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Lecture 21

FIN2120 Lecture 21: hca14e_sm_ch21

by OneClass493612 , Winter 2013
48 Pages
164 Views
Winter 2013

Department
FIN
Course Code
FIN2120
Professor
Robert Novoselic
Lecture
21

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21-1
CHAPTER 21
CAPITAL BUDGETING AND COST ANALYSIS
21-1 No. Capital budgeting focuses on an individual investment project throughout its life,
recognizing the time value of money. The life of a project is often longer than a year. Accrual
accounting focuses on a particular accounting period, often a year, with an emphasis on income
determination.
21-2 The five stages in capital budgeting are the following:
1. An identification stage to determine which types of capital investments are available to
accomplish organization objectives and strategies.
2. An information-acquisition stage to gather data from all parts of the value chain in order to
evaluate alternative capital investments.
3. A forecasting stage to project the future cash flows attributable to the various capital
projects.
4. An evaluation stage where capital budgeting methods are used to choose the best
alternative for the firm.
5. A financing, implementation and control stage to fund projects, get them under way and
monitor their performance.
21-3 In essence, the discounted cash-flow method calculates the expected cash inflows and
outflows of a project as if they occurred at a single point in time so that they can be aggregated
(added, subtracted, etc.) in an appropriate way. This enables comparison with cash flows from
other projects that might occur over different time periods.
21-4 No. Only quantitative outcomes are formally analyzed in capital budgeting decisions.
Many effects of capital budgeting decisions, however, are difficult to quantify in financial terms.
These nonfinancial or qualitative factors (for example, the number of accidents in a
manufacturing plant or employee morale) are important to consider in making capital budgeting
decisions.
21-5 Sensitivity analysis can be incorporated into DCF analysis by examining how the DCF of
each project changes with changes in the inputs used. These could include changes in revenue
assumptions, cost assumptions, tax rate assumptions, and discount rates.
21-6 The payback method measures the time it will take to recoup, in the form of expected
future net cash inflows, the net initial investment in a project. The payback method is simple and
easy to understand. It is a handy method when screening many proposals and particularly when
predicted cash flows in later years are highly uncertain. The main weaknesses of the payback
method are its neglect of the time value of money and of the cash flows after the payback period.
The first drawback, but not the second, can be addressed by using the discounted payback
method.
21-7 The accrual accounting rate-of-return (AARR) method divides an accrual accounting
measure of average annual income of a project by an accrual accounting measure of investment.
The strengths of the accrual accounting rate of return method are that it is simple, easy to
understand, and considers profitability. Its weaknesses are that it ignores the time value of money
and does not consider the cash flows for a project.
21-2
21-8 No. The discounted cash-flow techniques implicitly consider depreciation in rate of
return computations; the compound interest tables automatically allow for recovery of
investment. The net initial investment of an asset is usually regarded as a lump-sum outflow at
time zero. Where taxes are included in the DCF analysis, depreciation costs are included in the
computation of the taxable income number that is used to compute the tax payment cash flow.
21-9 A point of agreement is that an exclusive attachment to the mechanisms of any single
method examining only quantitative data is likely to result in overlooking important aspects of a
decision.
Two points of disagreement are (1) DCF can incorporate those strategic considerations that
can be expressed in financial terms, and (2) “Practical considerations of strategy” not expressed
in financial terms can be incorporated into decisions after DCF analysis.
21-10 All overhead costs are not relevant in NPV analysis. Overhead costs are relevant only if
the capital investment results in a change in total overhead cash flows. Overhead costs are not
relevant if total overhead cash flows remain the same but the overhead allocated to the particular
capital investment changes.
21-11 The Division Y manager should consider why the Division X project was accepted and
the Division Y project rejected by the president. Possible explanations are:
a. The president considers qualitative factors not incorporated into the IRR computation
and this leads to the acceptance of the X project and rejection of the Y project.
b. The president believes that Division Y has a history of overstating cash inflows and
understating cash outflows.
c. The president has a preference for the manager of Division X over the manager of
Division Y—this is a corporate politics issue.
Factor a. means qualitative factors should be emphasized more in proposals. Factor b. means
Division Y needs to document whether its past projections have been relatively accurate. Factor
c. means the manager of Division Y has to play the corporate politics game better.
21-12 The categories of cash flow that should be considered in an equipment-replacement
decision are:
1a. Initial machine investment,
b. Initial working-capital investment,
c. After-tax cash flow from current disposal of old machine,
2a. Annual after-tax cash flow from operations (excluding the depreciation effect),
b. Income tax cash savings from annual depreciation deductions,
3a. After-tax cash flow from terminal disposal of machines, and
b. After-tax cash flow from terminal recovery of working-capital investment.
21-13 Income taxes can affect the cash inflows or outflows in a motor vehicle replacement
decision as follows:
a. Tax is payable on gain or loss on disposal of the existing motor vehicle,
b. Tax is payable on any change in the operating costs of the new vehicle vis-à-vis the
existing vehicle, and
c. Tax is payable on gain or loss on the sale of the new vehicle at the project termination
date.
d. Additional depreciation deductions for the new vehicle result in tax cash savings.
21-3
21-14 A cellular telephone company manager responsible for retaining customers needs to
consider the expected future revenues and the expected future costs of “different investments” to
retain customers. One such investment could be a special price discount. An alternative
investment is offering loyalty club benefits to long-time customers.
21-15 These two rates of return differ in their elements:
Real-rate of return Nominal rate of return
1. Risk-free element 1. Risk-free element
2. Business-risk element 2. Business-risk element
3. Inflation element
The inflation element is the premium above the real rate of return that is demanded for the
anticipated decline in the general purchasing power of the monetary unit.
21-16 Exercises in compound interest, no income taxes.
The answers to these exercises are printed after the last problem, at the end of the chapter.
(Please alert students that in some printed versions of the book there is a typographical
error in the solution to part 5. The interest rate is 8%, not 6%.)
21-17 (20–25 min.) Capital budget methods, no income taxes.
1a. The table for the present value of annuities (Appendix A, Table 4) shows:
8 periods at 8% = 5.747
Net present value = $67,000 (5.747) – $250,000
= $385,049 – $250,000 = $135,049
1b. Payback period = $250,000 ÷ $67,000 = 3.73 years
1c. Discounted Payback Period
Period
Cash
Savings
Discount
Factor (8%)
Discounted
Cash
Savings
Cumulative
Discounted
Cash
Savings
Unrecovered
Investment
0 $250,000
1 $67,000 .926 $62,042 $ 62,042 $187,958
2 $67,000 .857 $57,419 $119,461 $130,539
3 $67,000 .794 $53,198 $172,659 $ 77,341
4 $67,000 .735 $49,245 $221,904 $ 28,096
5 $67,000 .681 $45,627 $267,531
$28,096 ÷ $45,627 = 0.6158
Discounted Payback period = 4.62 years

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Description
CHAPTER 21 CAPITAL BUDGETING AND COST ANALYSIS 21-1 No. Capital budgeting focuses on an individual investment project throughout its life, recognizing the time value of mone y. The life of a project is often longer than a year. Accrual accounting focuses on a particular accounting peri od, often a year, with an emphasis on income determination. 21-2 The five stages in capital budgeting are the following: 1. An identification stage to determine which types of capital investments are available to accomplish organization objectives and strategies. 2. An information-acquisition stage to gather data from all parts of the value chain in order to evaluate alternative capital investments. 3. A forecasting stage to project the future cash flows attributable to the various capital projects. 4. An evaluation stage where capital budgeting methods ar e used to choose the best alternative for the firm. 5. A financing, implementation and control stage to fund projects, get them under way and monitor their performance. 21-3 In essence, the discounted cash-flow method calculates the expected cash inflows and outflows of a project as if they occurred at a single point in time so that they can be aggregated (added, subtracted, etc.) in an appropriate way. This enables comparison with cash flows from other projects that might occur over different time periods. 21-4 No. Only quantitative outcomes are formally analyzed in capital budgeting decisions. Many effects of capital budgeting decisions, however, are difficult to quantify in financial terms. These nonfinancial or qualitative factors (f or example, the number of accidents in a manufacturing plant or employee morale) are im portant to consider in making capital budgeting decisions. 21-5 Sensitivity analysis can be incorporated into DCF analysis by examining how the DCF of each project changes with changes in the inputs used. These could include changes in revenue assumptions, cost assumptions, tax rate assumptions, and discount rates. 21-6 The payback method measures th e time it will take to recoup, in the form of expected future net cash inflows, the net initial investment in a project. The payback method is simple and easy to understand. It is a handy method when sc reening many proposals and particularly when predicted cash flows in later years are highly uncertain. The ma in weaknesses of the payback method are its neglect of the time value of money and of the cash flows after the payback period. The first drawback, but not the second, can be addressed by using the discounted payback method. 21-7 The accrual accounting rate-of-return (AARR) method divides an accrual accounting measure of average annual income of a project by an accrual accounting measure of investment. The strengths of the accrual accoun ting rate of return method are that it is simple, easy to understand, and considers profitability. Its weaknesses are that it ignores the time value of money and does not consider the cash flows for a project. 21-1 21-8 No. The discounted cash-flow techniques implic itly consider depreciation in rate of return computations; the compound interest tables automatically allow for recovery of investment. The net initial investme nt of an asset is usually rega rded as a lump-sum outflow at time zero. Where taxes are included in the DCF an alysis, depreciation costs are included in the computation of the taxable income number that is used to compute the tax payment cash flow. 21-9 A point of agreement is that an exclusive attachment to the mechanisms of any single method examining only quantitative data is likely to result in overlooking important aspects of a decision. Two points of disagreement are (1) DCF can incorporate those strategic considerations that can be expressed in financial terms, and (2) “Pra ctical considerations of strategy” not expressed in financial terms can be incorporated into decisions after DCF analysis. 21-10 All overhead costs are not relevant in NPV an alysis. Overhead costs are relevant only if the capital investment results in a change in total overhead cash flows. Overhead costs are not relevant if total overhead cash flows remain the same but the overhead allocated to the particular capital investment changes. 21-11 The Division Y manager should consider w hy the Division X project was accepted and the Division Y project rejected by the president. Possible explanations are: a. The president considers qualitative factors not incorporated into the IRR computation and this leads to the acceptance of the X project and rejection of the Y project. b. The president believes that Division Y ha s a history of overstating cash inflows and understating cash outflows. c. The president has a preference for the mana ger of Division X over the manager of Division Y—this is a corporate politics issue. Factor a. means qualitative factor s should be emphasized more in proposals. Factor b. means Division Y needs to document whether its past proj ections have been relatively accurate. Factor c. means the manager of Division Y has to play the corporate politics game better. 21-12 The categories of cash flow that should be considered in an equipment-replacement decision are: 1a. Initial machine investment, b. Initial working-capital investment, c. After-tax cash flow from current disposal of old machine, 2a. Annual after-tax cash flow from operations (excluding the depreciation effect), b. Income tax cash savings from annual depreciation deductions, 3a. After-tax cash flow from terminal disposal of machines, and b. After-tax cash flow from terminal recovery of working-capital investment. 21-13 Income taxes can affect the cash inflows or outflows in a motor vehicle replacement decision as follows: a. Tax is payable on gain or loss on disposal of the existing motor vehicle, b. Tax is payable on any change in the opera ting costs of the new vehicle vis-à-vis the existing vehicle, and c. Tax is payable on gain or loss on the sale of the new vehicle at the project termination date. d. Additional depreciation deductions for the new vehicle result in tax cash savings. 21-2 21-14 A cellular telephone company manager respon sible for retaining customers needs to consider the expected future revenues and the expected future costs of “different investments” to retain customers. One such investment coul d be a special price di scount. An alternative investment is offering loyalty club benefits to long-time customers. 21-15 These two rates of return differ in their elements: Real-rate of return Nominal rate of return 1. Risk-free element 1. Risk-free element 2. Business-risk element 2. Business-risk element 3. Inflation element The inflation element is the premium above the real rate of return that is demanded for the anticipated decline in the general purchasing power of the monetary unit. 21-16 Exercises in compound interest, no income taxes. The answers to these exercises are printed after the last problem, at the end of the chapter. (Please alert students that in some printed versions of the book there is a typographical error in the solution to part 5. The interest rate is 8%, not 6%.) 21-17 (20–25 min.) Capital budget methods, no income taxes. 1a. The table for the present value of annuities (Appendix A, Table 4) shows: 8 periods at 8% = 5.747 Net present value = $67,000 (5.747) – $250,000 = $385,049 – $250,000 = $135,049 1b. Payback period = $250,000 ÷ $67,000 = 3.73 years 1c. Discounted Payback Period Cumulative Discounted Discounted Cash Discount Cash Cash Unrecovered Period Savings Factor (8%) Savings Savings Investment 0 $250,000 1 $67,000 .926 $62,042 $ 62,042 $187,958 2 $67,00.$7,$1,30,539 3 $67,000 .794 $53,198 $172,659 $ 77,341 4 $67,000 .735 $49,245 $221,904 $ 28,096 5 $67,00.$5,62,531 $28,096 ÷ $45,627 = 0.6158 Discounted Payback period = 4.62 years 21-3 1d. Internal rate of return: $250,000= Present value of annuity of $67,000 at R% for 8 years, or what factor (F) in the table ofpresent values of an annuity (Appendix A, Table 4) will satisfy the following equation. $250,000 =$67,000F F = 250000/67000= 3.73 On the 8-year line in the table for the present value of annuities (Appendix A, Table 4), find the column closest to 3.73; it is between a rate of return of 20% and 22%. Interpolation is necessary: Present Value Factors 20% 3.837 3.837 raIeR – 3.730 22% 3.619 –– Difference 0.218 0.107 Internal rate of return = 20% + (.107/.218) * (2%) = 20% + .4908 (2%) = 20.98% 1d. Accrual accounting rate of return based on net initial investment: Net initial investment = $250,000 Estimated useful life = 8 years Annual straight-line depreciation = $250,000 ÷ 8 = $31,250 Accrualaccounting = Increasein expectedaverageannualoperatingincome rateof return Netinitialinvestment = ($67,000 – $31,250) / $250,000 = $35,750 / $250,000 = 14.3% Note how the accrual accounting rate of return can produce results that differ markedly from the internal rate of return. 2. Other than the NPV, rate of return and the payback period on the new computer system, factors that Riverbend should consider are: • Issues related to the financing the project, and the availability of capital to pay for the system. • The effect of the system on employee morale, particularly those displaced by the system. Salesperson expertise and real-time help from experienced employees is key to the success of a hardware store. • The benefits of the new system for customers (faster checkout, fewer errors). • The upheaval of installing a new computer syst em. Its useful life is estimated to be 8 years. This means that Riverbend could f ace this upheaval again in 8 years. Also, ensure that the costs of trai ning and other “hidden” start- up costs are included in the estimated $250,000 cost of the new computer system. 21-4 21-18 (25 min.) Capital budgeting methods, no income taxes. The table for the present value of annuities (Appendix A, Table 4) shows: 10 periods at 14% = 5.216 1a. Net present value = $ 28,000 (5.216) – $110,000 = $146,048 – $110,000 = $36,048 b. Payback period = $110,000 = 3.93 years $28,000 c. For a $110,000 initial outflo w, the project generates $28,000 in cash flows at the end of each of years one through ten. Using either a calculator or Excel, the internal rate of return for this stream of cash flows is found to be 21.96%. d. Accrual accounting rate of return based on net initial investment: Net initial investment = $110,000 Estimated useful life = 10 years Annual straight-line depreciation = $110,000 ÷ 10 = $11,000 $28,000 − $11,000 Accrual accounting rate of return = $110,000 = $17,000 = 15.45% $110,000 e. Accrual accounting rate of return based on average investment: Average investment = ($110,000 + $0) / 2 $55,000 = $28,000−$11,000 Accrual accounting rate of return = = 30.91% . $55,000 2. Factors City Hospital should consider include: a. Quantitative financial aspects. b. Qualitative factors, such as the benefits to its customers of a better eye-testing machine and the employee-morale advantages of having up-to-date equipment. c. Financing factors, such as the availability of cash to purchase the new equipment. 21-5 21-19 (35min.) Capital budgeting, income taxes. 1a. Net after-tax initial investment = $110,000 Annual after-tax cash flow from operations (excluding the depreciation effect): Annual cash flow from operation with new machine $28,000 Deduct income tax payments (30% of $28,000) 8,400 Annual after-tax cash flow from operations $19,600 Income tax cash savings from annual depreciation deductions 30% × $11,000 $ 3,300 These three amounts can be combined to determine the NPV: Net initial investment; $110,000 × 1.00 $(110,000) 10-year annuity of annual after-tax cash flows from operations; $19,600 × 5.216 102,234 10-year annuity of income tax cash savings from annual depreciation deductions; $3,300 × 5.216 17,213 Net present value $ 9,447 b. Payback period $110,000 = ($19,600 + $3,300) $110,000 = $22,900 y4.r0= 21-6 c. For a $110,000 initial outflow, the project now generates $22,900 in after-tax cash flows at the end of each of years one through ten. Using either a calculator or Excel, the internal rate of return for this stream of cash flows is found to be 16.17%. d. Accrual accounting rate of return based on net initial investment: AARR = $22,900 − $11,000 = $11,900 $110,000 $110,000 10.82% e. Accrual accounting rate of return based on average investment: $22,900 − $11,000 $11,900 AARR = = $55,000 $55,000 21.64% 2a. Increase in NPV. To get a sense for the magnitude, note that from Table 2, the present value factor for 10 periods at 14% is 0.270. Therefore, the $10,000 terminal disposal price at the end of 10 years would have an after-tax NPV of: $10,000 × (1 − 0.30) × 0.270 = $1,890 b. No change in the payback period of 4.80 years. The cash inflow occurs at the end of year 10. c. Increase in internal ra te of return. The $10,000 terminal disposal price would raise the IRR because of the additional inflow. (The new IRR is 16.54%.) d. The AARR on net initial investment w ould increase because accrual accounting income in year 10 would increase by the $7,000 ($10,000 gain from disposal, less 30% × $10,000) after- tax gain on disposal of equipment. This incr ease in year 10 income would result in higher average annual accounting income in the numerator of the AARR formula. e. The AARR on average investment would also increase, for the same reasons given in the previous answer. Note that the denominator is unaffected because the investment is still depreciated down to zero terminal disposal value, and so th e average investment remains $55,000. 21-7 21-20 (25 min.) Capital budgeting with uneven cash flows, no income taxes. 1. Present value of savings in cash operating costs: $10,000 × 0.862 $ 8,620 8,000 × 0.743 5,944 6,000 × 0.641 3,846 5,000 × 0.552 2,760 Present value of savings in cash operating costs 21,170 Net initial investment (23,000 ) Net present value $ (1,830) 2. Paybacpkeriod: Cumulative Initial Investment Yet to Be Year Cash Savings Cash Savings Recovered at End of Year 0 – – $23,000 1 $10,000 $10,000 13,000 2 8,000 18,000 5,000 3 6,000 24,000 – $5,000 Payback period = 2 years + = 2.83 years $6,000 3. Discounted Payback Period Cumulative Cash Disc Factor Discounted Discounted Unrecovered Period Savings (16%) Cash Savings Cash Savings Investment 0 $23,000 1 $10,000 .862 $8,620 $ 8,620 $14,380 2 $ 8,000 .743 $5,944 $14,564 $ 8,436 3 $ 6,000 .641 $3,846 $18,410 $ 4,590 4 $ 5,000 .552 $2,760 $21,170 $ 1,830 At a 16% rate of return, this project does not save enough to make it worthwhile using the discounted payback method. 4. From requirement 1, the net present value is negative with a 16% required rate of return. Therefore, the internal rate of return must be less than 16%. P.V. P.V. P.V. Cash P.V. Factor at 14% P.V. Factor at 12% P.V. Factor at 10% Year Savings at 14% (4) = at 12% (6) = at 10% (8) = (1) (2) (3) (2) × (3) (5) (2) × (5) (7) (2) × (7) 1 $10,000 0.877 $ 8,770 0.893 $ 8,930 0.909 $ 9,090 2 8,000 0.769 6,152 0.797 6,376 0.826 6,608 3 6,000 0.675 4,050 0.712 4,272 0.751 4,506 4 5,000 0.592 2,960 0.636 3,180 0.683 3,415 $21,932 $22,758 $23,619 Net present value at 14% = $21,932 – $23,000 = $(1,068) 21-8 Net present value at 12% = $22,758 – $23,000 = $(242) Net present value at 10% = $23,619 – $23,000 = $619 619 Internal rate of return = 10% + 619+ 242 (2%) = 10% + (0.719) (2%) = 11.44% 5. Accrual accounting rate of return based on net initial investment: $29,000 Average annual savings in cash operating costs = = $7,250 4 years Annual straight-line depreciation =23,000 = $5,750 4 years Accrual accounting rate of return =$7,250−$5,750 $23,000 $1,500 = = 6.52% $23,000 21-9 21-21 (30min.) Comparison of projects, no income taxes. 1. Total PVreseet Year Present Discount Value Factors at 10% 0 1 2 3 Plan I $ (100,000) 1.000 $ (100,000) (3,778,950) 0.826 $(4,575,000) $(3,878,950) Plan II $(1,550,000) 1.000 $(1,550,000) (1,408,950) 0.909 $(1,550,000) (1,280,300) 0.826 $(1,550,000) $(4,239,250) Plan III $ (200,000) 1.000 $ (200,000) (1,340,775) 0.909 $(1,475,000) (1,218,010)765,000) (1,1$(1,0.5,100) $(3,866,850) 2. Plan III has the lowest net present value cost, and is therefore preferable on financial criteria. 3. Factors to consider, in addition to NPV, are: a. Financialfactorsincluding: • Competing demands for cash. • Availability of financing for project. b. Nonfinancialfactorsincluding: • Risk of building contractor not remaini ng solvent. Plan II exposes New Bio most if the contractor becomes bankrupt before completion because it requires more of the cash to be paid earlier. • Ability to have leverage over the contractor if quality problems arise or delays in construction occur. Plans I and III gi ve New Bio more negotiation strength by being able to withhold sizable payment am ounts if, say, quality problems arise in Year 1. • Investment alternatives available. IfNew Bio has capital constraints, the new building project will have to compete with other projects for the limited capital available. 21-10 21-22 (30min.) Payback and NPV methods, no income taxes. 1a. Payback measures the time it will take to recoup, in the form of expected future cash flows, the net initial investment in a project. Pa yback emphasizes the early recovery of cash as a key aspect of project ranking. Some managers argue that this emphasis on early recovery of cash is appropriate if there is a high level of uncertainty about future cash flows. Projects with shorter paybacks give the organization more flexibi lity because funds for other projects become available sooner. Strengths • Easy to understand • One way to capture uncertainty about expected cash flows in later years of a project (although sensitivity analysis is a more systematic way) Weaknesses • Fails to incorporate the time value of money, unless discounted payback is used • Does not consider a project’s cash flows after the payback period 1b. Project A Outflow, $3,000,000 Inflow, $1,000,000 (Year 1) + $1,000,000 (Year 2) + $1,000,000 (Year 3) + $1,000,000(Year 4) Payback = 3 years Project B Outflow, $1,500,000 Inflow, $400,000 (Year 1) + $900,000(Year 2) + $800,000(Year 3) ($1,500,000−$400,000−$900,000) Payback = 2 years + = 2.25 years $800,000 21-11 Project C Outflow, $4,000,000 Inflow, $2,000,000 (Year 1) + $2,000,000(Year 2) + $200,000 (Year 3) + $100,000 (Year 4) Payback = 2 years Payback Period 1. Project C 2 years 2. Project B 2.25 years 3. Project A 3 years If payback period is the deciding factor, Andr ews will choose Project C (payback period = 2 years; investment = $4,000,000) and Project B (payback period = 2.25 years; investment = $1,500,000), for a total capital investment of $5,500, 000. Assuming that each of the projects is an all-or-nothing investment, Andrews will have $500,000 left over in the capital budget, not enough to make the $3,000,000 investment in Project A. 2. Solution Exhibit 21-22 shows the following ranking: NPV 1. Project B $ 207,800 2. Project A $ 169,000 3. Project C $(311,500) 3. Using NPV rankings, Projects B and A, which require a total investment of $3,000,000 + $1,500,000 = $4,500,000, which is le ss than the $6,000,000 capital budget, should be funded. This does not match the rankings based on pa yback period because Projects B and A have substantial cash flows after the payback period, cash flows that the payback period ignores. Nonfinancial qualitative fact ors should also be consider ed. For example, are there differential worker safety issues across the proj ects? Are there differences in the extent of learning that can benefit other projects? Are there differences in the customer relationships established with different projects that can benefit Andrews Construction in future projects? 21-12 4 3 2 Sketch of Relevant Cash Flows 0 909 $1,000,000 909 $ 400,000 Presente 10% DisFactors at $1.,000,000) 0.683 1.000 $(1,500,000)0.751.000 $$1,000,00)0 0.683 0 0.909 $2,000,000 Value Total Present $1,000,000 $1,000,000 A PROJECTti27tal ive7,.NetPRresJnt value00)Net $resentv,0u0eC0i00es$Net2p0e,sn0t value SOLUTION EXHIBIT 21-22 21-23 (22–30min.) DCF, accrual accounting rate of return, working capital, evaluation of performance, no income taxes. 1. Present value of annuity of savings in cash operating costs ($31,250 per year for 8 years at 14%): $31,250 × 4.639 $144,969 Present value of $37,500 terminal disposal price of machine at end of year 8: $37,500 × 0.351 13,163 Present value of $10,000 recovery of working capital at end of year 8: $10,000 × 0.351 3,510 Gross present value 161,642 Deduct net initial investment: Centrifuge machine, initial investment $137,500 Additional working capital investment 10,000 147,500 Net present value $ 14,142 2. The sequence of cash flows from the project is: For a $147,500 initial outflow, th e project now generates $31,250 in cash flows at the end of each of years one through seven and $78,750 (= $31,250 + $37,500) at the end of year 8. Using either a calculator or Excel, the internal rate of return for this stream of cash flows is found to be 16.51%. 3. Accrual accounting rate of return based on net initial investment: Net initial investment = $137,500 + $10,000 $147,500 = Annual depreciation ($137,500 – $37,500) ÷ 8 years = $12,500 $31,250−$12,500 Accrual accounting rate of return = = 12.71% . $147,500 4. Accrual accounting rate of return based on average investment: Average investment = ($147,500 + $10,000) / 2 $78,750 = $31,250−$12,500 Accrual accounting rate of return = = 23.81% . $78,750 5. If your decision is based on the DCF model, the purchase would be made because the net present value is positive, and the 16.51% internal rate of return exceeds the 14% required rate of return. However, you may believe that your pe rformance may actually be measured using accrual accounting. This approach would show a 12.71% return on the initial investment, which is below the required rate. Your reluctance to make a “buy” decision would be quite natural unless you are assured of reasonable consis tency between the decision model and the performance evaluation method. 21-14 21-24 (40 min.) New equipment purchase, income taxes. 1. The after-tax cash inflow per year is $29,600 ($21,600 + $8,000), as shown below: Annual cash flow from operations $36,000 Deduct income tax payments (0.40 × $36,000) 14,400 Annual after-tax cash flow from operations $21,600 Annual depreciation on machine [($88,000 – $8,000) ÷ 4] $20,000 Income tax cash savings from annual depreciation deductions (0.40 × $20,000) $ 8,000 a. Solution Exhibit 21-24 shows the NPV computation. NPV = $7,013 b. Payback = $88,000 ÷ ($21,600 + $8,000) = 2.97 years c. For a $88,000 initial outflow, the project now generates $29,600 in after-tax cash flows at the end of each of years one through four and an additional $8,000 at the end of year 4. Using either a calculator or Excel, the internal rate of return for this stream of cash flows is found to be 15.59%. 2. Accrual accounting rate of return based on net initial investment: Net initial investment = $88,000 Annual after-tax operating income = $29,600 - $20,000 depreciation = $9,600 $9,600 Accrual accounting rate of return = = 10.91% . $88,000 21-15 SOLUTION EXHIBIT 21-24 Present Value Total Discount Present Factor Value at 12% Sketch of Relevant After-Tax Cash Flows 0 1 2 3 4 1a. Initial machine investment $(88,000) 1.000 $(88,000) 1b. Initial working capital investment 0 1.000 $0 2a. Annual after-tax cash flow from operations (excl. depr.) Year 1 19,289 0.893 $21,600 Year 2 17,215 0.797 $21,600 Year 3 15,379 0.712 $21,600 Year 4 13,738 0.636 $21,600 2b. Income tax cash savings from annual depreciation deductions Year 1 7,144 0.893 $8,000 Year 2 6,376 0.797 $8,000 Year 3 5,696 0.712 $8,000 Year 4 5,088 0.636 $8,000 3. After-tax cash flow from: a. Terminal disposal of machine 5,088 0.636 $8,000 b. Recovery of working capital $636 Net present value if new machine is purchased $ 7,013 21-16 21-25 (40 min.) New equipment purchase, income taxes. 1. The after-tax cash inflow per year is $21,500 ($16,250 + $5,250), as shown below: Annual cash flow from operations $25,000 Deduct income tax payments (0.35 × $25,000) 8,750 Annual after-tax cash flow from operations $16,250 Annual depreciation on motor ($75,000 ÷ 5 years) $15,000 Income tax cash savings from annual depreciation deductions (0.35 × $15,000) $ 5,250 a. Solution Exhibit 21-25 shows the NPV computation. NPV= $6,486 An alternative approach: Present value of 5-year annuity of $21,500 at 10% $21,500 × 3.791 $81,507 Present value of cash outlays, $75,000 × 1.000 75,000 valureeset et * $ 6,507 * Minor difference from solution exhibit 21-25 due to rounding. b. Payback = $75,000 ÷ $21,500 = 3.49 years c. Discounted Payback Period Cumulative Cash Disc Factor Discounted Disc Cash Unrecovered Period Savings (10%) Cash Savings Savings Investment $75,000.00 0 1 $21,50 .00919,543190,$55.456.50 2 $21,50 .02617,759370,$37.697.50 3 $21,50 .05116,146530,$21.551.00 4 $21,500 .683 $14,684.50 $68,133.50 $ 6,866.50 5 $21,50 .02113,351810,485.00 $6,866.50 ÷ $13,351.50 = 0.51 Discounted Payback Period = 4.51 years d. For a $75,000 initial outflow, the project now generates $21,500 in after-tax cash flows at the end of each of years one through five. Using either a calculator or Excel, the internal rate of return for this stream of cash flows is found to be 13.34%. 21-17 2. Both the net present value and internal rate of return methods use the discounted cash flow approach in which all expected future cash inflows and outflows of a project are measured as if they occurred at a single point in time. The net present value approach computes the surplus generated by the project in today’s dollars while the internal rate of return attempts to measure its effective return on investment earned by the project. The payback method, by contrast, considers nominal cash flows (w ithout discounting) and measures the time at which the project’s exp ected future cash inflows recoup the net initial investment in a project. The payback method thus ignores the profitability of the project’s entire stream of future cash flows. The discounted payback method shares this last defect, but looks at the time taken to recoup the initial investment based on the discounted present value of cash inflows. The two payback methods are becoming increasingly important in the global economy. When the local environment in an international location is unstable and therefore highly risky for a potential investment, a company would likely pay close attention to the payback period for making its investment decision. In general, the more unstable the environment, the shorter the payback period desired. 21-18 ,50 $0 $0 250 , 250 , 250 , ,50 0.6210.621 Discount 10% Sketch of Relevant After-Tax Cash Flows Present Value $001.000 0 Total $ 6,486 Presente 0 5 4 3 2 1 0 1a.mIoiirlstIaitatpn.pernalta,-romarea1s,v99n0.aa3cta1hs$250,250r.fl0.90.82.7b. weoNentprpsrohoseiue if,250.683 SOLUTION EXHIBIT 21-25 21-26 (60min.) Selling a plant, income taxes. 1. Option 1 Current disposal price $450,000 Deduct current book value 0 Gain on disposal 450,000 Deduct 35% tax payments 157,500 Net present value $292,500 Optio2n Crossroreceitesee sources of cash inflows: a. Rent. Four annual payments of $110,000. The after-tax cash inflow is: $110,000 × (1 – 0.35) = $71,500 per year b. Discount on material purchases, payable at year-end for each of the four years: $20,000 The after-tax cash inflow is: $20,000 × (1 – 0.35) = $13,000 c. Sale of plant at year-end 2012. The after-tax cash inflow is: $75,000 × (1 – 0.35) = $48,750 Present Value Total Discount Present Factors at Value 10% Sketch of Relevant After-Tax Cash Flows 0 1 2 3 4 1. Rent ` $ 64,994 0.909 $71,500 59,059 0.826 $71,500 53,697 0.751 $71.500 48,835 0.683 $71,500 2. Discount on Purchases $11,817 0.909 $13,000 10,738 0.826 $13,000 9,763 0.751 $13,000 0.6838,$81739,000 3. Sale of plant $ 33,296 0.683 $48,750 Net present value $301,078 21-20 O3ption Contrijmcaot:in Seplrnegc $55.00 Variable costs 43.00 Contribm1i.n$n 2012 2013 2014 2015 Contribution margin $12.00 × 9,000; 13,000; 15,000; 5,000 $108,000 $156,000 $180,000 $60,000 Fixed overhead (cash) costs 10,000 10,000 10,000 10,000 Annual cash flow from operations 98,000 146,000 170,000 50,000 Income tax payments (35%) 34,300 51,100 59,500 17,500 After-tax cash flow from operations (excl. depcn.) $ 63,700 $ 94,900 $110,500 $32,500 Depreciation: $80,000 ÷ 4 = $20,000 per year Income tax cash savings from depreciation deduction: $20,000 × 0.35 = $7,000 per year Sale of plant at end of 2015: $135,000 × (1 – 0.35) = $87,750 Solution Exhibit 21-26 presents the NPV calculations: NPV = $243,590 21-21 SOLUTION EXHIBIT 21-26 2015 2014 2013 2012 2011 1a. Initial plant equipment upgrade investment 1b. Initial working capital investment 2a. Annual after-tax cash flow from operations (excluding depreciation effects) Year 1 Year 2 Year 3 Year 4 2b. Income tax cash savings from annual depreciation deductions Year 1 Year 2 Year 3 Year 4 3. After-tax cash flow From a. Terminal disposal of plant b. Recovery of working capital Net present value 1 O $2ti2,500 2 O $3ti1,078 3 O $2ti3,590 2. 21-27 (60 min.) Equipment replacement, no income taxes. 1. Cash flows for modernizing alternative: Net Cash Initial Sale of Equip. Year UniStsld Contributions InvestmeTetst ination a (1) (2) (3) = (2) × $18,000 (4) (5) Jan. 1, 2012 –– –– $(33,600,000) –– Dec. 31,2012 552 $ 9,936,000 Dec. 31, 2013 612 11,016,000 Dec. 31, 2014 672 12,096,000 Dec. 31, 2015 732 13,176,000 Dec. 31, 2016 792 14,256,000 Dec. 31, 2017 852 15,336,000 Dec. 31, 2018 912 16,416,000 $6 ,000,000 a $80,000 – $62,000 = $18,000 cash contribution per prototype. Cash flows for replacement alternative: Net Cash Initial Sale of Equip. Year UniStsld Contributions Investments b (1) (2) (3) = (2) × $24,000 (4) (5) Jan. 1, 2012 –– –– $(58,800,000) $3,600,000 Dec. 31, 2012 552 $13,248,000 Dec. 31, 2013 612 14,688,000 Dec. 31, 2014 672 16,128,000 Dec. 31, 2015 732 17,568,000 Dec. 31, 2016 792 19,008,000 Dec. 31, 2017 852 20,448,000 Dec. 31, 2018 912 21,888,000$14 ,400,000 b$80,000 – $56,000 = $24,000 cash contribution per prototype. 21-23 2. Payback period calculations for modernizing alternative: Cumulative Net Initial Investment Year Cash Inflow Cash Inflow Unrecovered at End of Year (1) (2) (3) (4) Jan. 1, 2012 –– –– $33,600,000 Dec. 31, 2012 $ 9,936,000 $ 9,936,000 23,664 ,000 Dec. 31, 2013 11,016,000 20,952,000 12,648 ,000 Dec. 31, 2014 12,096,000 33,048,000 552 ,000 Dec. 31, 2015 13,176,000 Payback = 3 + ($552,000 ÷ $13,176,000) = 3.04 years Payback period calculations for replace alternative: Cumulative Net Initial Investment Year Cash Inflow Cash Inflow Unrecovered at End of Year (1) (2) (3) (4) Jan. 1, 2012 –– –– $55,200,000 Dec. 31, 2013 $13,248,000 $13,248,000 41,952 ,000 Dec. 31, 2014 14,688,000 27,936,000 27,264 ,000 Dec. 31, 2015 16,128,000 44,064,000 11,136 ,000 Dec. 31, 2016 17,568,000 Payback = 3 + ($11,136,000 ÷ $17,568,000) = 3.63 years 21-24 3. Modernizing alternative: PrVeseute Discount Factors Net Cash Present Year At 12% Flow Value Jan. 1, 2012 1.000 $(33,600,000) $(33,600,000) Dec. 31, 2012 0.893 9,936,000 8,872 ,848 Dec. 31, 2013 0.797 11,016,000 8,779,752 Dec. 31, 2014 0.712 12,096,000 8,612,352 Dec. 31, 2015 0.636 13,176,000 8,379,936 Dec. 31, 2016 0.567 14,256,000 8,083,152 Dec. 31, 2017 0.507 15,336,000 7,775,352 Dec. 31, 2018 0.452 22,416,000 10,132,032 Total $27,035,424 ReApltcrenative: PrVeseute Discount Factors Net Cash Present Year At 12% Flow Value Jan. 1, 2012 1.000 $(55,200,000) $(55,200,000) Dec. 31, 2012 0.893 13,248,000 11,830,464 Dec. 31, 2013 0.797 14,688,000 11,706,336 Dec. 31, 2014 0.712 16,128,000 11,483,136 Dec. 31, 2015 0.636 17,568,000 11,173,248 Dec. 31, 2016 0.567 19,008,000 10,777,536 Dec. 31, 2017 0.507 20,448,000 10,367,136 Dec. 31, 2018 0.452 36,288,000 16,402,176 Total 28,540,032 4. Using the payback period, the moderni ze alternative is preferred to the replace alternative. On the other hand, the replace alternative has a higher NPV than the modernize alternative and so should be preferred. Howeve r, the NPV amounts are based on best estimates. Pro Chips should examine the sensitivity of the NPV amounts to variations in the estimates. Nonfinaqnucatatcitve ors should be considered. These could include the quality of the prototypes produced by the modernize and replace alternatives. These alternatives may differ in capacity and their ability to meet surges in demand be yond the estimated amounts. The alternatives may also differ in how workers increase their shop floor-capabilities. Such differences could provide labor force externalities that can be the source of future benefits to Pro Chips. 21-25 21-28 (40 min.) Equipment replacement, income taxes (continuation of 21-27). 1. & 2. Income tax rate = 30% Modernize Alternative Adnnuraelciation: $33,600 ,000 ÷ 7 years = $4,800,000 a year. Income tax cash savings from annual depreciation deductions: $4 ,800,000 × 0.30 = $1,440,000 a year. Terminal disposal of equipment = $6,000,000. After-tax cash flow from terminal disposal of equipment: $6,000,000 × 0.70 = $4,200,000. The NPV components are: a. Initial investment: Jan. 1, 2012 $(33,600,000) × 1.000 $(33,600,000) b. Annual after-tax cash flow from operations (excldeireciation): Dec. 31, 2012 9,936,000 × 0.70 × 0.893 6,210,994 2013 11,016 ,000 × 0.70 × 0.797 6,145,826 2014 12,096,000 × 0.70 × 0.712 6,028,646 2015 13,176 ,000 × 0.70 × 0.636 5,865,955 2016 14,256 ,000 × 0.70 × 0.567 5,658,206 2017 15,336 ,000 × 0.70 × 0.507
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