a) The payback method measures the number of years required for the after-tax cash inflows to fully recover the initial cash investment in a project The payback method emphasizes an organization’s financial liquidity and the riskiness of the capital project in terms of investment recovery Since long-term forecasts contain more uncertainty than short-term forecasts (i.e., it is easier to predict what will happen next year than what will happen 10 years from now), the least risky projects will have the shortest payback period (b) The net present value method recognizes the time value of money by discounting the after-tax cash flows for a project over its life to time zero using the firm’s weighted average cost of capital The net present value is the difference between the present value of the after-tax cash inflows, measured over the life of the capital project, and the cash outflow required to undertake the capital project Projects that have a positive net present value are acceptable, while those that have a negative net present value are unacceptable (c) The internal rate of return method (also called the discounted cash flow rate of return method) incorporates the time value of money by determining the compound interest rate for a capital project that would result in a net present value of zero A proposal would be acceptable if the internal rate of return exceeds the weighted average cost of capital, and unacceptable if it is less (2) In order to maximize the value of the company, Caledonia Division should use the net present value method or the internal rate of return method to decide which capital projects should be included in the capital budget submitted to Quible Industries Both of these methods would identify Projects A, B, D, E, and F as acceptable (each has a positive net present value and an internal rate of return in excess of the company’s hurdle rate), and Project C as unacceptable (the net present value is negative and the internal rate of return is less than the company’s hurdle rate) However, Projects A and D are mutually exclusive (meaning that ultimately only one of the two can be pursued) The selection between the two depends upon the criteria used to rank the projects, i.e., the capital expenditure evaluation method employed in the selection process If the net present value method is used, Caledonia would select Project D because it has a higher net present value than Project A ($74,374 for D compared to $69,683 for A) On the other hand, if the internal rate of return method is used, Caledonia would select Project A because it has a higher internal rate of return than Project D (35% for A compared to 22% for D) 23-34 Chapter 23 C23-1 (Concluded) (3) In order to maximize the value of the company in this capital rationing situation, the net present value should be used to select the projects to be included in the capital budget because the cash inflows are assumed to be reinvested at the hurdle rate (the company has a demonstrated earning rate equal to its weighted average cost of capital) The internal rate of return should not be used, because it violates the reinvestment rate assumption and may be unreliable as a basis for maximizing the value of the company in a capital rationing situation Using the net present value method, the most profitable combination of projects within the $450,000 budget constraint would be to include Projects A, B, and F because this combination yields the greatest total net present value (net present value of $162,929 for an initial investment of $436,000) (Note that the combination of A, D, and F is not possible because A and D are mutually exclusive projects, and that the combination of B, D, and F is not possible because it would require a combined investment in excess of $450,000.) C23-2 (1) The 18.2% rate of return on the investment differs from the 24% internal rate of return because the methods used to measure the returns are different The return on investment (18.2%) calculation is based on accrual accounting concepts If the reduced operating expenses—less depreciation—remain constant as planned, the numerator in the ROI fraction will not change over the life of the investment The denominator in the fraction, the investment base, decreases each year by the amount of the annual depreciation Consequently, the rate of return calculated will increase each year over the life of the investment The internal rate of return calculation (24%) is based on discounted cash flow concepts The cash flows expected to be received over the life of the investment, discounted to the acquisition date at 24%, exactly equaled the initial cost of the machine This measure of return on investment provides a percentage that is constant for each year of life of the investment This rate can be computed for each year’s actual operating results if the annual savings in operating expenses are constant and the new equipment is depreciated using the effective interest method based on an interest rate of 24% The method would be essentially the same as that employed in amortizing leaseholds and bonds The depreciation charge each year would have to be such that the numerator and the denominator of the ROI computation would change at the same rate in order to keep the annual return on investment ratio constant Chapter 23 23-35 C23-2 (Concluded) (2) Recap Corporation can restructure the data from the cash flow analysis to make it consistent with the accounting reports (which contain straight-line depreciation) received by the department manager Once the investment is accepted on the basis of its internal rate of return, the data can be converted into the format consistent with the accounting basis used for reporting Annual contribution from the new investment would be calculated by subtracting the straight-line depreciation from the net cash operating savings The accounting book value for each of the years of the investment life would also be calculated The annual contribution would be divided by the investment base (book value) for each year to obtain the rates of return This would then present the manager with the different rates of return for each of the years of the investment’s life Thus, the rates would be more comparable with the actual return on investment rates experienced each year Alternatively, rather than computing an annual rate of return, it may be more expedient to compare actual net cash operating savings each year with those forecast in the capital expenditure analysis If actual periodic savings equal those forecast, the internal rate of return would be equal to the 24% budgeted ... Marginal cost 7.20% (from part (1)) Current cost 9.33% (from part (2)) Total cost Marginal cost Portion of Total Required $ 10,000,000 $100,000,000 $ 90,000,000 $100,000,000 Weighted Average Cost. .. (1)) Current cost 9.33% (from part (2)) Total cost $100,000,000 $ 90,000,000 $100,000,000 8.40% Marginal cost 11.05% (from part (1)) Current cost 9.33% (from part (2)) Total cost $ 10,000,000... of Total 50% 10% Pretax Cost 8.0% 9.0% After-Tax Cost 4.8% 9.0% 4,000,000 $10,000,000 40% 100% 12.5% 12.5% (5) Weighted Cost (2) × (4) 2.4% 9% 5.0% 8.3% Weighted average cost of capital after bond