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MANAGEMENT ADVISORY SERVICES CASH FLOW COMPUTATIONS Cash Flow from Sale of Old Machine Sold at a Loss 43 Hoff is considering the sale of a machine with a book value of $80,000 and years remaining in its useful life Straight-line depreciation of $25,000 annually is available The machine has a current market value of $50,000 What is the cash flow from selling the machine if the tax rate is 40%? a $25,000 c $62,000 b $50,000 d $80,000 D, L & H 9e 43 Hoff is considering the sale of a machine with a book value of $160,000 and years remaining in its useful life Straight-line depreciation of $50,000 annually is available The machine has a current market value of $100,000 What is the cash flow from selling the machine if the tax rate is 40%? a $50,000 c $124,000 b $100,000 d $160,000 L & H 10e 72 Pebble Co recently sold a used machine for $40,000 The machine had a book value of $60,000 at the time of the sale What is the after-tax cash flow from the sale, assuming the company's marginal tax rate is 20 percent? a $40,000 c $44,000 b $60,000 d $32,000 Barfield The Alpha Beta Corporation disposes of a capital asset with an original cost of $85,000 and accumulated depreciation of $54,500 for $25,000 Alpha Beta's tax rate is 40% Calculate the after-tax cash inflow from the disposal of the capital asset (M) a $2,200 c $27,200 b ($2,200) d $31,500 Horngren Sold at a Gain 42 Acme is considering the sale of a machine with a book value of $80,000 and years remaining in its useful life Straight-line depreciation of $25,000 annually is available The machine has a current market value of $100,000 What is the cash flow from selling the machine if the tax rate 40% a $25,000 c $92,000 b $80,000 d $100,000 D, L & H 9e CMA EXAMINATION QUESTIONS CAPITAL BUDGETING 42 Acme is considering the sale of a machine with a book value of $160,000 and years remaining in its useful life Straight-line depreciation of $50,000 annually is available The machine has a current market value of $200,000 What is the cash flow from selling the machine if the tax rate is 40%? a $50,000 c $184,000 b $160,000 d $200,000 L & H 10e A corporation with a taxable income of $200,000 and a 40 percent tax rate is considering the sale of an asset The original cost of the asset is $10,000, with $6,000 of its depreciated How much total after-tax cash will be produced from the sale of the asset for $12,000? a $10,400 d $(3,200) b $12,000 e $8,800 c $11,200 H&M Initial Net Cash Investment After Tax Cash Inflow of Sale of Old Machine at a Gain 36 Eyring Industries has a truck purchased seven years ago at a cost of $6,000 At the time of purchase, the ultimate salvage value was estimated at $500, but salvage value was ignored in depreciation deductions The truck is now fully depreciated Assuming a tax rate of 40%, if the truck is sold for $500, the after-tax cash inflow for capital budgeting purposes will be: (E) a $500 c $200 b $300 d $100 G & N 9e Old Machine Sold at Book Value 50 Hatchet Company is considering replacing a machine with a book value of $400,000, a remaining useful life of years, and annual straight-line depreciation of $80,000 The existing machine has a current market value of $400,000 The replacement machine would cost $550,000, have a 5-year life, and save $75,000 per year in cash operating costs If the replacement machine would be depreciated using the straight-line method and the tax rate is 40%, what would be the net investment required to replace the existing machine? (D) a $90,000 c $330,000 b $150,000 d $550,000 D, L & H 9e 56 Big City Motors is trying to decide whether it should keep its existing car washing machine or purchase a new one that has technological advantages (which translate into cost savings) over the existing machine Information on each machine follows: Old machine New machine Original cost $9,000 $20,000 Page of 137 MANAGEMENT ADVISORY SERVICES Accumulated depreciation Annual cash operating costs Current salvage value of old machine Salvage value in 10 years Remaining life The incremental cost to purchase the new machine is a $11,000 c $13,000 b $20,000 d $18,000 CAPITAL BUDGETING 5,000 9,000 2,000 500 10 yrs 4,000 1,000 10 yrs Barfields Old Machine Sold at a Gain Regal Industries is replacing a grinder purchased years ago for $15,000 with a new one costing $25,000 cash The original grinder is being depreciated on a straight-line basis over 15 years to a zero salvage value Regal will sell this old equipment to a third party for $6,000 cash The new equipment will be depreciated on a straight-line basis over 10 years to a zero salvage value Assuming a 40% marginal tax rate, Regal’s net cash investment at the time of purchase if the old grinder is sold and the new one is purchased is a $19,000 c $17,400 b $15,000 d $25,000 CMA 1292 4-9 A machine that cost $50,000 and is fully depreciated is sold for $10,000 The $10,000 is then used as a down payment on the purchase of a new machine costing $75,000 Assuming a 40% tax rate, the out-of-pocket cost of the new machine is: A $75,000 C $65,000 B $71,000 D $69,000 C&U Old Equipment Sold at a Loss * In making a decision to invest in a project the cash flow should be adjusted for their tax effect Assume an income tax rate of 35% an old machine with a book value of P70,000 will be replaced by a new machine costing P150,000 The market value of the old machine is P50,000 The after tax investment outlay is (E) a P82,500 c P107,000 b P93,000 d P135,000 RPCPA 1085 * In deciding the investment in a project, cash flows should be adjusted for their tax effect Assume an income tax rate of 35% An old equipment with a book value of P15,000 will be replaced by a new equipment costing P50,000 The market value of the old equipment is P11,000 The after-tax investment outlay is (E) a P34,400 c P39,000 CMA EXAMINATION QUESTIONS b P37,600 d P40,400 RPCPA 0581 Old Equipment Sold at a Loss, Additional Working Capital * Diliman Republic Publishers, Inc is considering replacing an old press that cost P800,000 six years ago with a new one that would cost P2,250,000 Shipping and installation would cost an additional P200,000 The old press has a book value of P150,000 and could be sold currently for P50,000 The increased production of the new press would increase inventories by P40,000, accounts receivable by P160,000 and accounts payable by P140,000 Diliman Republic’s net initial investment for analyzing the acquisition of the new press assuming a 35% income tax rate would be (D) a P2,450,000 c P2,600,000 b P2,425,000 d P2,250,000 RPCPA 0595 44 Superstrut is considering replacing an old press that cost $80,000 six years ago with a new one that would cost $245,000 The old press has a net book value of $15,000 and could be sold for $5,000 The increased production of the new press would require an investment in additional working capital of $6,000 The company's tax rate is 40% Superstrut's net investment now in the project would be: (M) a $256,000 c $250,000 b $242,000 d $245,000 CMA adapted Old Machine Sold at a Loss, Cash Cost Savings on New Machine A company is considering replacing existing 2-year-old equipment This project will require a discounted cash flow analysis to determine if the benefits exceed the costs Year-end data regarding the existing and new equipment are shown below Existing Equipment New Equipment Original cost $600,000 $540,000 Useful life (in years) Remaining life (in years) 3 Annual depreciation $120,000 $180,000 Accumulated depreciation $240,000 N/A* Book value $360,000 N/A* Current cash disposal value $100,000 N/A* * Value is not applicable here The new equipment will result in cash operating cost savings of $150,000 annually, before taxes The new equipment would be purchased late in the current year to be operational at the beginning of the first year of the project The existing equipment would be sold early in the first year of the project, meaning no further depreciation would be taken on it The company has an Page of 137 MANAGEMENT ADVISORY SERVICES effective income tax rate of 40% Of the following, which are the correct figures to be used in the cash flow analysis for the first year of this proposed project? CIA 0596 III-78 After-Tax Cash Proceeds from Sale Tax Benefit from Sale Operating Savings of Existing Equipment of Existing Equipment A $90,000 $100,000 $0 B $60,000 $ 60,000 $104,000 C $90,000 $100,000 $104,000 D $60,000 $ 40,000 $156,000 Old Machine Traded-in A machine that cost $50,000 and is fully depreciated is allowed as a $10,000 trade-in on a machine costing $75,000 Assuming a 40% tax rate, the out-of-pocket cost of the new machine is: A $75,000 C $65,000 B $71,000 D $69,000 C&U Old Machine Traded-in, Avoidable Cost * Key Corp plans to replace a production machine that was acquired several years ago Acquisition cost is P450,000 with salvage value of P50,000 The machine being considered is worth P800,000 and the supplier is willing to accept the old machine at a trade-in value of P60,000 Should the company decide not to acquire the new machine, it needs to repair the old one at a cost of P200,000 Tax-wise, the trade-in transaction will not have any implication but the cost to repair is tax-deductible The effective corporate tax rate is 35% of net income subject to tax For purposes of capital budgeting, the net investment in the new machine is (M) a P540,000 c P660,000 b P610,000 d P800,000 RPCPA 0597 Old Machine Traded-in, Other Assets Written Off, Avoidable Cost, Additional Working Capital * Great Value Company is planning to purchase a new machine costing P50,000 with freight and installation costs amounting to P1,500 The old unit is to be traded-in will be given a trade-in allowance of P7,500 Other assets that are to be retired as a result of the acquisition of the new machine can be salvaged and sold for P3,000 The loss on retirement of these other assets is P1,000 which will reduce income taxes of P400 If the new equipment is not purchased, repair of the old unit will have to be made at an estimated cost of P4,000 This cost can be avoided by purchasing the new equipment Additional gross working capital of P12,000 will be needed to support operation planned with the new equipment The net investment assigned to the new machine for decision analysis is (D) CMA EXAMINATION QUESTIONS CAPITAL BUDGETING a P50,200 b P52,600 c P53,600 d P57,600 RPCPA 1080 Initial Cash Outlay Lawson Inc is expanding its manufacturing plant, which requires an investment of $4 million in new equipment and plant modifications Lawson's sales are expected to increase by $3 million per year as a result of the expansion Cash investment in current assets averages 30% of sales; accounts payable and other current liabilities are 10% of sales What is the estimated total investment for this expansion? (E) A $3.4 million C $4.6 million B $4.3 million D $4.9 million CMA 1295 4-8 Kline Corporation is expanding its plant, which requires an investment of $8 million in new equipment Kline's sales are expected to increase by $6 million per year as a result of the expansion Cash investment in current assets averages 30% of sales, and accounts payable and other current liabilities are 10% of sales What is the estimated total cash investment for this expansion? (E) A $6.8 million C $9.2 million B $8.6 million D $9.8 million Gleim Tax on Sale of Old Machine A machine with a book value of $30,000 could be sold for $40,000 The corporation that owns the machine has taxable income of $35,000 and a 40 percent tax rate What would be the tax on the sale of the machine? a $0 d $4,000 b $10,000 e $13,600 c $6,000 H&M Opportunity Costs 11 A firm owns a building with a book value of $100,000 and a market value of $250,000 If the building is utilized for a project, then the opportunity cost ignoring taxes is: A $100,000 C $250,000 B $150,000 D None of the above B&M 12 A firm has a general-purpose machine which has a book value of $500,000 and is sold for $600,000 in the market If the tax rate is 30%, what is the opportunity cost of using the machine in a project? A $500,000 C $570,000 Page of 137 MANAGEMENT ADVISORY SERVICES B $600,000 CAPITAL BUDGETING D None of the above B&M Working Capital 23 For project A in year 2, inventories increase by $16,000 and accounts payable by $4,000 Calculate the increase or decrease in net working capital for year (E) A Increases by $12,000 C Increases by $16,000 B Decreases by $12,000 D Decreases by $16,000 B&M 24 For project X, year inventories decrease by $5,000, accounts receivable by $3,000 and accounts payables by $2,000 Calculate the increase or decrease in working capital for year (E) A Increases by $6,000 C Increases by $8,000 B Decreases by $6,000 D Decreases by $7,000 B&M 34 A corporation is considering expanding operations to meet growing demand With the capital expansion, the current accounts are expected to change Management expects cash to increase by $20,000, accounts receivable by $40,000, and inventories by $60,000 At the same time accounts payable will increase by $50,000, accruals by $10,000, and long-term debt by $100,000 The change in net working capital is (E) A an increase of $120,000 C a decrease of $120,000 B a decrease of $40,000 D an increase of $60,000 Gitman 35 A corporation is considering expanding operations to meet growing demand With the capital expansion the current accounts are expected to change Management expects cash to increase by $10,000, accounts receivable by $20,000, and inventories by $30,000 At the same time accounts payable will increase by $40,000, accruals by $30,000, and long-term debt by $80,000 The change in net working capital is (E) A an increase of $10,000 C a decrease of $90,000 B a decrease of $10,000 D an increase of $80,000 Gitman Cash Inflow Before-tax Cash Inflow 69 C Corp faces a marginal tax rate of 35 percent One project that is currently under evaluation has a cash flow in the fourth year of its life that has a present value of $10,000 (after-tax) C Corp assumes that all cash flows occur at the end of the year and the company uses 11 percent as its discount rate What is the pre-tax amount of the cash flow in year 4? (Round to the nearest dollar.) (M) a $15,181 c $9,868 CMA EXAMINATION QUESTIONS b $23,356 d $43,375 Barfield 43 At the Bartholomew Company last year all sales were for cash and all expenses were paid in cash The tax rate was 30% If the after-tax net cash inflow from these operations last year was $10,500, and if the total before tax cash expenses were $35,000, then the total before-tax cash sales must have been: (M) a $65,000 c $45,000 b $60,000 d $50,000 G & N 9e Timing of Cash Flow 10 Assume that the interest rate is greater than zero Which of the following cash-inflow streams should you prefer? Gleim Year Year Year Year A $400 $300 $200 $100 B $100 $200 $300 $400 C $250 $250 $250 $250 D Any of these, since they each sum to $1,000 After-tax Net Cash Inflow for a Certain Year You are given the following data for year Revenue = $43; Total costs = $30; Depreciation = $3; Tax rate = 30% Calculate the cash flow for the project for year (E) A $7 C $13 B $10 D None of the above B&M You are given the following data for year 1: Revenues = 100, Fixed costs = 30; Total variable costs = 50; Depreciation = $10; Tax rate = 30% Calculate the after tax cash flow for the project for year (E) A $17 C $10 B $7 D None of the above B&M After-Tax Net Cash Inflow 40 Last year the sales at Jersey Company were $200,000 and were all cash sales The expenses at Jersey were $125,000 and were all cash expenses The tax rate was 30% The after-tax net cash inflow at Jersey last year from these operations was: (E) a $37,500 c $22,500 b $60,000 d $52,500 G & N 9e Page of 137 MANAGEMENT ADVISORY SERVICES 41 Last year a firm had taxable cash receipts of $800,000 and the tax rate was 30% The after-tax net cash inflow from these receipts was (E) a $800,000 c $560,000 b $640,000 d $240,000 G & N 9e 46 Last year the sales at Seidelman Company were $700,000 and were all cash sales The company's expenses were $450,000 and were all cash expenses The tax rate was 35% The after-tax net cash inflow at Seidelman last year was: (E) a $700,000 c $162,500 b $250,000 d $87,500 G & N 9e 11 A project is expected to result in the following adjustments over the next year: Cash sales increase by 400,000 Expenses (except depreciation) increase by 180,000 Depreciation increases by 80,000 Assume the corporate tax rate is 34% The total relevant net cash flows during that year are A 92,400 C 172,400 B 140,000 D 220,000 CIA 0591 IV-52 Annual Cash Inflow 12 A company considers a project that will generate cash sales of $50,000 per year Fixed costs will be $10,000 per year, variable costs will be 40% of sales, and depreciation of the equipment in the project will be $5,000 per year Taxes are 40% The expected annual cash flow to the company resulting from the project is A $15,000 C $19,000 B $9,000 D $14,000 CIA 1193 IV-50 * Guemon Company is taking into account the replacement of an old machine now in use with a new machine costing P100,000 The replacement is expected to produce an annual cash savings of P22,500 before income taxes The estimated useful life of the new machine is ten years with no residual value The book value of the old machine is P37,500 and is expected to last for another five years It is being depreciated at P8,000 per year The income tax rate is 25% The annual cash savings after tax is (M) a P15,375 c P17,375 b P16,875 d P20,520 RPCPA 0583 CMA EXAMINATION QUESTIONS CAPITAL BUDGETING Total Cash Inflow 13 The Phenom Corporation has an annual cash inflow from operations from its investment in a capital asset of $50,000 for five years The corporation's income tax rate is 40% Calculate the five years total after-tax cash inflow from operations (M) a $250,000 c $150,000 b $175,000 d $50,000 Horngren Cash Outflow Before-Tax Cash Outflow 39 Consider a machine which costs $115,000 now and which has a useful life of seven years This machine will require a major overhaul at the end of the fourth year which will cost "X" dollars If the tax rate is 40%, and if the after-tax cash outflow for this overhaul is $3,600, then the amount of "X" in dollars is: (E) a $6,000 c $2,160 b $9,000 d $1,440 G & N 9e “End-of-Life” Cash Flow Based on Internal Rate of Return * A company is considering putting up P50,000 in a three-year project The company’s expected rate of return is 12% The present value of P1.00 at 12% for one year is 0.893, for two years is 0.797, and for three years is 0.712 The cash flow, net of income taxes will be P18,000 (present value of P16,074) for the first year and P22,000 (present value of P17,534) for the second year Assuming that the rate of return is exactly 12%, the cash flow, net of income taxes, for the third year would be (M) a P7,120 c P16,392 b P10,000 d P23,022 RPCPA 1081 Machine Sold at a Gain, Working Capital Released 14 Garfield Inc is considering a 10-year capital investment project with forecasted revenues of $40,000 per year and forecasted cash operating expenses of $29,000 per year The initial cost of the equipment for the project is $23,000, and Garfield expects to sell the equipment for $9,000 at the end of the tenth year The equipment will be depreciated over years The project requires a working capital investment of $7,000 at its inception and another $5,000 at the end of year Assuming a 40% marginal tax rate, the expected net cash flow from the project in the tenth year is (D) a $32,000 c $20,000 b $24,000 d $11,000 CMA 1292 4-10 Page of 137 MANAGEMENT ADVISORY SERVICES Machine Sold at a Gain, Cost to Remove * Lor Industries is analyzing a capital investment proposal for new machinery to produce a new product over the next ten years At the end of the ten years, the machinery must be disposed of with a zero net book value but with a scrap salvage value of P20,000 It will require some P30,000 to remove the machinery The applicable tax rate is 35% The appropriate “end-oflife” cash flow based on the foregoing information is (D) a Inflow of P30,000 c Outflow of P10,000 b Outflow of P6,500 d Outflow of P17,000 RPCPA 0596 Machine Sold at a Taxable Loss, Cost to Remove 15 Kore Industries is analyzing a capital investment proposal for new equipment to produce a product over the next years The analyst is attempting to determine the appropriate “end-oflife” cash flows for the analysis At the end of years, the equipment must be removed from the plant, and will have a net book value of zero, a tax basis of $75,000, a cost to remove of $40,000, and scrap salvage value of $10,000 Kore’s effective tax rate is 40% What is the appropriate “end-of-life” cash flow related to these items that should be used in the analysis? (D) a $45,000 c $12,000 b $27,000 d $(18,000) CMA 1295 4-15 16 Metrejean Industries is analyzing a capital investment proposal for new equipment to produce a product over the next years At the end of years, the equipment must be removed from the plant and will have a net book value of $0, a tax basis of $150,000, a cost to remove of $80,000, and scrap salvage value of $20,000 Metrejean’s effective tax rate is 40% What is the appropriate “end-of-life” cash flow related to these items that should be used in the analysis? (D) a $90,000 c $24,000 b $54,000 d $(36,000) Gleim Tax Savings On Depreciation 17 If the tax rate is 40% and a company has $400,000 of income, a depreciation deduction of $50,000 would result in a tax savings of a $17,000 c $30,000 b $20,000 d $33,000 H&M 18 If the tax rate is 40% and a company has $400,000 of income, a depreciation deduction of $80,000 would result in a tax savings of CMA EXAMINATION QUESTIONS CAPITAL BUDGETING a $52,800 b $48,000 c $32,000 d $27,200 H&M 25 If the depreciation amount is $100,000 and the marginal tax rate is 30%, then the tax shield due to depreciation is: (E) A $333,333 C $30,000 B $100,000 D None of the above B&M 26 If the depreciation amount is 600,000 and the marginal tax rate is 35%, then the tax shield due to depreciation is: (E) A $180,000 C $210,000 B $600,000 D None of the above B&M 45 Kane Company is in the process of purchasing a new machine for its production line It is near the end of the year, and the machine is being offered at a special discount if purchased before the end of the year Kane has determined that the depreciation deduction for tax purposes on the new machine for the year of purchase would be $13,000 The tax rate is 30% If Kane purchases the machine and reports a positive net income for the year, then the tax savings from the deprecation tax shield related to this machine for the year of purchase would be: (E) a $3,900 c $13,000 b $9,100 d $0 G & N 9e 38 Suppose a machine that costs $80,000 has a useful life of 10 years Also suppose that depreciation on the machine is $8,000 for tax purposes in year The tax rate is 40% The tax savings from the depreciation tax shield in year would be: (E) a $4,800 inflow c $4,800 outflow b $3,200 inflow d $3,200 outflow G & N 9e Incremental Before-tax Profit 19 Maxwell Company has an opportunity to acquire a new machine to replace one of its present machines The new machine would cost $90,000, have a 5-year life, and no estimated salvage value Variable operating costs would be $100,000 per year The present machine has a book value of $50,000 and a remaining life of years Its disposal value now is $5,000, but it would be zero after years Variable operating costs would be $125,000 per year Ignore income taxes Considering the years in total, what would be the difference in profit before income taxes by acquiring the new machine as opposed to retaining the present one? A $10,000 decrease C $35,000 increase B $15,000 decrease D $40,000 increase C&U Page of 137 MANAGEMENT ADVISORY SERVICES Net Cash Flow Present Value of Net Cash Flow 20 At the end of the next four years, a new machine is expected to generate net cash flows of $8,000, $12,000, $10,000, and $15,000, respectively What are the cash flows worth today if a 3% interest rate properly reflects the time value of money in this situation? (E) A $41,556 C $32,400 B $47,700 D $38,100 S, S & T As a 19th century economist, you are faced with the following problem The world's shipping fleet consists of steamships and sailing ships Each can be used to carry cargo or passengers The ships have similar sailing capacities but differ in their annual operating costs as follows: Steam Sail Cargo $80,000 $95,000 Passenger $90,000 100,000 Assume: (i) Fares are competitively determined, (ii) demand is not expected to change, (iii) each vessel has a life of 15 years, (iv) current salvage value of either ship (sailing or steam) is $114,091, and (v) Cost of capital is 10%, (vi) no taxes What is the present value of a steam ship? A $190,152 C $609,486 B $251,326 D None of the above B&M As a 19th century economist, you are faced with the following problem The world's shipping fleet consists of steamships and sailing ships Each can be used to carry cargo or passengers The ships have similar sailing capacities but differ in their annual operating costs as follows: Steam Sail Cargo $80,000 $95,000 Passenger $90,000 100,000 Assume: (i) Fares are competitively determined, (ii) demand is not expected to change, (iii) each vessel has a life of 15 years, (iv) current salvage value of either ship (sailing or steam) is $114,091, and (v) Cost of capital is 10%, (vi) no taxes If the cost of carrying cargo by sailing ship were $75,000 per year, what would be the present value of a steamship? A $114,091 C $215,000 B $152,814 D None of the above B&M CMA EXAMINATION QUESTIONS CAPITAL BUDGETING Present Value of Computations Present Value of Taxable Cash Receipts 24 A company anticipates a taxable cash receipt of $50,000 in year of a project The company's tax rate is 30% and its discount rate is 12% The present value of this future cash flow is closest to: (M) a $22,243 c $9,533 b $35,000 d $15,000 G & N 9e 25 A company anticipates a taxable cash receipt of $20,000 in year of a project The company's tax rate is 30% and its discount rate is 8% The present value of this future cash flow is closest to: (M) a $6,000 c $14,000 b $4,763 d $11,114 G & N 9e 26 A company anticipates a taxable cash receipt of $50,000 in year of a project The company's tax rate is 30% and its discount rate is 14% The present value of this future cash flow is closest to: (M) a $10,125 c $23,624 b $35,000 d $15,000 G & N 9e Present Value of After-Tax Cash Expense 27 A company anticipates a taxable cash expense of $10,000 in year of a project The company's tax rate is 30% and its discount rate is 8% The present value of this future cash flow is closest to: (M) a ($3,000) c ($7,000) b ($2,572) d ($6,001) G & N 9e 28 A company anticipates a taxable cash expense of $40,000 in year of a project The company's tax rate is 30% and its discount rate is 10% The present value of this future cash flow is closest to: (M) a ($23,140) c ($12,000) b ($9,917) d ($28,000) G & N 9e 29 A company anticipates a taxable cash expense of $60,000 in year of a project The company's tax rate is 30% and its discount rate is 14% The present value of this future cash flow is closest to: (M) a ($13,850) c ($32,318) b ($42,000) d ($18,000) G & N 9e Page of 137 MANAGEMENT ADVISORY SERVICES CAPITAL BUDGETING 37 Suppose a machine costs $20,000 now, has an expected life of eight years, and will require a $7,000 overhaul at the end of the third year If the tax rate is 40%, then the after-tax cost of this overhaul would be: (E) a $12,000 c $8,000 b $4,200 d $2,800 G & N 9e 42 A company had tax-deductible cash expenses of $650,000 last year and the tax rate was 30% The after-tax net cash outflow for these expenses was: (E) a $195,000 c $650,000 b $455,000 d $390,000 G & N 9e Present Value of Depreciation Tax Shield 30 A company anticipates a depreciation deduction of $20,000 in year of a project The company's tax rate is 30% and its discount rate is 12% The present value of the depreciation tax shield resulting from this deduction is closest to: (M) a $11,161 c $6,000 b $14,000 d $4,783 G & N 9e 31 A company anticipates a depreciation deduction of $30,000 in year of a project The company's tax rate is 30% and its discount rate is 12% The present value of the depreciation tax shield resulting from this deduction is closest to: (M) a $21,000 c $6,406 b $14,947 d $9,000 G & N 9e 32 A company anticipates a depreciation deduction of $70,000 in year of a project The company's tax rate is 30% and its discount rate is 14% The present value of the depreciation tax shield resulting from this deduction is closest to: (M) a $16,159 c $21,000 b $49,000 d $37,704 G & N 9e Present Value of Salvage Value 21 The following information pertains to an investment: Investment Annual revenues Annual variable costs Annual fixed out-of-pocket costs Salvage value CMA EXAMINATION QUESTIONS $120,000 $70,000 $15,000 $11,000 $27,000 Discount rate Expected life of project Ignoring income taxes, the present value of the salvage value is (rounded) (E) a $15,673 c $17,307 b $17,550 d $23,220 16% years Present Value of Working Capital Released at End-of-Life 77 A project under consideration by the White Corp would require a working capital investment of $200,000 The working capital would be liquidated at the end of the project's 10-year life If White Corp has an after-tax cost of capital of 10 percent and a marginal tax rate of 30 percent, what is the present value of the working capital cash flow expected to be received in year 10? a $36,868 c $53,970 b $77,100 d $23,130 Barfield 33 A company needs an increase in working capital of $20,000 in project that will last years The company's tax rate is 30% and its discount rate is 10% The present value of the release of the working capital at the end of the project is closest to: (M) a $6,000 c $9,562 b $13,660 d $14,000 G & N 9e 34 A company needs an increase in working capital of $50,000 in project that will last years The company's tax rate is 30% and its discount rate is 8% The present value of the release of the working capital at the end of the project is closest to: (M) a $36,751 c $25,726 b $15,000 d $35,000 G & N 9e 35 A company needs an increase in working capital of $70,000 in project that will last years The company's tax rate is 30% and its discount rate is 8% The present value of the release of the working capital at the end of the project is closest to: (M) a $49,000 c $38,898 b $21,000 d $55,568 G & N 9e Present Value of Annuity of Computation Present Value of Annuity of Depreciation Tax Shield 70 The Salvage Co is considering the purchase of a new ocean-going vessel that could potentially reduce labor costs of its operation by a considerable margin The new ship would cost $500,000 and would be fully depreciated by the straight-line method over 10 years At the end of 10 years, the ship will have no value and will be sunk in some already polluted harbor Page of 137 MANAGEMENT ADVISORY SERVICES CAPITAL BUDGETING The Salvage Co.'s cost of capital is 12 percent, and its marginal tax rate is 40 percent What is the present value of the depreciation tax benefit of the new ship? (Round to the nearest dollar.) a $113,004 c $169,506 b $282,510 d $200,000 Barfield 78 B Company is considering two alternative ways to depreciate a proposed investment The investment has an initial cost of $100,000 and an expected five-year life The two alternative depreciation schedules follow: Method Method Year depreciation $20,000 $40,000 Year depreciation $20,000 $30,000 Year depreciation $20,000 $20,000 Year depreciation $20,000 $10,000 Year depreciation $20,000 $0 Assuming that the company faces a marginal tax rate of 40 percent and has a cost of capital of 10 percent, what is the difference between the two methods in the present value of the depreciation tax benefit? a $7,196 c $2,878 b $0 d $6,342 Barfield Present Value of & Annuity of Computation Present Value of Salvage Value & Annual Net Cash Inflow Questions and are based on the following information The following information pertains to an investment: Investment Annual revenues Annual variable costs Annual fixed out-of-pocket costs Salvage value Discount rate Expected life of project H&M $70,000 $48,000 $16,000 $10,000 $ 6,000 12% years 22 Ignore income taxes The present value of the salvage value is (rounded) a $2,424 c $3,114 b $2,869 d $3,224 a $68,411 b $76,269 c $102,442 d $109,296 Comprehensive Questions through are based on the following information CMA 1295 4-3 to The Moore Corporation is considering the acquisition of a new machine The machine can be purchased for $90,000, it will cost $6,000 to transport to Moore’s plant and $9,000 to install It is estimated that the machine will last 10 years, and it is expected to have an estimated salvage value of $5,000 Over its 10-year life, the machine is expected to produce 2,000 units per year with a selling price of $500 and combined materials and labor costs of $450 per unit Federal tax regulations permit machines of this type to be depreciated using the straight-line method over years with no estimated salvage value Moore has a marginal tax rate of 40% 24 What is the net cash outflow at the beginning of the first year that Moore Corporation should use in a capital budgeting analysis? a $(85,000) c $(96,000) b $(90,000) e $(105,000) 25 What is the net cash flow for the third year that Moore Corporation should use in a capital budgeting analysis? a $68,400 c $64,200 b $68,000 d $79,000 26 What is the net cash flow for the tenth year of the project that Moore Corporation should use in a capital budgeting analysis? a $100,000 c $68,400 b $81,000 d $63,000 Questions 10 through 13 are based on the following information Gleim The Dickins Corporation is considering the acquisition of a new machine at a cost of $180,000 Transporting the machine to Dickins’ plant will cost an additional $18,000 It has a 10-year life and is expected to have a salvage value of $10,000 Furthermore, the machine is expected to produce 4,000 units per year with a selling price of $500 and combined direct materials and direct labor costs of $450 per unit Federal tax regulations permit machines of this type to be depreciated using the straight-line method over years with no estimated salvage value Dickins has a marginal tax rate of 40% 23 Ignore income taxes The present value of the annual net cash inflows from operations is (rounded) CMA EXAMINATION QUESTIONS Page of 137 MANAGEMENT ADVISORY SERVICES CAPITAL BUDGETING 27 What is the net cash outflow at the beginning of the first year that Dickens should use in a capital budgeting analysis? a $(170,000) c $(192,000) b $(180,000) d $(210,000) b 12.5% * 28 What is the net cash flow for the third year that Dickins Corporation should use in a capital budgeting analysis? a $136,800 c $128,400 b $136,000 d $107,400 d 32.0% L & H 10e The Habagat Inc is planning to spend P600,000 for a machine that it will depreciate on a straight-line basis over a ten-year period with no terminal disposal price The machine will generate cash flow from operations of P120,000 a year Ignoring income taxes, what is the accounting rate of return on the net initial investment? (M) a 5% c 10% b 12% d 15% RPCPA 0595 32 29 What is the net cash flow for the tenth year of the project that Dickins should use in a capital budgeting analysis? a $200,000 c $136,800 b $158,000 d $126,000 A project requires an investment of $80,000 in equipment Annual cash inflows of $16,000 are expected to occur for the next years No salvage value is expected The company uses the straight-line method of depreciation with no mid-year convention Ignore income taxes The accounting rate of return on original investment for the project is (M) a 6.25% c 16.00% b 7.50% d 20.00% H&M 30 What is the approximate payback period on the new machine? a 1.05 years c 1.33 years b 1.54 years d 2.22 years ACCOUNTING RATE OF RETURN Numerator 31 Lin Co is buying machinery it expects will increase average annual operating income by $40,000 The initial increase in the required investment is $60,000, and the average increase in required investment is $30,000 To compute the accrual accounting rate of return, what amount should be used as the numerator in the ratio? (E) a $20,000 c $40,000 b $30,000 d $60,000 ARR on Net Initial Investment Cash Flows Given, Ignore Income Tax 46 An investment opportunity costing $150,000 is expected to yield net cash flows of $45,000 annually for five years The cost of capital is 10% The book rate of return would be (M) a 10% c 30% b 20% d 33.3% L & H 10e 50 An investment opportunity costing $80,000 is expected to yield net cash flows of $25,000 annually for four years The cost of capital is 10% The book rate of return would be (M) a 10.0% c 21.3% CMA EXAMINATION QUESTIONS * Doro Co is considering the purchase of a $100,000 machine that is expected to result in a decrease of $25,000 per year in cash expenses after taxes This machine, which has no residual value, has an estimated useful life of 10 years and will be depreciated on a straightline basis For this machine, the accounting rate of return based on the initial investment will be (M) a 10% c 25% b 15% d 35% AICPA 1189 II-40 68 (Ignore income taxes in this problem.) The Jason Company is considering the purchase of a machine that will increase revenues by $32,000 each year Cash outflows for operating this machine will be $6,000 each year The cost of the machine is $65,000 It is expected to have a useful life of five years with no salvage value For this machine, the simple rate of return is: (E) a 20% c 49.2% b 40% d 9.2% G & N 9e Old Machine has Scrap Value, Net Cost Savings, Ignore Income Tax 67 (Ignore income taxes in this problem.) Denny Corporation is considering replacing a technologically obsolete machine with a new state-of-the-art numerically controlled machine The new machine would cost $450,000 and would have a ten-year useful life Unfortunately, the new machine would have no salvage value The new machine would cost $20,000 per year to operate and maintain, but would save $100,000 per year in labor and other costs The Page 10 of 137 12% discount rate is used, and the PVIF is used Answer (D) is incorrect because $31,182 results if a 12% discount rate is used 226 Answer (C) is correct The NPV of Project B equals the present value of the cash inflows minus the investment cost The present value of the cash inflows equals the PVIFA for two periods at the 12% discount rate times the periodic amount The present value of the cash inflows must be $67,604 ($40,000 x 1.6901) Thus, the NPV must be $17,604 ($67,604 - $50,000 investment cost) Answer (A) is incorrect because ($18,112) results if the PVIF for 12% and two periods is used Answer (B) is incorrect because ($16,944) results if the PVIF and a 10% discount rate are used Answer (D) is incorrect because $19,420 results if a 10% discount rate is used 227 Answer (B) is correct The IRR (12%) is the discount rate that sets the NPV equal to zero Thus, the NPV of Project C will equal zero when the investment cost equals the present value of the cash inflows Given that the investment cost is $60,000, the sum of the present values of the cash inflows must also equal $60,000 The present value of the cash inflow at the end of year is $17,858 ($20,000 x 8929 PVIF for one period at 12%) The present value of the cash inflow at the end of year is $27,902 ($35,000 x 7972 PVIF for two periods at 12%) Accordingly, the present value of the cash inflow at the end of year must be $14,240 ($60,000 - $17,858 - $27,902), and the undiscounted cash inflow must be $20,006 ($14,240 ÷ 7118 PVIF for three periods at 12%) Answer (A) is incorrect because $17,162 results if a 10% IRR is used Answer (C) is incorrect because $24,126 results if the project cash inflows are treated as a level annuity and a 10% discount rate is used Answer (D) is incorrect because $24,981 results if the project cash inflows are treated as a level annuity and a 12% discount rate is used 228 Answer (B) is correct After years, the cumulative cash inflows for Project B equal $80,000 Consequently, the investment outlay of $50,000 has been fully recovered Answer (A) is incorrect because, after year, Project B has had a $50,000 outflow but only $40,000 of inflows, so the investment outlay has not been fully recovered Answer (C) is incorrect because the investment outlay for Project C will not be recovered until the third year Answer (D) is incorrect because the investment outlay for Project C will not be recovered until the third year 229 Answer (C) is correct The payback period is the time required to recover the initial cash outlay The cost of A is $700,000, and the cumulative cash inflow at the end of the second year is $700,000 ($400,000 + $300,000) Answer (A) is incorrect because a payback period cannot be years unless the project is cost free Answer (B) is incorrect because only $400,000 has been recouped after one year Answer (D) is incorrect because the initial cash outlay is expected to be recovered after two years 230 Answer (A) is correct The net present value of Project A is calculated by subtracting the initial cash investment from the present value of the expected cash inflows It equals $362,340 [($400,000 x 9091) + ($300,000 x 8264) + ($600,000 x 7513) - $700,000] Answer (B) is incorrect because $1,062,340 results from not subtracting the initial investment Answer (C) is incorrect because $1,676,670 is calculated using present value factors for annuities Answer (D) is incorrect because $2,376,670 is calculated using present value factors for annuities without subtracting the initial investment of $700,000 231 Answer (C) is correct The approximate internal rate of return is defined as the discount rate at which the net present value is zero Using a discount rate of 24%, the net present value of Project B is -$4,675 [(1.9813 x $250,000) - $500,000] Answer (A) is incorrect because, at a discount rate of 16%, the net present value of Project B is $61,475 Answer (B) is incorrect because, at a discount rate of 20%, the net present value of Project B is $26,625 Answer (D) is incorrect because, at a discount rate of 28%, the net present value of Project B is -$32,900 232 Answer (A) is correct When investment projects are independent, the cash flows are unrelated The company may choose any or all of them, subject to capital availability Projects with positive net present values will be chosen Project A has a net present value of $362,340 [($400,000 x 9091) + ($300,000 x 8264) + ($600,000 x 7513) $700,000] The net present value of Project B is $121,825 [(2.4873 x $250,000) - $500,000] Answer (B) is incorrect because both projects have positive net present values and are therefore undertaken by the company Answer (C) is incorrect because both projects have positive net present values and are therefore undertaken by the company Answer (D) is incorrect because both projects have positive net present values and are therefore undertaken by the company 233 Answer (C) is correct The cash inflow occurs years after the cash outflow, and the NPV method uses the firm's cost of capital of 18% The present value of $1 due at the end of years discounted at 18% is 4371 Thus, the NPV of project A is $(265,460) [(.4371 x $7,400,000 cash inflow) - $3,500,000 cash outflow] Answer (A) is incorrect because $316,920 discounts the cash inflow over a 4-year period Answer (B) is incorrect because $23,140 assumes a 16% discount rate Answer (D) is incorrect because $(316,920) discounts the cash inflow over a 4-year period and also subtracts the present value of the cash inflow from the cash outflow 234 Answer (D) is correct The internal rate of return is the discount rate at which the NPV is zero Consequently, the cash outflow equals the present value of the inflow at the internal rate of return The present value of $1 factor for project B's internal rate of return is therefore 4020 ($4,000,000 cash outflow ÷ $9,950,000 cash inflow) This factor is closest to the present value of $1 for periods at 20% Answer (A) is incorrect because 15% results in a positive NPV for project B Answer (B) is incorrect because 16% is the approximate internal rate of return for project A Answer (C) is incorrect because 18% is the company's cost of capital 235 REQUIRED: The net present value of each project DISCUSSION: (B) The NPV is the excess of the present value of estimated cash inflows over the net cost of the investment At a zero cost of capital the NPV is simply the sum of a project’s undiscounted cash flows Thus, the NPV of Project A is $50,000 ($40,000 + $40,000 – $30,000), and the NPV of Project B is $200,000 ($700,000 + $500,000 – $1,000,000) Answer (A) is incorrect because $30,000 and $1,000,000 are the initial investment outlays for A and B, respectively Answer (C) is incorrect because $80,000 and $1,200,000 are the cash inflows for A and B, respectively Answer (D) is incorrect because $110,000 for Project A and $2,200,000 for Project B are calculated by adding the initial outlays to the sum of the cash inflows 236 REQUIRED: The internal rate of return for Project A DISCUSSION: (D) The internal rate of return is the discount rate that sets a project’s NPV equal to zero The internal rate of return may be determined as follows if IRR is the internal rate of return, t is the rime period, and n is the number of time periods: n NPV = ∑ t=1 Annual net cash inflow ( + IRR ) t - Net investment Substituting in the foregoing expression yields an internal rate of return of 100% 0= $40,000 $40,000 + - $30,000 (1 + IRR) ( + IRR ) IRR = 100% Answer (A) is incorrect because applying a discount rate of 10% results in a NPV of $69,421 Answer (B) is incorrect because applying a discount rate of 15% results in a NPV of $65,028 Answer (C) is incorrect because applying a discount rate of 25% results in a NPV of $57,600 237 REQUIRED: The difference between the net present value (NPV) and internal rate of return (IRR) DISCUSSION: (A) NPV assumes that cash inflows from the investment project can be reinvested at the cost of capital, whereas IRR assumes that cash flows from each project can be reinvested at the IRR for that particular project This underlying assumption is considered to be a weakness of the IRR technique The cost of capital is the appropriate reinvestment rate because it represents the opportunity cost for a project at a given level of risk The problem with the IRR method is that it assumes a higher discount rate even though a project may not have a greater level of risk Answer (B) is incorrect because NPV and IRR make consistent accept/reject decisions for independent projects When NPV is positive, IRR exceeds the cost of capital and the project is acceptable Answer (C) is incorrect because the NPV method can be used to rank mutually exclusive projects, whereas IRR cannot The reinvestment rate assumption causes IRR to make faulty project rankings under some circumstances Answer (D) is incorrect because IRR is expressed as a percentage and NPV in dollar terms 238 Calculate the after-tax component cost of debt as 10%(1 - 0.3) = 7% If the company has earnings of $100,000 and pays out 50% or $50,000 in dividends, then it will retain earnings of $50,000 The retained earnings breakpoint is $50,000/0.4 = $125,000 Since it will require financing in excess of $125,000 to undertake any of the alternatives, we can conclude the firm must issue new equity Therefore, the pertinent component cost of equity is the cost of new equity Calculate the expected dividend per share (note this is D1) as $50,000/10,000 = $5 Thus, the cost of new equity is $5/[($35(1 - 0.12)] + 6% = 22.23% Jackson’s WACC is 7%(0.6) + 22.23%(0.4) = 13.09% Only the return on Project A exceeds the WACC, so only Project A will be undertaken 239 The size of Gibson’s capital budget will be determined by the number of projects it can profitably undertake, that is, those projects for which IRR > applicable WACC First, find the costs of each type of financing: cost of retained earnings = ks = $4/$42 + 0.06 = 15.52% and cost of debt = kd = 11% To calculate the cost of new equity, ke we solve for ke = $4/($42-$2) + 0.06 = 0.16 = 16% Given the firm’s target capital structure and its retained earnings balance of $600,000, the firm can raise $1,000,000 with debt and retained earnings before it must use outside equity Therefore, the WACC for - $1,000,000 of financing = 0.4(0.11)(1 - 0.4) + 0.6(0.1552) = 11.95% Above $1,000,000, the firm must issue some new equity, so the WACC = 0.4(0.11)(1 - 0.4) + 0.6(0.16) = 12.24% Obviously, Projects A and B will be undertaken You must then determine whether Project C will be profitable Since in taking A and B we will need financing of $800,000, the $400,000 needed for Project C would involve financing $200,000 with debt and retained earnings and $200,000 with debt and new equity Thus, the WACC for Project C is ($200,000/$400,000) 0.1195 + ($200,000/$400,000) 0.1224 = 12.095% which is greater than Project C’s IRR Clearly, only Projects A and B should be accepted, and the firm’s capital budget is $800,000 240 Calculate the retained earnings break point (BPRE) as $300,000/0.6 = $500,000 Calculate ks as D1/P0 + g = $2(1.06)/$30 + 6% = 13.07% Calculate ke as D1/(P0 - F) + g = $2(1.06)/($30 - $5) + 6% = 14.48% Find WACC below BPRE as: WACC = 0.6(13.07%)+ 0.4(9%)(1 - 0.35) = 10.18% Thus, up to $500,000 can be financed at 10.18% Find WACC above BPRE as: WACC = 0.6(14.48%) + 0.4(9%)(1 - 0.35) = 11.03% Thus, financing in excess of $500,000 costs 11.03% Projects 2, 3, and all have IRRs exceeding either WACC and should be accepted These projects require $450,000 in financing Project is the next most profitable project Given its cost of $100,000, half or $50,000 can be financed at 10.18% and the other half must be financed at 11.03% The relevant cost of capital for Project is then 0.5(10.18%) + 0.5(11.03%) = 10.61% Since Project 1’s IRR is less than the cost of capital, it should not be accepted The firm’s optimal capital budget is $450,000 241 Step 1: Calculate the retained earnings breakpoint: BPRE = Retained earnings/wc = ($500,000 × 0.6)/0.6 = $500,000 Step 2: Calculate the WACCs: (There will be two: one with retained earnings and one with new equity.) WACC1 = [0.4 × 8% × (1 - 0.4)] + [0.6 × 12%] = 9.12% WACC2 = [0.4 × 8% × (1 - 0.4)] + [0.6 × 13%] = 9.72% Step 3: Determine the optimal capital budget: Now, work through the projects, starting with the highest-return project first, to determine the firm’s optimal capital budget Initially, the WACC is 9.12 percent for the first $500,000 of projects, providing they return more than 9.12 percent On the basis of this, we will take Projects A, B, and C, for a total budget of $400,000 Project D will be funded half by WACC1 and half by WACC2; however, since Project D returns 9.85 percent, we should still accept it because this is greater than WACC Project E returns 9.25 percent, but it will be funded entirely out of WACC funds at 9.72 percent, so we would not accept Project E Therefore, Projects A, B, C, and D should be accepted and the total capital budget is $600,000 242 REQUIRED: The characteristics of projects on an IOS DISCUSSION: (D) An IOS schedule is drawn for a set of independent projects The decision to be made is whether to accept or reject each project without regard to other investment opportunities Thus, the cash flows of one independent project are not influenced by those of another Independence should distinguished from mutual exclusivity Projects are mutually exclusive if acceptance of one requires rejection of the other Answer (A) is incorrect because IOS schedules not require that all projects have the same investment cost The steps of the schedule can be of varying lengths Answer (B) is incorrect because IOS schedules cannot be drawn for mutually exclusive projects Answer (C) is incorrect because IOS schedules not require that all projects have the same NPV The NPV of each project depends on the investment cost and on the present value of the expected cash flows Both costs and cash flows can vary for projects on an IOS 243 REQUIRED: The project(s) in which the company should invest and its optimal capital budget DISCUSSION: (B) The intersection of the IOS and MCC schedules determines the cost of capital and the optimal capital budget The company should begin with the project having the highest return and continue accepting projects as long as the IRR exceeds the MCC The highest rank project is A, with a $50 million cost and a 14% IRR The MCC is only 6% over this range of financing The next highest ranked project is B, with a $75 million cost and a 12% IRR When $125 million has been invested, the marginal cost of the next dollar of capital is 10%, so Project B is also acceptable, bringing the optimal capital budget to $125 million Project C is not acceptable because it has an 8% return The MCC is 10% for the first $50 million invested in this project and 12% for the remaining $75 million Answer (A) is incorrect because both A and B should be undertaken Answer (C) is incorrect because A is acceptable, but C is not Answer (D) is incorrect because C is not acceptable It offers an IRR less than the marginal cost of financing this project 244 REQUIRED: The marginal cost of capital and the appropriate discount rate DISCUSSION: (C) The appropriate discount rate (the cost of capital used in capital budgeting) theoretically is determined at the intersection of the IOS and MCC schedules This intersection is at an MCC of 10% and an optimal capital budget of $125 million However, if the optimal capital budget is assumed to be $150 million, the company is still in the second interval of the MCC schedule The marginal cost of financing in this part of the schedule is 10% Answer (A) is incorrect because 6% applies only to the first $75 million of new financing Given that the optimal capital budget exceeds $75 million, 6% cannot be the discount rate Answer (B) is incorrect because 8% is the IRR of Project C Answer (D) is incorrect because, at an investment level of $150 million, the MCC is 10% 245 REQUIRED: The reason for the increases in the MCC DISCUSSION: (D) The MCC is a weighted average of the costs of the different financing sources If the cost of any source of financing increases, the MCC curve will rise The MCC curve is upward sloping because the lowest cost financing sources are assumed to be used first Thus, as cumulative debt increases, the cost of debt also increases Answers (A) and (B) are incorrect because financing costs not depend on rates of return on investment Answer (C) is incorrect because, as additional funds are raised, an increase in the cost of a source of financing, not a decrease, will result in an increase in the MCC 246 REQUIRED: The NPV of the new machine DISCUSSION: (C) The #300,000 of annual savings discounted at 12% has a present value of $1,083,000 ($300,000 x 3.61 PV of an ordinary annuity for five periods at 12%) The net cost of the new machine is the $1,000,000 purchase price minus the $60,000 cash inflow from the sale of the old machine, or $940,000 The resulting NPV is $143,000 ($1,083,000 present value of future savings - $940,000 cash outlay) Answer (A) is incorrect because the $300,000 savings is an annual savings, which should be discounted at the present value of an annuity of $1 for periods at 12% or 3.61 ($300,000 x 3.61 = $1,083,000) The $300,000 annual savings should not be discounted using the present value of $1 for periods at 12%, or 0.57 ($300,000 x 0.57 = $171,000) Furthermore, the properly discounted amount ($1,083,000) should be reduced by the net cash outlay ($1,000,000 - $60,000) for the new equipment Answer (B) is incorrect because the NPV is equal to the present value of future cash savings minus net initial cash outlays, Answer (D) is incorrect because the cash inflows generated from the sale of old machinery should be added to the difference of the present value of cash inflows minus the purchase price of new machinery 247 REQUIRED: The IRR to the nearest percent for replacing the old machine DISCUSSION: (D) The IRR is the discount rate at which the present value of the cash flows equals the original investment Thus, the NPV of the project is zero at the IRR The IRR is also the maximum borrowing cost the firm could afford to pay for a specific project The IRR is similar to the yield rate/effective rate quoted in the business medial The formula for the IRR involving an annuity equates the annual cash flow, times an unknown annuity factor with the initial net investment: $940,000 = $300,000 x Factor The solution of the equation gives a factor of 3.1333, which is found in the 18% column on the five-period line Answers (A), (B), and (C) are incorrect because dividing the net investment by the annual savings yields a factor of 3.1333, which corresponds to an 18% IRR 248 REQUIRED: The payback period for the new machine DISCUSSION: (C) The payback method determines how long it takes for the investment dollars to be recovered by the annual net cash inflows The time is computed by dividing the net investment by the average periodic net cash inflow The initial net cash outlay divided by the annual cash savings equals 3.13 years ($940,000 ÷ $300,000) Answer (A) is incorrect because the initial cash outlay divided by the annual cash savings equals 3.13, not 1.14 Answer (B) is incorrect because the initial cash outlay divided by the annual cash savings equals 3.13, not 2.78 Answer (D) is incorrect because the initial cash outlay is $940,000 ($1,000,000 outlay - $60,000 inflow) 249 REQUIRED: The present value of the depreciation tax shield for the second year of the machine’s life DISCUSSION: (B) The applicable depreciation for 1997 is $380,000 At a tax rate of 40%, the savings is $152,000 ($380,000 x 40%) Its present value is $121,600 ($152,000 x 0.80 PC of $1 for two periods at 12%) Answer (A) is incorrect because the present value of the depreciation tax shield equals the present value of the product of 1990 depreciation multiplied by the tax rate of 40% Answer (C) is incorrect because $109,440 is the present value of the tax saving discounted at 18%, not the required 12% Answer (D) is incorrect because the present value of the depreciation tax shield is the PV of $1 for periods at 12% times the savings of $152,000 ($380,000 x 40%) 250 REQUIRED: The present value of the after-tax cash flow associated with the salvage of the old machine DISCUSSION: (A) The old machine will be sold for $60,000, and the entire selling price represents a taxable gain because the book value is zero At a 40% tax rate, the tax is $24,000 However, the tax will not be paid until the end of the year Discounting the tax payments results in a present value of $21,360 ($24,000 x 0.89) This amount is subtracted from the $60,000 selling price (not discounted because received immediately) to yield an after-tax NPV of $38,640 Answer (B) is incorrect because the $24,000 tax payment to be paid at year-end should be discounted using the present value factor of 0.89 Answer (C) is incorrect because the $60,000 payment received for the machinery is received immediately upon sale, and therefore should not be discounted Answer (D) is incorrect because only the discounted amount of income tax should be subtracted from the $60,000 received for the machinery 251 REQUIRED: The present value of the annual after-tax cash savings that arise from the new machine without consideration of the depreciation tax shield DISCUSSION: (D) The annual savings of $300,000 must be reduced by the 40% tax, so the net effect of purchasing the new machine is an annual cash savings of $180,000 [(1 – 0.4) x $300,000] The present value of the after-tax savings is therefore $649,800 ($180,000 x 3.61 PV of an ordinary annuity for five periods at 12%) Answer (A) is incorrect because $563,400 is the present value of the annual after-tax cash savings discounted at 18%, not the firm’s required 12% Answer (B) is incorrect because the annual savings must be reduced by the 40% tax This is achieved by multiplying annual savings by – 0.4, not – 0.6 Answer (C) is incorrect because the present value is the annual after-tax savings discounted at the PV of an ordinary annuity for five periods at 12% 252 REQUIRED: The present value of the additional after-tax cash flow resulting from a future sale of the new machine DISCUSSION: (B) At the time of sale, the new machine will be fully depreciated, and any sale proceeds will be fully taxable as a gain Hence, the $80,000 taxable gain will result in $32,000 of tax ($80,000 x 0.40), and the after-tax cash flow will be $48,000 Its present value will be $27,360 ($48,000 x 0.57 PV of $1 for five periods at 12%) Answer (A) is incorrect because the after-tax cash flow of $48,000, not the $32,0000 of tax, should be discounted at the PV factor of $1 for periods at 12% Answer (C) is incorrect because the $32,000 of tax should be deducted from the sale amount before discounting the after-tax cash flow Answer (D) is incorrect because $48,000 is the after-tax cash inflow, which needs to be discounted to its PV 253 254 (3,750+3,750+11,250+11,250)/4)/(100,000/2) Accrual accounting income = $103,000 - $48,000 = $ 55,000 = $103,000 - (($250,000 - $10,000)/5) AARR with initial investment = $55,000/($250,000 + $25,000) = $55,000/$275,000 = 0.20 a Cash flow from sale: $116,000 ($120,000 - 40% tax on the $10,000 tax gain) b Increase in annual cash outflows: $20,800 ($20,000 pretax cost increase + $800 increase in income taxes; the $20,000 increase in cash costs is more than offset by losing a $22,000 depreciation deduction) 255 Investment required ÷ Net annual cash inflow = Factor of the internal rate of return $83,150 ÷ Net annual cash inflow = 3.326 $83,150 ÷ 3.326 = Net annual cash inflow = $25,000 256 257 Year Estimated Demand in Units Unit Sales PriceUnit Variable Cost Unit Contribution MarginNet Pretax Cash Inflows From Sales110,000$15$7$8$80,000210,000157880,000310,000157880,000410,000157880,000510,000157880,000 Total net pretax cash inflows from sales $400,000 Initial cash outflow (cost of asset) $250,000 Less pretax estimated salvage value (50,000) 200,000 Excess of net pretax cash inflows over cost $ 200,000 258 a Cash flow from sale: $90,000 ($70,000 + 40% tax savings on the $50,000 tax loss) b Increase in annual cash outflows: $27,600 ($30,000 pretax cost increase - $2,400 decrease in income taxes; the $30,000 increase in cash costs is partially offset by losing a $24,000 depreciation deduction) 259 a Net investment: $124,000 [$300,000 - $160,000 - 40% x ($200,000 - 160,000)] b Increase in income taxes: $5,000 [40% x ($37,500 pretax flow - $75,000 depreciation + $50,000 lost depreciation)] c Increase in cash flows: $32,500 ($37,500 - $5,000 increase in income taxes) 260 a Net investment: $74,000 [$150,000 - $60,000 - 40%($100,000 - 60,000)] b Increase in income taxes: $16,000 [40% x ($50,000 pretax flow - $30,000 depreciation + $20,000 lost depreciation)] c Increase in cash flows: $34,000 ($50,000 - $16,000 increase in income taxes) 261 Predicted Cash FlowsYear(s)PV FactorPV of Cash FlowsInitial Investment$(160,000)01.000$(160,000)Salvage of old20,00001.00020,000Annual operations40,000132.32292,880Annual operations20,0004-6(3.889-2.322)31,340Save by not rebuilding40,00010.87735,080Salvage of new24,00060.45610,944 Net present value$ 30,244 262 DescriptionYearsAmount16% FactorPresent ValueVan & equipment0($125,000)1.000($125,000)Working capital0($ 60,000)1.000($ 60,000)Building rent1-6($ 35,000)3.685($128,975)Net annual cash inflow1-6$ 80,0003.685$294,800Salvage value, equipment6$ 5,0000.410$ 2,050Release of working capital6$ 60,0000.410$ 24,600Net present value$ 7,475 263 YearExplanationAmount12% FactorPresent Value0Investment to update assets$ (500,000)1.000$ (500,000)19Annual cash inflows 1,805,0005.3289,617,0409Selling price for the division 600,0000.361 216,600Net present value$9,333,640The sales price of $9,000,000 is less than the present value of the cash flows resulting from retaining the division General thus should not accept the offer 264 DescriptionYearsAmount10% FactorPresent ValueEquipment0($300,000)1.000($300,000)Working capital0($ 50,000)1.000($ 50,000)Net annual cash inflow 1-7$ 70,0004.868$340,760Salvage value, equipment 7$ 5,0000.513$ 2,565Release of working capital 7$ 50,0000.513$ 25,650 Net present value$ 18,975 265 DescriptionYearsAmount16% FactorPresent Value Equipment0($100,000)1.000($100,000)Working capital0($ 40,000)1.000($ 40,000)Building rent1-6($ 24,000)3.685($ 88,440)Net annual cash inflow1-6$ 60,0003.685$221,100Salvage value, equipment6$ 10,0000.410$ 4,100Release of working capital6$ 40,0000.410$ 16,400Net present value$ 13,160 266 Present Years Amount 14% Factor Value Working capital investment Now $(100,000) 1.000 $(100,000) Annual cash inflows 1-5 17,000 3.433 58,361 Working capital released 100,000 0.519 51,900 Net present value $ 10,261 Yes, the distributorship should be accepted since the project has a positive net present value 267 Item Investment Annual cash inflows Working capital required Working capital released Salvage value equipment Net present value 268 Years now 1-12 now 12 12 Project A: Cash investment now Cash inflow at the end of years Cash inflow at the end of years Net present value 269 270 Amount 14% Factor ($16,000) 1.000 3,600 5.660 (4,500) 1.000 4,500 0.208 2,000 0.208 Amount 12% Factor ($15,000) 1.000 $21,000 0.567 $21,000 0.404 Present Value ($16,000) 20,376 (4,500) 936 416 $ 1,228 Present Value ($15,000) $11,907 $ 8,484 $ 5,391 Project B: Cash investment now ($11,000) Annual cash outflow for years ($ 3,000) Additional cash inflow at the end of years $21,000 Net present value 1.000 3.605 0.567 ($11,000) ($10,815) $11,907 ($ 9,908) Project C: Cash investment now Annual cash inflow for years Cash outflow at the end of years Additional cash inflow at the end of years Net present value 1.000 3.037 0.712 0.636 ($21,000) $33,407 ($ 3,560) $ 9,540 $18,387 ($21,000) $11,000 ($ 5,000) $15,000 ÷ Net annual cash inflow = Payback period $60,000 - $5,000) ÷ ($18,000 + $12,000) = 1.83 years (rounded) b Incremental net income ÷ Investment = Simple rate of return $18,000 ÷ $55,000 = 32.7% (rounded) a Payback period: 3.0 years (30,000 + 60,000 + 90,000) b Book rate of return: 20% Average return: $54,000 ($270,000 total / years) Depreciation: 36,000 ($180,000 / years) a Investment required Average income $18,000 Average investment: $180,000 / = $90,000 Book rate of return = $18,000 / $90,000 = 20% 271 c NPV: $6,930 CashFactorPV130,000.89326,790260,000.79747,820390,000.71264,080460,000.63638,160530,000.567 17,010193,860Investment180,000NPV13,860 a Payback period: 3.15 years (75,000 + 90,000 + 115,000 + 15 x 130,000) b Book rate of return: Average return: Depreciation: Average income Average investment: Book rate of return = 33.3% $100,000 ($600,000 total / years) 50,000 ($30,000 / years) $50,000 $300,000 / = $150,000 $50,000 / 150,000 = 33.3% c NPV: $130,530 CashFactorPV175,000.90968,175290,000.82674,3403115,000.75186,3654130,000.68388,7905100,000.62162,10090,0 00.56450,760430,530Investment300,000PV130,530 272 (1) $100,000/$16,000 = 6.25 years payback period (2) [($160,000 - $90,000)/10 yrs.] / [($100,000 + $10,000)/2] = 12.73% accounting rate of return on average investment (3) Net present value = PV of ten annual cash inflows of $16,000 + PV of inflow from salvage in tenth year – Original investment $2,180 = ($16,000 x 6.145 + ($10,000 x 0.386) – ($100,000) 273 123 a.Cost savings per year$5,000 Maintenance per year (700)Net cash flows per year$4,300 CashDiscount factorPresent investment$ (6,200.36) value$30,0001.0000$(30,000.00) 4,3005.5348 23,799.64 Net present value of b.Payback equals $30,000/$4,300 = 6.976 years 274 120 (a) Cash flow YearAmountDiscount factorPresent valueInvestment0$(100,000) 1.00 $(100,000) Working cap 0$(200,000) 1.00 (200,000)Cash inflow1100,000 8621 86,210Cash inflow2150,000 7432 111,480Cash inflow3200,000 6407 128,140Cash inflow4200,000 5523 110,460Working cap 4200,000 5523 110,460Net present value$246,750 (b) After the first two years, $250,000 of the original $300,000 investment would be recouped It would take one-quarter of the third year ($50,000/$200,000) to recoup the last $50,000 Thus, the payback period is 2.25 years 275 a Present value factor for 10 years Initial investment Annual cash inflow x 5.650 $339,000 b Payback period = $339,000/$60,000 = 5.65 years c Initial investment PV of salvage value ($10,000 x 0.275) Net PV of annual net cash inflow Annual cash inflow = $60,150/3.020 = $19,917.22 d Payback = $62,900/$19,917.22 = 3.158 $62,900 (2,750) $60,150 $ 60,000 e Annual net cash inflow = $226,000/5.650 = $40,000 f PV factor for 10 years = $226,000/$40,000 = 5.650 Look up value 5.650 in PV of annuity table under 10 years and the internal rate of return is 12% a Annual cash flow: 60% x [125,000 x ($200 - $130)] – (60% x $6,000,000) + (40% x $7,200,000/4) = $2,370,000 NPV: [($2,370,000 x 3.037) - $7,200,000 - 500,000 + ($500,000 x 636)] = ($184,310) 276 b PI: 0.976 [($2,370,000 x 3.037 + 500,000 x 636)/($7,200,000 + 500,000)] 277 a Predicted Cash FlowsYear(s)PV FactorPV of Cash FlowsInitial investment$(20,960)01.000$(20,960)Annual operations5,000104.83324,165 Net present value$ 3,205 b Present value factor of an annuity of $1.00 = $20,960/$5,000 = 4.192 From annuity table, the 4.192 factor is closest to the 10-year row at the 20% column Therefore, the IRR is 20% 278 a Predicted Cash FlowsYear(s)PV FactorPV of Cash FlowsInitial investment$(95,000)01.000$(95,000)Annual operations, net18,0001 - 84.63983,502Salvage value, work cap14,50080.3515,090 Net present value$ (6,408) b Trial and error is necessary You know it is below 14% because the answer to Part A was negative and, therefore, less than the discount rate Therefore, let's try 12% Predicted Cash FlowsYear(s)PV FactorPV Of Cash FlowsInitial investment$(95,000)01.000$(95,000)Annual operations, net18,0001 - 84.968 89,424Salvage value, work cap14,50080.404 5,858 Net present value$ 282 The (almost) zero net present value indicates an internal rate of return of approximately 12% 279 a b Payback period: years c IRR: 15% NPV: $78,000 [(5.650 x $120,000) - $600,000] ($600,000/$120,000) (5.0 is about halfway between 5.216 and 4.833) 280 a b Payback period: years c IRR: between 18 % and 20% 281 NPV: $36,300 [(3.605 x $60,000) - $180,000] ($180,000/$60,000) (3.0 is between 3.127 and 2.991) a Predicted Cash FlowsYear(s)PV FactorPV of Cash FlowsInvestment$(36,586)01.000$(36,586)Working capital needed(4,000)01.000(4,000)Annual operations10,0001-53.43334,330Working capital returned4,00050.5192,076Salvage value4,00050.5192,076Net present value$(2,104) b Trial and error is required Because net present value is negative in part a, the internal rate of return is less than 14% Start by trying 12% Predicted Cash FlowsYear(s)PV FactorPV of Cash FlowsInvestment$(36,586)01.000$(36,586)Working capital needed (4,000)01.000 (4,000)Annual operations 10,0001-53.605 36,050Working capital returned 4,00050.567 2,268Salvage value 4,00050.567 2,268Net present value$-0With a zero net present value, the internal rate of return is 12% c Payback period = ($36,586 + $4,000)/$10,000 = 4.06 years 282 (1) $100,000/$29,129 = 3.4 years payback period (2) ($29,129 x 3.605) - $100,000 = $5,010 net present value (3) $100,000/$29,129 = 3.433 discount factor Present value of $1 received annually for years at 14% interest has a factor equal to 3.433 The internal rate of return on the purchase is 14% (4) Yes The net present value is positive and the internal rate of return (14%) is more than the discount rate (12%) 283 a Since depreciation is the only noncash item on the income statement, the net annual cash flow can be computed by adding back depreciation to net income Net income … $200,000 Depreciation … 100,000 Net annual cash flow … $300,000 Initial investment Net annual cash flows Net present value Years Now 1-10 Amount $(1,000,000) 300,000 12% Factor 1.000 5.650 Present Value $(1,000,000) 1,695,000 $ 695,000 b The formula for computing the factor of the internal rate of return (IRR) is: Investment required ÷ Net annual cash inflow = Factor of the IRR $1,000,000 ÷ $300,000 = 3.333 26% factor … True factor … 28% factor 3.465 3.333 _ 0.132 3.465 3.269 0.196 26% + 2%(0.132 ÷0.196) = 27.3% c The formula for the payback period is: Investment required ÷ Net annual cash inflow = Payback period $1,000,000 ÷ $300,000 = 3.33 years d The formula for the simple rate of return is: Net income ÷ Initial investment = Simple rate of return $200,000 ÷ $1,000,000 = 20.0% 284 (1) $45,000 initial outlay/$12,000 annual outflow = 3.75 payback years (2) Cash inflow ($12,000 x 3.791) Investment Net present value $45,492 45,000 $ 492 (3) $45,000 x 621 = $27,945 285 Investment required Annual cost savings Salvage value Net present value a now 1-15 15 Year ($25,000) 3,500 1,000 Amount 1.000 7.606 0.239 10% Factor ($25,000) 26,621 239 $ 1,860 Present Value b Year Amount 10% Factor Present Value Annual cash inflows 1-8 $ 5,000 5.335 $26,675 Since the present value of the cash inflows is $26,675, the company should be willing to pay up to this amount to acquire the machine c Investment required ÷ Net annual cash flow = Factor of the internal rate of return $30,000 ÷ %6,000 = 5.000 14% factor 5.216 5.216 True factor 5.000 16% factor 4.833 0.216 0.383 14% + 2%(0.216 ÷ 0.383) = 15.1% The machine should be purchased, since the internal rate of return is greater than the required rate of return 286 a The present value of the $12,000 annuity is found by multiplying $12,000 by the annuity discount factor associated with percent interest for four years: $12,000 3.4651 = $41,581.20 From the information on the profitability index, it is known that the present value of the cash inflows is 1.03953 times the initial investment Thus, the initial investment is $41,581.20/1.03953 = $40,000 b By dividing $40,000 by the annual cash inflow of $12,000, it is determined that the discount factor associated with the IRR is 3.3333 This discount factor is associated with an interest rate that lies between and percent Using interpolation, the IRR is computed to be approximately 7.72 percent 287 a Annual cash flows: $27,000 [$35,000 - 40% x ($35,000 - $15,000)] b Payback period: 5.56 years ($150,000/$27,000) 288 a Annual net cash flows: $14,800 [$18,000 pretax - 40% x ($18,000 - $10,000 depreciation)] b NPV: Negative $16,380 [($14,800 x 5.650) - $100,000] 289 250,000 x ($60 - $40) - $3,000,000 - $5,000,000/4 Income tax Net income Plus depreciation Net cash flow a $ 750,000 (300,000) $ 450,000 1,250,000 $1,700,000 Income before taxes, b Payback period: 2.94 years ($5,000,000/$1,700,000) c NPV: $389,000 [($1,700,000 x 3.170) - $5,000,000] 290 291 a Annual cash flows: $46,400 [$56,000 - 40% x ($56,000 - 32,000)] b Payback period: 3.45 years ($160,000/$46,400) c NPV: $7,272 [($46,400 x 3.605) - $160,000] [200,000 x ($40 - $27) - $1,500,000 - $3,500,000/4] Income tax (40%) Plus depreciation Net cash flow a $ 225,000 ( 90,000) 875,000 $1,010,000 Income before taxes, b Payback period: 3.47 years ($3,500,000/$1,010,000) c NPV: negative $298,300 [($1,010,000 x 3.170) - $3,500,000] 292 a Increase in annual net cash flow: $148,000 [$200,000 - 40% x ($200,000 - $70,000)] b Profitability index: 1.19 [($148,000 x 5.65)/$700,000] 293 a Increase in annual net cash flow: $22,000 [$30,000 - (40% x ($30,000 - $10,000)] b Profitability index: 1.24 [($22,000 x 5.65)/$100,000] c Effect on profitability index: Increase (PI would increase because the tax shield of depreciation would occur earlier and so be more valuable when considering the time value of money.) 294 a Annual net cash flows: $57,600 [$80,000 pretax - 40% x ($80,000 - $24,000 depreciation)] b NPV: $17,640 [($57,600 x 5.650) - $240,000 - $100,000 + ($100,000 x 322)] c PI: 1.052 {[($57,600 x 5.650) + ($100,000 x 322)]/($240,000 + $100,000)} 295 a Annual net cash flows: $550,000 [$750,000 - 40% x ($750,000 - $250,000 depreciation)] b NPV: $434,400 [($550,000 x 4.968) - $2,000,000 - $500,000 + ($500,000 x 404)] c PI: 1.17 {[($550,000 x 4.968) + ($500,000 x 404)]/($2,000,000 + $500,000)} a Annual net cash flows: $2,325,000 [$2,875,000 pretax - 40% x ($2,875,000 - $1,500,000 depreciation)] pretax income = 275,000 x ($60 - $35) - $4,000,000 = $2,875,000 296 b NPV: $775,050 [($2,325,000 x 2.914) - $6,000,000] c Allowable loss of X-10 sales, approximately 36,941 units [($775,050/2.914)/60%]/12 d Allowable error in per-unit VC, $1.61 {[($775,050/2.914)/60%]/275,000 units} 297 a Annual net cash flows: $26,200 [$33,000 pretax - 40% x ($33,000 - $16,000 depreciation)] b NPV: Negative $11,970 [($26,200 x 5.650) - $160,000] c IRR: between 10% and 12% [factor of 6.107 (160,000/26,200) is between 6.145 and 5.650] 126 a.Revenue$100,000 - cash expenses (60,000)Annual inflow$ 40,000 b.PV inflow $40,000 4.4941 =$179,764 PV outflow $160,000 1.0 =(160,000) NPV =$ 19,764 c.IRR factor = $160,000/$40,000 = 4.0 which is approximately 23% d.Payback = $160,000/$40,000 = yrs e.$179,764/$160,000 = 1.123525 f.Car wash exceeds minimum on SRR and IRR, but not payback 298 299 Present value of keeping current system: Predicted Cash FlowsYear(s)PV FactorPV of Cash FlowsOverhaul$(40,000)01.000$ (40,000)Annual operations(70,000)1-52.991(209,370)Salvage value5,00050.4022,010 Net present value$(247,360) Present value of new system: Predicted Cash FlowsYear(s)PV FactorPV of Cash FlowsInvestment$(100,000)01.000$(100,000)Salvage value, old20,00001.00020,000Annual operations(40,000)152.991(119,640)Salvage value20,00050.4028,040 Net present value$(191,600) Buying the new equipment is the most desirable by $55,760 ($247,360 - $191,600) 300 a Payback Method Proposal AProposal BProposal CYear 1$80,000$45,000$90,000Year $90,000$90,000$90,000Payback years2 years1 year Net Present Value Proposal A:Predicted Cash FlowsYear(s)PV FactorPV of 10,000 45,000 Cash FlowsInvestment$(90,000)01.000$(90,000)Annual operations:Year 80,00010.877 70,160Year 10,00020.769 7,690Year 45,00030.675 30,375 Net present value$ 18,225 Proposal B:Predicted Cash FlowsYear(s)PV FactorPV of Cash FlowsInvestment$(90,000)01.000$(90,000)Annual operations:Year 245,00020.76934,605Year 345,00030.67530,375Net present value$ 14,445 145,00010.87739,465Year Proposal C:Predicted Cash FlowsYear(s)PV FactorPV of Cash FlowsInvestment$(90,000)01.000$(90,000)Annual operations:Year 190,00010.87778,930 11,070 Accrual Accounting Rate of Return: Proposal A: [80,000 + 10,000 + 45,000)/3 - (90,000/3)]/90,000 = 0.167 Net present value$ Proposal B: (45,000-30,000)/90,000 = 0.167 Proposal C: (90,000- 90,000)/90,000 = 0.0 b Summary: MethodProposal AProposal BProposal CPayback method ranks2.52.51.0Net present value1.02.03.0AARR1.51.53.0Even though Proposal C is Number for payback, it comes in last with the other two methods Because the net present value method takes into account the time value of money and the other proposals are less comprehensive, Proposal A would be the best alternative 125 a.Old loss $(2,000)New receipts $20,000 5% =$ 1,000 Depr $12,000/10 yrs = (1,200)New (Loss)$ (200)b.Change in annual cash inflow is $3,000Payback = $12,000/$3,000 = yrs.c.1.PV of inflow $3,000 4.1925 =$12,577.50 PV of outflow $12,000 1.0 =(12,000.00)NPV$ 577.50 2.IRR is approximately 23%d.Change in inflow = $2,700 PV inflow $2,700 4.1925 =$11,319.75 PV outflow $12,000 1.0 =(12,000.00) NPV$ (680.25)e.$12,000/4.1925 = $2,862.25Receipts = ($2,862.25 - $2,000)/.05 = $17,245 301 302 a 1 7 Net present value Year $150,000 32,000 57,000 5,000 28,000 16,000 3,000 15,000 70,000 Cash flow 1.0000 9009 8116 7312 6587 5935 5346 4817 4817 Discount factor $(150,000.00) 28,828.80 46,261.20 3,656.00 8,443.60 9,496.00 1,603.80 7,225.50 33,719.00 $ (766.10) Present value b Profitability index equals present value of cash flows divided by investment: $149,233.90/$150,000 = 995 c Payback period is 6.11 years, computed as follows: Year Cash Flow $32,000 57,000 5,000 28,000 16,000 3,000 85,000 Cumulative Cash Flow $ 32,000 89,000 94,000 122,000 138,000 141,000 226,000 $150,000 - $141,000 = $9,000/$85,000 = 11 d The project is quantitatively unacceptable because it has a negative NPV, a less-than-one PI, and a payback period of over six years However, the NPV and PI are extremely close to being acceptable Because the new machine will provide XYZ zero-defect production, the investment may be desirable if additional qualitative factors are considered such as improved competitive position, customer satisfaction, goodwill generated, improved product quality and reliability, and a desire to be in the forefront of manufacturing capability XYZ may want to attempt to quantify these benefits and reevaluate the machine's acceptability as an investment 303 118 No matter what happens, the tax rate for the next two years is 30 percent Using the differences in depreciation amounts, one can determine the difference in present values between the two methods at the end of year when the tax rate is expected to change Present value calculations for years and 2: Year ($20,000) 30 9091 =$ (5,455)Year ($25,000) 30 8265 =$ (6,199)Total present value difference at end$(11,654)So, after the first two years, Method has generated $11,654 more present value than Method This simply means that at the point of indifference, Method would be required to generate $11,654 more present value than Method in the last three years For the last three years of the project's life, the difference in depreciation amounts is $15,000 This $15,000 amount can be used in the following equation to solve for the tax rate that yields a present value of $11,654: $11,654 = $15,000 tax rate (.7513 + 6830 + 6209) $11,654 = $30,828 tax rate Tax rate = $11,654/$30,828 Tax rate = 37.8% Thus, an increase in the tax rate to about 37.8 percent would cause management to be indifferent between the two depreciation methods 304 Dividing $200,000/$60,000, gives the annuity discount factor (3.3333) for 11 percent associated with the minimal required time for this project to be successful According to the tables in Appendix A, the project will have a positive net present value if the cash flows last through year 305 (1) YearUnadjusted Estimate of Cash InflowsInflation AdjustmentInflation Adjusted Estimate of Cash Inflows1$50,0001.100$55,000240,0001.21048,400330,0001.33139,930$120,000$143,330 (2) YearUnadjusted Cash FlowsAdjusted Cash FlowsPV of $1@ 16%PV of Unadjusted Cash FlowsPV of Adjusted Cash Flows0$(100,000)$(100,000)1.000$(100,000)$(100,000)150,00055,000 862 43,100 47,410240,00048,400 743 29,720 35,961330,00039,930 641 19,230 25,595Net present value of investment$ (7,950)$ 8,966 306 YearEstimated Net Pretax Cash Inflows4% Annual Price-level AdjustmentPrice-level Adjusted Net Cash Inflows1$10,000(1 + 04)1 = 1.040$10,400215,000(1 + 04)2 = 1.08216,230315,000(1 + 04)3 = 1.12516,875415,000(1 + 04)4 = 1.17017,550510,000(1 + 04)5 = 1.21712,17065,000(1 + 04)6 = 1.2656,325 Total price-level adjusted net pretax cash inflows from operations $79,550 Plus cash inflow from salvage $2,500 Price-level adjustment 1.265 3,163 Total price-level adjusted net pretax cash inflows over initial cash outflow $82,713 Less initial cash outflow 50,000 Excess of net pretax cash inflows over initial cash outflow $ 32,713 307 (1)(2)(1) x (2) = (3) YearPeriodic Cash Inflows4% Price-level AdjustmentInflation Adjusted Estimate of Cash Inflows1$25,000(1 + 04)1 = 1.040$26,000227,000(1 + 04)2 = 1.08229,214329,000(1 + 04)3 = 1.12532,625423,000(1 + 04)4 = 1.17026,910520,000(1 + 04)5 = 1.21724,340615,000(1 + 04)6 = 1.26518,975$ 139,000$ 158,064 (1)(2)(1) x (2) = (3) YearDepreciable Basis of Property5-Year Property Recovery Percentage Tax Depreciation1$100,0000.200$20,0002100,0000.32032,0003100,0000.19219,2004100,0000.11511,5005100,0000.11511 ,5006100,0000.0585,800$ 100,000 (1)(2)(1) - (2) = (3)(3) x (4) (5)(1) - (5) (6)(4)YearAdjusted Estimate of Net Cash Inflows Tax DepreciationTaxable Income (Loss) Income Tax Net After-tax Cash InflowsFederal and State Income Tax Rate1$26,000$20,000$ 6,000$ 2,400$23,60040%229,21432,000(2,786) (1,114)30,32840%332,62519,20013,4255,37027,25540%426,91011,50015,4106,16420,74640%524,34011,50012,8405,13 619,20440%618,9755,80013,1755,27013,70540% Total estimated net after-tax cash inflows from project $134,838 Less initial cash outflow for machinery 100,000 Excess of after-tax cash inflows from project over initial cash outflow $ 34,838 308 Funds—SourceProportion of FundsAfter-tax CostWeighted CostBonds.25.071.018Preferred stock.25.152.0375Common stock and retained earnings.50.143.0701.00.1255or 12.55% Computations: 12 - (.12 x 4) $15/$100 = 15 $105,000/25,000 = $4.20; $4.20/$30 = 14 ... of 137 MANAGEMENT ADVISORY SERVICES B $600,000 CAPITAL BUDGETING D None of the above B&M Working Capital 23 For project A in year 2, inventories increase by $16,000 and accounts payable by $4,000... receivable by $3,000 and accounts payables by $2,000 Calculate the increase or decrease in working capital for year (E) A Increases by $6,000 C Increases by $8,000 B Decreases by $6,000 D Decreases by. .. QUESTIONS Page of 137 MANAGEMENT ADVISORY SERVICES CAPITAL BUDGETING 27 What is the net cash outflow at the beginning of the first year that Dickens should use in a capital budgeting analysis?
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