CHAPTER 20 CAPITAL BUDGETING CHAPTER 20 CAPITAL BUDGETING
QUESTIONS QUESTIONS
20-1
20-1 The three The three major steps major steps in capital budgeting decisions are: in capital budgeting decisions are: project identiproject identificatficationion and definition, evaluation and selection, and monitoring and r
and definition, evaluation and selection, and monitoring and review.eview.
20-2
20-2 Firms make capital investments to improve efficiency and productivity and toFirms make capital investments to improve efficiency and productivity and to expand into new territories or products with the ultimate objective of earning a expand into new territories or products with the ultimate objective of earning a higher profit. This interest in profit is enhanced by the fact that all firms regularly higher profit. This interest in profit is enhanced by the fact that all firms regularly compute and report periodic net incomes and that reported periodic incomes compute and report periodic net incomes and that reported periodic incomes often play important roles in performance evaluations. As a result, many firms often play important roles in performance evaluations. As a result, many firms focus on effects that capital investments may have on the periodic net income focus on effects that capital investments may have on the periodic net income that will be reported when they consider capital investments.
that will be reported when they consider capital investments. Although
Although net net income income is is a a measure measure on on the the outcome outcome of of a a capital capital investment,investment, overemphasizing the importance of net income can lead to erroneous capital overemphasizing the importance of net income can lead to erroneous capital investment decisions because of the requirement to conform with the generally investment decisions because of the requirement to conform with the generally acce
acceptepted d accoaccountunting ing priprincincipleples s whewhen n comcomputputing ing periperiodic odic net net inincomcome e whiwhich,ch, among others, mandate the use of an accrual basis in all process. In contrast, among others, mandate the use of an accrual basis in all process. In contrast, capital investment decisions use cash flow data.
capital investment decisions use cash flow data.
The periodicity reporting requirement and the arbitrary process involved in The periodicity reporting requirement and the arbitrary process involved in determining net income lessen the usefulness of net income as an objective determining net income lessen the usefulness of net income as an objective criterion. A net income is the result of applying accounting methods the firm criterion. A net income is the result of applying accounting methods the firm chose to use. With a different, yet equally acceptable, accounting method the net chose to use. With a different, yet equally acceptable, accounting method the net income of a period can be substantially different.
income of a period can be substantially different.
20-3
20-3 Cash inflows:Cash inflows: •
• Fees from patientsFees from patients •
• Proceeds from disposal of equipment no longer neededProceeds from disposal of equipment no longer needed •
• Investment tax credits.Investment tax credits. Cash outflows:
Cash outflows: •
• SalSalary, ary, wagwages, es, and and benbenefefits its fofor r addadditiitionaonal l profprofessessionional al medmedicaicall staffs including: staffs including: ♦ ♦ PhysiciansPhysicians ♦ ♦ TechniciansTechnicians ♦ ♦ NursesNurses ♦ ♦ ClerksClerks •
• Operating expenses of the scanner such as:Operating expenses of the scanner such as: ♦
♦ UtilitiesUtilities ♦
♦ SuppliesSupplies ♦
20-4
20-4 After 20 years of oper After 20 years of operation, a chemical company needs to ation, a chemical company needs to ensure that there is noensure that there is no residual effect on the environment before abandoning the factory. Restoration of residual effect on the environment before abandoning the factory. Restoration of the site to remove any environmental effect to the neighborhood the factory might the site to remove any environmental effect to the neighborhood the factory might have caused over the years is
have caused over the years is the most critithe most critical step the firm needs to take. Verycal step the firm needs to take. Very likely it is also among the most expensive processes.
likely it is also among the most expensive processes.
20.5
20.5Direct cash effects in capital budgeting are immediate effects that cash receipts,Direct cash effects in capital budgeting are immediate effects that cash receipts, cash payments, or cash commitments have on cash flows of the firm. Direct cash cash payments, or cash commitments have on cash flows of the firm. Direct cash effects in acquiring a new factory can include:
effects in acquiring a new factory can include: •
• acquisition or construction cost of the factory building,acquisition or construction cost of the factory building, •
• purchase costs for machinery and equipment needed for the factory,purchase costs for machinery and equipment needed for the factory, •
• working capital for additional materials, payrolls, and operating expenses,working capital for additional materials, payrolls, and operating expenses, •
• cash receipts from selling the products,cash receipts from selling the products, •
• proproceceeds eds frfrom om sasaleles s of of ththe e olold d fafactctoryory, , mamachchininerery, y, anand d eqequiuipmepmentnt replaced.
replaced.
20-6
20-6 Tax effects are the effect that a decision or transaction has on the tax liability of Tax effects are the effect that a decision or transaction has on the tax liability of the firm. Tax effects of a decision to acquire a new factory include:
the firm. Tax effects of a decision to acquire a new factory include: •
• decreases in taxes because of the depreciation expenses of thedecreases in taxes because of the depreciation expenses of the new factory
new factory •
• increaincreases in ses in tax payments for gains or tax payments for gains or decreasedecreases s in tax paymentsin tax payments for losses on disposal of the replaced factory, machinery, or equipment or the for losses on disposal of the replaced factory, machinery, or equipment or the abandonment of the investment at the end of its useful life
abandonment of the investment at the end of its useful life •
• increaincreases ses in tax payments for gains in tax payments for gains from operatifrom operations or ons or decreasedecreasess in tax payments for losses on operations
in tax payments for losses on operations •
• investment tax creditinvestment tax credit
20-7
20-7 A A book book value value by by itself itself is is irrelevant irrelevant in in capital capital budgeting budgeting since since it it has has no no effect effect onon cash flow. However, a
cash flow. However, a capitacapital l budgetibudgeting ng decisidecision often involves disposal of on often involves disposal of oneone or more assets the firm no longer needs. Book values of the disposed assets are or more assets the firm no longer needs. Book values of the disposed assets are the bases in determining gains or losses on disposals. These gains or losses the bases in determining gains or losses on disposals. These gains or losses affect the tax payment of the firm, which, in turn, affect the cash flows of the firm. affect the tax payment of the firm, which, in turn, affect the cash flows of the firm.
20.8
20.8 Among the limitations of the payback Among the limitations of the payback period technique period technique are its are its failure to cfailure to consider anonsider an investment project’s total profitability and
investment project’s total profitability and the time value of money.the time value of money.
The present value payback period technique considers the time value of The present value payback period technique considers the time value of money. It fails, however, to consider an investment project’s total profitability.
money. It fails, however, to consider an investment project’s total profitability.
20-9
20-9 The book rate of return of an investment is not likely to yield a true measure of The book rate of return of an investment is not likely to yield a true measure of return on the investment because it does not consider the time value of money return on the investment because it does not consider the time value of money an
and d ininclclududes es in in itits s cocompmputautatition on memeasasureures s ththat at are are reresulsults ts of of ththe e arbarbititrarrarililyy selected accounting procedures the firm chooses to follow.
selected accounting procedures the firm chooses to follow.
The internal rate of return may not be a true measure of return on investment The internal rate of return may not be a true measure of return on investment either, because it implies that all cash inflows from the investment have the same either, because it implies that all cash inflows from the investment have the same rate of return over the project’s entire useful years.
20-10
20-10 The decision criterion for the NPV method is the amount and direction of the netThe decision criterion for the NPV method is the amount and direction of the net present value. A capital investment with a positive NPV is deemed a good present value. A capital investment with a positive NPV is deemed a good investment. Furthermore, a higher NPV signals a better capital investment.
investment. Furthermore, a higher NPV signals a better capital investment.
The IRR method uses a different decision criterion for evaluating capital The IRR method uses a different decision criterion for evaluating capital investments. The decision criterion is the desired rate of return for the investment investments. The decision criterion is the desired rate of return for the investment project. A project is a good investment if the rate of return on the project exceeds project. A project is a good investment if the rate of return on the project exceeds the desired rate of return. The desired rate of return can be the cost of capital of the desired rate of return. The desired rate of return can be the cost of capital of the firm, opportunity cost of the fund, hurdle rate the firm has for its investments, the firm, opportunity cost of the fund, hurdle rate the firm has for its investments, or a rate
or a rate that the firm sets for the investment.that the firm sets for the investment.
20-11
20-11 DCF techniques such as NPV or IRR assess impacts on cash flows of anDCF techniques such as NPV or IRR assess impacts on cash flows of an investment. The focus of the technique is on cash flows and might leave out other investment. The focus of the technique is on cash flows and might leave out other im
impoportartant nt fafactctors ors rerelelevavant nt to to a a cacapipitatal l ininveveststmement nt susuch ch as as efeffefectcts s of of ththee investment on the firm’s strategic position, competitive advantage, community in investment on the firm’s strategic position, competitive advantage, community in which the firm locates or serves, or
which the firm locates or serves, or relationships with unions.relationships with unions.
20-12
20-12 A A sound sound capital capital investment investment decision decision needs needs to to consider consider both both quantitative quantitative andand qua
qualilitatatitive ve fafactctorsors. . UnUnfofortrtunaunatetelyly, , quaqualilitatatitive ve fafactctors ors ofofteten n are are didifffficicult ult or or imp
impossossiblible e to to quaquantintifyfy. . DecDecisiision-maon-makerkers s may may lealeave ve out out the the impimpactacts s of of non non--qua
quantintitattative ive facfactortors s in in invinvestestmenment t decdecisiisions ons becbecause ause thethere re are are no no numnumberberss attached to these factors.
attached to these factors. Among
Among cost-benefit cost-benefit features features that that are are often often left left out out are are effects effects on on strategicstrategic pos
positiition, on, comcompetpetitiitive ve advaadvantantage ge of of the the firfirm, m, comcommunmunitity, y, envenviroironmenment, nt, andand relationships with unions.
relationships with unions.
20-13
20-13 All investments r All investments require equire careful analyses careful analyses and evaluand evaluations. Availability ations. Availability of funds of funds for for investment is but one factor in a capital investment decision. With unlimited funds investment is but one factor in a capital investment decision. With unlimited funds available at 10 percent cost, the firm needs to ensure that its investment will earn available at 10 percent cost, the firm needs to ensure that its investment will earn a return on investments of at least 10 percent, the investment is part of the firm’s a return on investments of at least 10 percent, the investment is part of the firm’s strategic plan, and that the firm has the requisite knowledge and time to manage strategic plan, and that the firm has the requisite knowledge and time to manage the investment well.
the investment well.
With limited funds available for investment, the firm also needs to compare With limited funds available for investment, the firm also needs to compare relative returns of competing investment opportunities, strategic direction of the relative returns of competing investment opportunities, strategic direction of the firm, additional demands on management’s time, impacts on community, among firm, additional demands on management’s time, impacts on community, among others.
others.
20-14
20-14 Among important behavioral factors that might affect capital investment decisions Among important behavioral factors that might affect capital investment decisions are:
are:
•
• DeDesirsires es of of mamananagegers rs to to grogrow w ththrorough ugh acacquiquisisititionons s anand d neneww investments.
investments. •
• Tendency to escalate commitmentTendency to escalate commitmentss •
• Effects of prospects on capital Effects of prospects on capital investment decisions.investment decisions. •
• PrPropeopensnsitity y of of nonot t wawantntining g to to spespend nd adadditditioionanal l titime me anand d efeffofortrt needed to secure capital investments.
needed to secure capital investments. •
• Intolerance of uncertainty.Intolerance of uncertainty.
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20-15
20-15 NPV method and IRR method may yield conflicting results when two investmentNPV method and IRR method may yield conflicting results when two investment projects differ in:
projects differ in: •
• size of initial investmentsize of initial investment •
• timing of net cash inflowstiming of net cash inflows •
• pattern of net cash inflowpattern of net cash inflow •
• length of useful lifelength of useful life
20-16
20-16 The size of initial investment has no effect on the rate of return as determinedThe size of initial investment has no effect on the rate of return as determined using the IRR method. A project with a larger initial investment, however, will using the IRR method. A project with a larger initial investment, however, will most likely have a higher NPV than a project with a smaller initial investment and most likely have a higher NPV than a project with a smaller initial investment and often becomes the preferred investment when using a NPV method to analyzing often becomes the preferred investment when using a NPV method to analyzing capital investments.
capital investments.
20-17
20-17 The net present value method weighs early net cash inflows heavier than late netThe net present value method weighs early net cash inflows heavier than late net cash inflows in at least two ways. First, amounts of discount applied to early net cash inflows in at least two ways. First, amounts of discount applied to early net cash inflows are less than those of late net cash inflows. Thus, one dollar to be cash inflows are less than those of late net cash inflows. Thus, one dollar to be received in the first year increases the net present value of the investment project received in the first year increases the net present value of the investment project more than that of one dollar to be received in, say, the fifth years. Second, each more than that of one dollar to be received in, say, the fifth years. Second, each dollar earns additional returns in each of the subsequent periods. Thus, an early dollar earns additional returns in each of the subsequent periods. Thus, an early dollar earns returns over a longer period of time than that of a late dollar.
dollar earns returns over a longer period of time than that of a late dollar.
20-18
20-18 Depreciation expenses affect capital investment decisions in two ways:Depreciation expenses affect capital investment decisions in two ways: 1.
1. DepDeprecireciatiation expeon expenses denses decreacrease periose periodic net idic net inconcomes frmes from inom invesvestmetmentnt and, thereby, reduce tax payments.
and, thereby, reduce tax payments. 2.
2. DepDeprecireciatiation expon expensenses decres decreasease the booe the book value ok value of the if the invenvestmstmenent andt and,, as a result, increase the gain or decrease the loss from the disposal of the as a result, increase the gain or decrease the loss from the disposal of the investment which, in turn, affect the tax liability at the time the firm disposes investment which, in turn, affect the tax liability at the time the firm disposes of of the investment.
the investment.
20-19
20-19 The desired rate of return of a firm may change from one year to the nextThe desired rate of return of a firm may change from one year to the next because of changes in, among others:
because of changes in, among others: 1.
1. invesinvestment tment opportunopportunities ities availaavailable to ble to the the firmfirm,, 2.
2. banbank or k or loaloan in intenterest rest raterates,s, 3.
3. mamarkerket t sisitutuatatioion,n, 4.
4. priprioriority oty of tf the he fifirmrm..
20-20
20-20 a.a. The fThe firm can irm can expect to eaexpect to earn a highern a higher return thr return than the an the cost of fcost of funds neunds needed for eded for the investment if the internal rate of return is 11 percent and the cost of capital the investment if the internal rate of return is 11 percent and the cost of capital is 10%.
is 10%. b.
b. A capitA capital projecal project that ht that has a net as a net present present value of value of $148,0$148,000 comput00 computed based oned based on 10 percent discount rate indicates that the investment will earn the firm a 10 percent discount rate indicates that the investment will earn the firm a return of $148,000 above the required 10 percent return on the investment. return of $148,000 above the required 10 percent return on the investment.
20-21
20-21 A A firm firm that that chooses chooses to to build build often often faces faces many many uncertainties, uncertainties, uses uses evolvingevolving technologies, and traverses in environments that are not familiar to management technologies, and traverses in environments that are not familiar to management and can change rapidly. Capital budgeting processes in these firms are often less and can change rapidly. Capital budgeting processes in these firms are often less forma
formal, l, rely rely less on less on formaformal l analyanalyses, use ses, use more nonfinamore nonfinanciancial l and nonquantiand nonquantifiabfiablele dat
data a sucsuch h as as mamarkrket et shshare are popotetentntiaial l anand d cocompempetititotorsrs’ ’ acactitionons, s, anand d apapplplyy subjective criteria in evaluating capital investment projects. These firms are likely subjective criteria in evaluating capital investment projects. These firms are likely to require long payback periods or use a low hurdle rate.
to require long payback periods or use a low hurdle rate.
In contrast, a firm that chooses to harvest is more likely to be in a mature In contrast, a firm that chooses to harvest is more likely to be in a mature ma
markerket. t. As As a a resresultult, , itits s cacapitpital al budbudgetgetining g proprocescesses ses are are momore re lilikekely ly to to bebe formalized. Most data needed for capital investment decisions are quantifiable formalized. Most data needed for capital investment decisions are quantifiable and financial in nature. Its required payback period tends to be short and the and financial in nature. Its required payback period tends to be short and the hurdle rate high.
hurdle rate high.
20-22
20-22 11.. CCaappiittaal l bbuudgdgeettiinng g iis s a a pproroccesess s oof f aasssseesssisinng g prproojjeecctts s tthahat t rereququiriree commitments of large sums of funds and generate benefits stretching well into commitments of large sums of funds and generate benefits stretching well into the future. Among uses of capital budgeting are assessments of purchasing the future. Among uses of capital budgeting are assessments of purchasing new
new equiequipmepment, nt, acqacquiriuiring ng new new facfaciliilitieties, s, devedevelopiloping ng and and intintroduroducincing g newnew products, and expanding into new sales territories.
products, and expanding into new sales territories. 2.
2. DiDiffffererenenceces s bebetwetween en papaybayback ck anand d nenet t prepresensent t vavalue lue memeththodods s of of cacapipitatall budgeting include recognition of time value of money, decision criterion for budgeting include recognition of time value of money, decision criterion for se
selelectctining g ththe e bebest st ininveveststmementnt, , anand d nunumbmber er of of perperioiods ds coconsnsididereered. d. ThThee payback method ignores the time value of money and treats one dollar today payback method ignores the time value of money and treats one dollar today as the same as one dollar in the future. These two methods also differ in their as the same as one dollar in the future. These two methods also differ in their decision criteria. Using the payback period method, a superior investment is decision criteria. Using the payback period method, a superior investment is the one with a short or quick payback. The decision criterion of the net the one with a short or quick payback. The decision criterion of the net pre
presesent nt vavalue lue memeththod od is is ththe e amamouount nt of of nenet t prpreseesent nt vavalulues. es. A A susupeperiorior r investment is the one with the highest net present value. In addition, the investment is the one with the highest net present value. In addition, the payback period method considers only cash flows needed to recover the payback period method considers only cash flows needed to recover the initial investment. Cash flows after the payback period are not included in initial investment. Cash flows after the payback period are not included in evaluations of capital investments when using a payback period method. In evaluations of capital investments when using a payback period method. In contrast, a net present value method includes all cash flows.
contrast, a net present value method includes all cash flows. 3.
3. The coThe cost of capist of capital of a firm is thtal of a firm is the weighe weighted aveted average of the corage of the cost of the funst of the fundsds that comprise the firm’s capital structure.
that comprise the firm’s capital structure. 4.
4. FinFinancancial accoial accountunting dating data a oftoften are en are not suinot suitabtable for use le for use in capiin capital budgetal budgetintingg because:
because: a.
a. fifinannanciacial l accaccountounting uses ing uses accaccrual accourual accountinting in ng in all of all of its measuits measuremerementsnts.. Th
The e nenet t inincocome me of of a a pepeririod od mamay y ininclcludude e rerevevenunues es nonot t yeyet t papaid id byby customers and exclude payments made to suppliers for future deliveries. customers and exclude payments made to suppliers for future deliveries. Receivables included in the revenues of the period are not available to the Receivables included in the revenues of the period are not available to the firm for payments. The amount of cash paid is no longer
firm for payments. The amount of cash paid is no longer available for other available for other payments, even though the payment is not an expense of the period.
payments, even though the payment is not an expense of the period. b.
b. fifinannanciacial accounl accountiting data ofteng data often are n are not suinot suitabtable also becaule also because of the needse of the need to use arbitrary accounting procedures in financial accounting data.
to use arbitrary accounting procedures in financial accounting data.
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EXERCISES 20.23 EFFECTS ON CASH FLOWS (5 min)
a. $500,000 outflow at the time of payment. No effect on other years.
b. Advertising expense: $50,000 x (1 - 20%) = $40,000 Depreciation expense: $30,000 x 20% = <6,000>
20.24 Basic Capital Budgeting Techniques (10 min) a. Project A:
Or, 2 years and 10 months
Net Cumulative
b. Year Cash Inflow Net Cash Inflow
1 $ 500 $ 500
2 1,200 1,700
3 2,000 3,700
4 2,500
Project B: Payback period:
Or, 3 years and 7 months
c. Depreciation expense per year: $5,000 ÷ 5 = $1,000 Taxable income each year: $2,500 - $1,000 = $1,500
Income taxes each year: $1,500 x 25% = $375
Annual after-tax net cash inflow: $2,500 - $375 = $2,125 Project C Payback period:
Or, 2 years and 5 months
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years
Period
Payback
2
.
78
800
,
1
$
000
,
5
$
= = years Period Payback3
.
52
500
,
2
$
)
700
,
3
$
000
,
5
($
3
+ − = = years Period Payback 2.35 125 , 2 $ 000 , 5 $ = =20-24 (Continued)
d. (a) Depreciation expense per year: ($5,000 - $500) ÷ 5 = $900 Taxable income:
Sales $4,000
Expenses:
Cash expenditures $1,500
Depreciation 900 2,400
Operating income before taxes $1,600
Income taxes (25%) 400
Net after taxes income $1,200 Book rate of return = $1,200 ÷ $5,000 = 24%
(b) Average book value = ($5,000 + $500) ÷ 2 = $2,750
Book rate of return = $1,200÷ $2,750 = 43.64%
e. Project A: $1,800 x 3.993 - $5,000 = $2,187 Project B:
Year Net Cash Inflow 8% discount Factor Present Value
0 <$5,000> 1 $ 500 .926 463 2 1,200 .857 1,028 3 2,000 .794 1,588 4 2,500 .735 1,838 5 2,000 .681 1,362
Net Present Value $1,279
Project C: $2,125 x 3.993 - $5,000 = $3,485 Project D:
Present value of cash inflows:
Year 1 through 4 ($1,200 + $900) x 3.312 = $6,955 Year 5 (2,100 + $500) x 0.681 = 1,771 Present value of cash inflows $8,726 Initial investment 5,000
20-25 Cost Of Capital (10 min)
a. Bond interest before taxes $5,000,000 x 9% = $450,000 Income taxes on bond interest $450,000 x 30% = 135,000
After-tax bond interest $315,000
Market value of bond: $5,000,000 x 110% = $5,500,000 After-tax cost of bond: $315,000 ÷ $5,500,000 = 5.73% b. $3 ÷ $30 = 10%
c. Interest After-tax Weighted
or Rate of Total Average
Dividend Expected Market Cost of Book Value Rate Return Value Weight Capital Bond $5,000,000 9% 5.73% $ 5,500,000 0.275 1.58% Preferred Stock 5,000,000 10% 10.00% 6,000,000 0.300 3.00% Common Stock 500,000 20.00% 8,500,000 0.425 8.50% Total $10,500,000 $20,000,000 1.000 13.08% Solutions Manual
20-26 Future And Present Values (5 min)
a. 1. The Excel function is FV (0.03, 600, 0, 24, 0) The output is $1,209,333,448. 2. FV(.04, 600, 0, 24, 0) = $398,304,149,423 3. a. FV (0.015, 1200, 0, 24, 0) = $1,378,675,128 b. FV (0.02, 1200, 0, 24, 0) = $501,669,104,924 4. FV(.04, 12, 0, 9,500,000,000, 0) = $15,209,806,076 b. 1. $25.2 x 5.65 = $142.38 millions 2. $25.2 + $25.2 x 5.328 = $159.4656 millions 3. $25.2 x (1 – 45%) x 5.65 = $78.309 millions
20-27 After-Tax Net Present Value And IRR (10 min)
a. 1. Net cash inflow each year: $62,000 - $30,000 = $32,000
Present value of net cash inflows = $32,000 x 3.17 = $101,440 NPV = $101,440 - $60,000 = $41,440
2. Net cash inflow before depreciation $32,000
Depreciation expense 15,000
Increase in net income before taxes $17,000
Income taxes rate x 30%
Income taxes $5,100
Net after-tax cash inflow = $32,000 - $5,100 = $26,900 per year
Present value of net cash inflows = $26,900 x 3.17 = $85,273 NPV = $85,273 - $60,000 = $25,273
3. Double-declining balance depreciation
Beginning Depreciation Accumulated Ending Year Book Value Expense Depreciation Book Value
0 $60,000 1 $60,000 $30,000 $30,000 30,000 2 30,000 15,000 45,000 15,000 3 15,000 7,500 52,500 7,500 4 7,500 7,500 60,000 0 Net 30% After-tax 10%
Cash Depreciation Taxable Income Net Cash Discount Present Year Inflow Expense Income Taxes Inflow Factor Value
0 <$60,000>
1 $32,000 $30,000 $ 2,000 $ 600 $31,400 0.909 28,543 2 32,000 15,000 17,000 5,100 26,900 0.826 22,219 3 32,000 7,500 24,500 7,350 24,650 0.751 18,512 4 32,000 7,500 24,500 7,350 24,650 0.683 16,836
Net Present Value 26,110
20-27 (Continued-2)
b. 1. $60,000 = $32,000 x A?, 4
A?, 4 = 1.875, which has a rate of return greater than 30%.
2. $60,000 = $26,900 x A?, 4
A?, 4 = 2.230, which has a discount rate falls between
25% and 30%
Discount Rate Discount Factor 25% 25%2.362 2.362
? 2.230
30% 2.166
Difference 5% ? 0.196 0.132 Internal rate of return:
% 37 . 28 % 5 196 . 0 132 . 0 % 25 + × =
20-28 Basic Capital Budgeting Techniques: Uniform Net cash inflows (10 min)
1. a. Payback period:
$500,000 ÷ $120,000 = 4.17 years, or 4 years and 2 months b. Book rate of return:
Effect of the investment on net income in each of the next 10 years:
Increase in net cash inflow $120,000 Depreciation expense $500,000 ) 10 = 50,000
Increase in net income $ 70,000
(a) On initial investment: $70,000 ) $500,000 = 14%
(b) On average investment:
Average investment: ($500,000 + 0) ) 2 = $250,000 Book rate of return: $70,00 ÷ $250,000 = 28% c. NPV:
Present value of net cash inflows: $120,000 x 5.65 = $678,000
Initial investment <500,000>
Net present value $178,000
20-28 (Continued-1)
d. Present value payback period:
Year Present Value of Net cash inflow
Cumulative Cash Flow 0 <$500,000> <$500,000> 1 107,160 < 392,840> 2 95,640 < 297,200> 3 85,440 < 211,760> 4 76,320 < 135,440> 5 68,040 < 67,400> 6 60,840 < 6,560> 7 54,240 47,680
months)
2
years
(6
years
6.12
=
$54,240
$6,560
+
years
6
e. Internal rate of return: PV of net cash inflows
At 20%: $120,000 x 4.192 =
$503,040
At 25%: $120,000 x 3.571 = 428,520
Difference in PV with 5% difference in discount rate $ 74,520 20.20% = 5% $74,520 $500,000 -$503,040 + 20% = Return of Rate Internal ×
20-28 (Continued-2)
2. Assume that you have typed in the desired rate of return, 0.12, in a1, the required total initial investment, -500,000, in a2, and the periodic cash inflows, 120,000 in a3 through a12 and the cursor is at a15,
Microsoft Excel:
For NPV: Insert ! Function ! Financial ! NPV
= NPV(a1, a2:a12) = $158,952
(Notice this answer is off by $19,075. This discrepancy can be avoided if you use the following function instead)
Or, Insert ! Function ! Financial ! PV
= PV(a1, 10, a3) = $678,027
and then determining the NPV by subtracting the initial investment from the output,
$678,027 - $500,000 = $178,027 Or, Insert ! Function ! Financial ! NPV
= NPV(a1, a3:a13) = $678,027 (with 0 in Cell a13) For IRR: Insert ! Function ! Financial ! IRR
= IRR(a2:a12) = 20% Quattro Pro:
For NPV: Insert ! Function ! Financial-Annuity ! @PV
@PV (a3, a1, 10) = $678,027
Determine the NPV by subtracting the initial investment,
$678,027 - $500,000 = $178,027
or, Insert ! Function ! Financial-Cash Flow ! @NETPV
@NETPV (a1, a3.A12, A2) = $178,027
For IRR: Insert ! Function ! Financial- Annuity ! @IRATE
@ IRATE (10, -120000, 500000, 0) = .2018 or, Insert ! Function ! Financial-Cash Flow ! @IRR
@IRR (.1, a2.A12) = .2018
20.29 Basic Capital Budgeting Techniques: Uneven Net cash inflow with Taxes (40 min)
1. a. Payback period:
Year Net Cash Inflow Depreciation Expense Taxable Income Saving or <Expense> on Income Tax Net After-tax Income <Loss> Net After-tax Cash Inflow Cumulative Net After-tax cash inflow 0 <500,000> <500,000> 1 50,000 <50,000> 0 0 0 50,000 <450,000> 2 80,000 <50,000> 30,000 <9,000> 21,000 71,000 <379,000> 3 120,000 <50,000> 70,000 <21,000> 49,000 99,000 <280,000> 4 200,000 <50,000> 150,000 <45,000> 105,000 155,000 <125,000> 5 240,000 <50,000> 190,000 <57,000> 133,000 183,000 58,000 6 300,000 <50,000> 250,000 <75,000> 175,000 225,000 7 270,000 <50,000> 220,000 <66,000> 154,000 204,000 8 240,000 <50,000> 190,000 <57,000> 133,000 183,000 9 120,000 <50,000> 70,000 <21,000> 49,000 99,000 10 40,000 <50,000> <10,000> 3,000 <7,000> 43,000 Total <500,000> 1,160,000 <348,000> 812,000 years 4.68 = $183,000 $125,000 + years 4 = Period Payback
20-29 (Continued-1)
b. Average net income of the investment period: $812,000/10 = $81,200 Book rate of return:
a. On initial investment: $81,200/$500,000 = 16.24% b. On average investment:
Average investment: ($500,000 + 0)/2 = $250,000
Book rate of return: $81,200/$250,000 = 32.48% c. Net present value:
Year Net After-tax cash inflow
Discount Factor at 12%
Present Value of Net cash inflow
1 $50,000 0.893 $44,650 2 71,000 0.797 56,587 3 99,000 0.712 70,488 4 155,000 0.636 98,580 5 183,000 0.567 103,761 6 225,000 0.507 114,075 7 204,000 0.452 92,208 8 183,000 0.404 73,932 9 99,000 0.361 35,739 10 43,000 0.322 13,846 Total $703,866 NPV = $703,866 - $500,000 = $203,866 Solutions manual 17
20-29 (Continued-2) d. Internal rate of return:
Year Net After-tax cash inflow 18% Discount Factor PV of Net cash inflow at 18% 20% Discount Factor PV of Net cash inflow at 20% 1 $50,000 0.847 $42,350 0.833 $41,650 2 71,000 0.718 50,978 0.694 49,274 3 99,000 0.609 60,291 0.579 57,321 4 155,000 0.516 79,980 0.482 74,710 5 183,000 0.437 79,971 0.402 73,566 6 225,000 0.370 83,250 0.335 75,375 7 204,000 0.314 64,056 0.279 56,916 8 183,000 0.266 48,678 0.233 42,639 9 99,000 0.225 22,275 0.194 19,206 10 43,000 0.191 8,213 0.162 6,966 Total $540,042 $497,623
PV of net cash inflows at 18%: $540,042 PV of net cash inflows at 20%: $497,623 Difference in PV with 2% difference in discount rate $ 42,419 Internal rate of return =
19.89%
=
2%
$42,419
$500,000
-$540,042
+
18%
×20-29 (Continued-3)
2.
A B C D E F G
1 Year Net Cash Inflow Depreciation Expense Taxable Income Saving or <Expense> on Income Tax Net After-tax Income <Loss> Net After-tax Cash Inflow 2 0 <500,000> 3 1 50,000 <50,000> 0 0 0 50,000 4 2 80,000 <50,000> 30,000 <9,000> 21,000 71,000 5 3 120,000 <50,000> 70,000 <21,000> 49,000 99,000 6 4 200,000 <50,000> 150,000 <45,000> 105,000 155,000 7 5 240,000 <50,000> 190,000 <57,000> 133,000 183,000 8 6 300,000 <50,000> 250,000 <75,000> 175,000 225,000 9 7 270,000 <50,000> 220,000 <66,000> 154,000 204,000 10 8 240,000 <50,000> 190,000 <57,000> 133,000 183,000 11 9 120,000 <50,000> 70,000 <21,000> 49,000 99,000 12 10 40,000 <50,000> <10,000> 3,000 <7,000> 43,000 13 Total <500,000> 1,160,000 <348,000> 812,000 Solutions manual 19
20-29 (Continued-4) 2. NPV
Microsoft Excel:
Insert ! Function ! Financial ! NPV
= NPV(0.12, b2, f3:f12) = $181,948
(Notice this answer is off by $21,918. This discrepancy can be mitigated if you add 0 to Cell f13, as shown below)
Or, Insert ! Function ! Financial ! NPV
= NPV(0.12, f3:f13) = $703,781
and then determining the NPV by subtracting the initial investment from the output,
$703,781 - $500,000 = $203,781
For IRR: Insert ! Function ! Financial ! IRR
= IRR(f2:f12) = 20% (-500,000 in cell f2)
Quattro Pro:
For NPV: Insert ! Function ! Financial- Cash Flow ! @NPV
@NPV (.12, f3:f12, 1) = $203,781 (-500000 in f2)
For IRR: Insert ! Function ! Financial-Cash Flow ! @IRR
20-30 Basic Capital Budgeting Techniques: Uneven Net cash inflows with MACRS (40 min)
1. Payback period: Year Net CashFlow
Return Depreciation Expense Taxable Income <Loss> Income Tax Expense <Saving> After-tax Net Income <Loss> After-tax Net cash inflow Cumulative After-tax Net cash inflow 0 <500,000> <500,000> 1 50,000 <100,000> <50,000> 15, 000 <35,000> 65,000 <435,000> 2 80,000 <160,000> <80,000> 24,000 <56,000> 104,000 <331,000> 3 120,000 <96,000> 24,000 <7,200> 16,800 112,800 <218,200> 4 200,000 <57,600> 142,400 <42,720> 99,680 157,280 < 60,920> 5 240,000 <57,600> 182,400 <54,720> 127,680 185,280 124,360 6 300,000 <28,800> 271,200 <81,360> 189,840 218,640 7 270,000 0 270,000 <81,000> 189,000 189,000 8 240,000 0 240,000 <72,000> 168,000 168,000 9 120,000 0 120,000 <36,000> 84,000 84,000 10 40,000 0 40,000 <12,000> 28,000 28,000 Total <500,000> 1,160,000 <348,000> 812,000 1,312,000 years 4.33 = $185,280 $60,920 + years 4 = Period Payback Solutions manual 21
20-30 (Continued-1) 2. Book rate of return:
Average net income per period: $812,000/10 = $81,200 Book rate of return:
a. On initial investment: $81,200/$500,000 = 16.24% b. On average investment:
Computation of Average investment:
Book Value Year Beginning of
the Year Depreciation End of the Year Average 1 $500,000 $100,000 $400,000 $450,000 2 400,000 160,000 240,000 320,000 3 240,000 96,000 144,000 192,000 4 144,000 57,600 86,400 115,200 5 86,400 57,600 28,800 57,600 6 28,800 28,800 0 14,400 7 0 0 0 8 0 0 0 9 0 0 0 10 0 0 0 Total $500,000 $1,149,200 Average investment: $1,149,200/10 = $114,920
20-30 (Continued-2) 3. Net present value:
Year After-tax Net cash inflow Discount Factor at 12% PV of Net cash inflow 1 $65,000 0.893 $58,045 2 104,000 0.797 82,888 3 112,800 0.712 80,314 4 157,280 0.636 100,030 5 185,280 0.567 105,054 6 218,640 0.507 110,850 7 189,000 0.452 85,428 8 168,000 0.404 67,872 9 84,000 0.361 30,324 10 28,000 0.322 9,016 Total $729,821 NPV = $729,821 - $500,000 = $229,821 Solutions manual 23
20-30 (Continued-3) 4. Internal rate of return:
Year After-tax Net cash Inflow 20% Discount Factor PV at 20% 22% Discount Factor PV at 22% 1 $ 65,000 0.833 $54,145 0.820 $53,300 2 104,000 0.694 72,176 0.672 69,888 3 112,800 0.579 65,311 0.551 62,153 4 157,280 0.482 75,809 0.451 70,933 5 185,280 0.402 74,483 0.370 68,554 6 218,640 0.335 73,244 0.303 66,248 7 189,000 0.279 52,731 0.249 47,061 8 168,000 0.233 39,144 0.204 34,272 9 84,000 0.194 16,296 0.167 14,028 10 28,000 0.162 4,536 0.137 3,836 Total $527,875 $490,273
PV of net cash inflows at 20%: $527,875 PV of net cash inflows at 22%: $490,273 Difference in PV with 2% difference in discount rate $ 37,602
21.48%
=
2%
$37,602
$27,875
+
20%
=
Return
of
Rate
Internal
×20-31 Straightforward Capital Budgeting with Taxes (5 min) 1. Depreciation per year: ($30,600 - $600) ) 6 = $5,000
Taxable income $8,000 - $5,000 = 3,000
Tax rate x 40%
Income taxes $1,200
Net after-tax annual cash inflow: $8,000 - $1,200 = $6,800
2. Payback period: $30,600 ) $5,000 = 6.12 years
3. PV of annual savings $5,000 x 4.623 = $23,115 PV of salvage value $600 x .63 = 378 Total $23,493 Initial investment 30,600 NPV <$7,107> Solutions manual 25
20-32 Capital Budgeting with Tax and Sensitivity Analysis (10 min) Annual after-tax net cash inflow:
Cash revenue $1,200 x (1 - 0.35) = $780 Tax saving on depreciation expense $600 x 0.35 = + 210
Total $990 1.Payback period:
years
6.06
=
$990
$6,000
2. Operating income in each of the 10 years:
Sales $1,200
Depreciation 600
Operating income before taxes $ 600
Taxes 210 Operating income $ 390
6.5%
=
$6,000
$390
=
return
of
rate
Book
3. $990 x 5.019 = $4,9694. Required net after-tax annual cash inflow:
$6,000 ) 5.019 = $1,195
Tax saving on depreciation expense - 210 Required net after-tax annual cash revenue $985
1 - tax rate ) 0.65
20-33 Basic Capital Budgeting (5 min) 1. $1,800 x 0.6 = $1,080 2. $12,500 x 0.6 x 3.17 = $23,775 3. $10,000 x 0.4 x 0.909 = $3,636 4. C Solutions manual 27
PROBLEMS 20-34Equipment Replacement (20 min)
1. & 3.
Discount Present Cash Flows in ‘000
Factor Value 0 1 2 3 4 5 Overhaul
AccuDril Operating Cost1 <48> <48> <38.4> <38.4> <38.4> Overhaul cost <100> Tax savings on depreciation2 4 4 16 16 16 Other Expenses3 <57> <57> <57> <57> <57> Year 1 .893 <$90,193> <101> Year 2 .797 <160,197> <201> Year 3 .712 < 56,533> <79.4> Year 4 .636 < 50,498> <79.4> Year 5 .567 < 45,020> <79.4> Total PV <$402,441> Buy RoboDril 1010K Equipment Purchase4 1.000 <$240,000> <240> Operating Cost5 3.605 <86,520> <24> <24> <24> <24> <24> Tax saving on depreciation6 3.605 69,216 19.2 19.2 19.2 19.2 19.2 Other expenses7 3.605 <118,965> <33> <33> <33> <33> <33> Salvage value8 .567 17,010 30 Total PV <$359,259> <240> <37.8> <37.8> <37.8> <37.8> <7.8> PV of the difference in cash flow between the alternatives $402,441 - $359,259 = $ 43,182 in favor of RoboDril
20-34 (Continued-1)
1Years 1 and 2: $10 per hour x 8,000 hours x (1 - Tax Rate 40%) = $48,000
Years 3, 4, and 5: $48,000 x (1 - Improvement in efficiency 20%) = $38,400
2Years 1 and 2:
Depreciation expense per year:
(Original Cost $120,000 - Salvage Value $20,000) ÷ 10 = $10,000
Tax Rate x 0.40
Tax savings on depreciation $ 4,000 Years 3, 4, and 5:
Book value before overhaul $ 20,000
Overhaul cost 100,000
Total amount to be depreciated $120,000
Number of years ÷ 3
Depreciation expense per year $ 40,000
Tax Rate x 40%
Tax savings on depreciation $ 16,000
3 $95,000 x (1 - Tax Rate 40%) = $57,000
4 Purchase price $250,000
Installation, testing, rearrangement, and training + 30,000
Subtotal $280,000
Trade-in allowance for AccuDril - 40,000
Net purchase cost $240,000
5 $10 per hour x 4,000 hours x (1 - Tax Rate 40%) = $24,000
6 Depreciation expense per year $240,000 ÷ 5 Years = $48,000
Tax Rate x 0.40
Tax savings on depreciation $19,200
7 $55,000 x (1 - Tax Rate 40%) = $33,000 8 $50,000 x (1 - Tax Rate 40%) = $30,000
20-34 (Continued-2)
2. Cash Flow Difference in Cumulative Year AccuDril RoboDril Cash Flow Difference
0 $0 <$240,000> <$240,000> <$240,000> 1 <$101,000> <37,800> 63,200 <176,800> 2 <201,000> <37,800> 163,200 < 13,600> 3 <79,400> <37,800> 41,600
years
2.33
=
$41,600
$13,600
+
years
2
=
period
Payback
4. Among other factors that the firm should consider before the final decision are:
• Changes in technology for equipment
• Changes in market, especially demand for the product and competitors
• Reliability of the new machine and the expected effects of overhaul
• Reliability of AccuDril and accuracy of the estimates given • Competitive strategy of the firm
20-35 Sensitivity Analysis (30 min)
1. Difference in PV between the two alternatives: $43,182 PV discount factor for annuities from years 3 through 5:
2.402 x 0.797 = 1.914
or, 0.712 + 0.636 + 0.567 = 1.914
Additional annual after-tax savings needed from improvement in machine efficiency to make the overhaul of AccruDril a financially more attractive choice: 561 $22, = 1.914 $43,182 Before-tax, 602 $37, = 0.6 1 $22,56
7%
4
=
$80,000
602
,
7
$3
For the replacement decision to be in error financially, the overhaul of AccuDril X10 needs to improve the operating efficiency by at least 53%.
20-35 (Continued-1)
2.
Discount Present Cash Flows in '000
Factor Value 0 1 2 3 4 5 Overhaul in 2 years
Tax savings from depreciation 4 4 16 16 16
Overhaul cost <100> .893 3,572 4 .797 <76,512> <96> .712 11,392 16 .636 10,176 16 .567 9,072 16 PV of overhaul in 2 years <42,300> Overhaul now and again in 2 years
Overhaul cost <80> <30> Savings from Improved efficiency1 9.6 9.6
Tax savings on depreciation2 24 24 4 4 4
1.000 <80,000> <80> .893 30,005 33.6 .797 2,869 3.6 .712 2,848 4 .636 2,544 4 .567 2,268 4 <39,466>
Difference in cost between the two alternatives: $42,300 - $39,466 = $2,834 It is better, financially, to overhaul now and again in 2 years.
20-35 (Continued-2)
1Savings from the improved productivity
$10 per hour x 8,000 hours x 20% = $16,000 Taxes on the saving $16,000 x 40% tax rate = - 6,400
Net after Tax savings $9,600
2Years 1 and 2:
Book value at the time of overhaul: $10,000 x 2 + $20,000 = $ 40,000
Overhaul cost + 80,000
Total amount to be depreciated $120,000
Number of years ÷ 2
Depreciation expense per year $60,000
Tax Rate x 0.40
Tax savings on depreciation $24,000
Years 3, 4, and 5:
Overhaul cost $30,000
Number of years ÷ 3
Depreciation expense per year $10,000
Tax Rate x 0.40
Tax savings on depreciation $ 4,000 3. Although the cost difference between the two alternatives is only $2,834, which is less than 0.3% of the annual sales, the benefit from offering higher quality products two years earlier will most likely persuade the firm to undertake the overhaul two years early.
20-36Comparison of Capital Budgeting Techniques (30 min) 1. Effects of the new equipment on net income:
Sales $195 x 10,000 =
$1,950,000
Cost of goods sold:
Variable manufacturing costs $ 90 Fixed manufacturing costs:
Additional fixed manufacturing overhead: $250,000 / 10,000 units = $25 Depreciation on new equipment:
($995,000 - $195,000) / 4 = $200,000/year
$200,000 / 10,000 units per year = + 20 + 45
Manufacturing cost per unit $135
Number of units x 10,000
Total cost of goods sold
-1,350,000
Gross margin $ 600,000
Marketing and other expenses:
Variable marketing: Cost per unit $ 10
Number of units x 10,000 $100,000 Additional fixed marketing cost + 200,000 300,000
Net income before taxes $300,000
Income taxes
-90,000
Net income $210,000
The firm will increase its net income by $210,000 each year.
2. Each of
Year 1 to 3 Year 4
Net income after taxes $210,000 $210,000
Add: Depreciation expenses included in fixed costs
$20 x 10,000 = 200,000 200,000 Cash inflow from disposal of equipment 195,000
Total cash inflow $410,000 $605,000
The new machine will increase cash inflows by $410,000 in each of the first three years and $605,000 in Year 4.
20-36 (Continued-1) 3.
years
2.4
=
$410,000
$995,000
=
Period
Payback
3 4. Average investment = ($995,000 + $195,000)/2 = $595,000 Average net income = $210,000Book rate of return = $210,000 / $595,000 = 35.29 percent 5. PV of net cash inflows
Year 1 through Year 3: $410,000 x 2.322 = $ 952,020 Year 4: $605,000 x 0.592 = + 358,160 Total present value net cash inflows $1,310,180
Initial investment - 995,000 NPV $ 315,180 6. PV of cash flows at 25%: $410,000 x 1.952 + $605,000 x 0.410 $1,048,370 PV of cash flows at 30% $410,000 x 1.816 + $605,000 x 0.350 $ 956,310 Changes in PV of cash flows $ 92,060
% 90 27. = % 5 060 92 $ $995,000 -370 8, 4 $1,0 + % 5 2 = return of rate Internal × ,
7.a. The most decrease in after-tax net income per year without
affecting the decision $315,180 / 2.914 = $108,161 Add: income taxes ($108,161 ÷ 0.7) - $108,161 = + 46,354 The most that variable cost per year can increase $154,515 Therefore, the variable cost per unit can increase by $154,515/10,000 = $15.45 per unit and the firm still will earn 14 percent on the investment.
b. The most that the unit selling price can decrease is
$154,515 / 20,000 units = $7.73
20-37Replacing a Small Machine: Capital Budgeting Techniques and Sensitivity Analysis (20 min)
1. Although the new machine has the capacity of turning out 18,000 units per year, the analysis should be based on 10,000 units per year because there is no demand for the last 8,000 units at present time. This is a mistake that students often make.
Year 0
Purchase price of the new machine <$100,000> Proceeds from disposal $3,000
Taxes on gains on disposal < 600> 2,400
Cash outflow <$97,600>
Year 1-4
Operating cost using the current machine
($40,000 + 10,000 + 10,000) x 0.8 = $48,000 Operating cost using the SP1000
($30,000 + 2,000 + 1,000) x 0.8 = 26,400 Savings in operating cost with the new machine $21,600 Savings in taxes on depreciation expense
Depreciation expense $100,000 ÷ 5 = $20,000
Tax rate x 20% 4,000
Net cash inflows in each of Years 1-4 $25,600 Year 5
After-tax cash inflow from savings in operating costs $25,600 After-tax cash inflow from disposed of the investment
$5,000 x 0.8 = 4,000 Total cash inflow in year 5 $29,600 2. PV of cash inflow in each of years 1-4: $25,600 x 3.465 = $ 88,704
PV of cash inflow in year 5: $29,600 x 0.747 = 22,111
Total PV of cash inflow $110,815
Less: Initial investment < 97,600>
NPV $ 13,215
20-37 (Continued-1)
4. The discount factor needed: $97,600 ÷ $25,000 = 3.904 Interest Rate Discount Factor
8% 8% 3.993 3.993 ? 3.904 9% 3.890 1% ? 0.103 0.089 8.86% = 1% 0.103 0.089 + 8% = return of rate Internal ×
5. Cash Discount PV at Discount PV at
Year Inflow factor at 10% 10% factor at 12% 12% 1 $20,000 0.909 $ 18,180 0.893 $17,860 2 22,000 0.826 18,172 0.797 17,534 3 25,000 0.751 18,775 0.712 17,800 4 30,000 0.683 20,490 0.636 19,080 5 40,000 0.621 24,840 0.567 22,680 $100,457 $94,954
Interest Rate PV of Net cash inflows 10% 10% $100,457 $100,457 ? 97,600 12% 94,954 2% ? $5,503 $2,857 11.04% = 2% $5,503 $2,857 + 10% = return of rate Internal ×
6. Allowable after-tax increase in cost $13,215 ÷ 4.212 = $3,137
1 - tax rate ÷ 0.8
Allowable cost increase before taxes $3,922
Number of units ÷ 10,000
Allowable cost increase per unit $0.3922
Indifference point: $3.30 + 0.3922 = $3.6922 per unit
The purchase of SP1000 will most likely be a right decision as long as the management is confident that the estimated new variable cost will be within 12 percent of the estimated amount ($0.3922/$3.30).
20-38Capital Budgeting with Sum-of-the-Years-Digit Depreciation (15
min)
After-tax net cash inflows
Before Tax After Tax
Cash Flow Depreciation Net Income Cash Flow Year Return Expense Income Tax (24%) Return
1 $ 9,000 $15,000 <$6,000> <$1,440> $10,440 2 12,000 12,000 - 0 - - 0 - 12,000 3 15,000 9,000 6,000 1,440 13,560 4 9,000 6,000 3,000 720 8,280 5 8,000 3,000 5,000 1,200 6,800 $53,000 $45,000 $51,080
1. After Tax Cash Cumulative After Tax Year Flow Return Net cash inflow
0 <$45,000> <$45,000> 1 10,440 < 34,560> 2 12,000 < 22,560> 3 13,560 < 9,000> 4 8,280 < 720> 5 6,800
years
4.11
=
$6,800
$720
+
years
4
=
period
Payback
20-38 (Continued)
2. After Tax Cash Discount Present Value of Cumulative Year Flow Return Factor (10%) After Tax Net cash inflow
1 $10,440 .909 $ 9,490 2 12,000 .826 9,912 3 13,560 .751 10,184 4 8,280 .683 5,655 5 6,800 .621 4,223 $39,464 NPV = $39,464 - $45,000 = <$5,536>
3. Net Cash PV Factor PV at PV Factor PV at
Year Inflow At 6% 6% at 4% 4% 1 $10,440 0.943 $ 9,845 0.962 $10,043 2 12,000 0.890 10,680 0.925 11,100 3 13,560 0.840 11,390 0.889 12,055 4 8,280 0.792 6,558 0.855 7,079 5 6,800 0.747 5,080 0.822 5,590 $43,553 $45,867
Discount Rate PV of Net Cash Inflows 4% 4% $45,867 $45,867 ? 45,000 6% 43,553 2% ? $ 2,314 $ 867
4.75%
=
2%
$2,314
$867
+
4%
=
return
of
rate
Internal
×20-39Working Backward: Determine Initial Investment Based on Book Rate of Return (5 min)
Let Y = Cost of the new machine Then, ($6,750 – .1 Y ) x 0.8 = 0.1Y ∴Initial investment = $30,000 10 . 0 ) 20 . 0 1 ( ) 10 750 , 6 ($ = − × − Y Y
20-40 Determine Initial Investment Based on Internal Rate of Return (5 min)
Let C be the cost of the machine.
Then, [$20,000 - ($20,000 - C/6) x 0.20] x 4.355 = C
∴Cost of the machine, C = $81,513
20-41 Determine Periodic Cash Flow Based on Book Rate of Return (5 min)
Let Y be the firm's after-tax operating income
0.15 =
$60,000 y
∴y = $9,000
Operating income before taxes = $9,000 ) (1 - 0.25) = $12,000
Total cash inflow before taxes:
=
24
,000
5
$60,000
+
,000
12
$
$20-42 Machine Replacement and Sensitivity Analysis Without Taxes (10 min)
Net additional cash outlay required for the new machine: $8,000 - $3,000 = $5,000
1.a. Payback period: $5,000/750 = 6.67 years
b. Old New Difference
Depreciation ($5,000 - $600)/11 ($8,000 - $400)/10
= $400 = $760 $360
Operating expense <750>
Difference in net income <$390>
Book value: Old New
Year 0 $5,000 - $400 = $4,600 $8,000
Year 10 600 400
Average Investment (book Value) $2,600 $4,200 Incremental average investment
on new machine = $4,200 - $2,600 = $1,600
%
24.3
=
$1,600
$390
=
return
of
rate
Accounting
8
c. NPV = $750 x 5.650 – ($8,000 - $3,000) - ($600 - $400) x 0.322 = $4,237.50 - $5,000 - $64.40 = <$826.90> Solutions manual 4320-42 (Continued)
d. Present value of net cash inflows at 7%:
$750 x 7.024 - $200 x 0.508 = $5,166 Present value of net cash inflows at 8% %:
$750 x 6.710 - $200 x 0.463 = 4,940
Difference $ 226
∴Internal rate of return:
7.73%
=
1%
226
166
+
7%
× 2. No. Because NPV < 0 (NPV is -$826.90) 3. Let required saving = y.5.650y - 200 x 0.322 = 5,000 5.65y = 5064.4
20-43 Value of Accelerated Depreciation (5 min)
1. PV
Depreciation Method Difference Factor PV of Year SYD S-L Amount Tax Effect at 8% Tax Effect
1 $40,000 $25,000 $15,000 $6,000 .926 $ 5,556 2 30,000 25,000 5,000 2,000 .857 1,714 3 20,000 25,000 < 5,000> <2,000> .794 <1,588> 4 10,000 25,000 <15,000> <6,000> .735<4,410> $100,000 $100,000 $1,272 2. PV
Depreciation Method Difference Factor PV of Year DD S-L Amount Tax Effect at 8% Tax Effect
1 $50,000 $25,000 $25,000 $10,000 .926 $9,260 2 25,000 25,000 - 0 - - 0 - .857 -0-3 12,500 25,000 <12,500> <5,000> .794 < 3,970> 4 12,500 25,000 <12,500> <5,000> .735 <3,675> $100,000 $100,000 $1,615 3. PV
Depreciation Method Difference Factor PV of Year DD S-L Amount Tax Effect at 8% Tax Effect
1 $33,330 $25,000 $8,330 $3,332 .926 $3,085 2 44,450 25,000 19,450 7,780 .857 6,667 3 14,810 25,000 <10,190> <4,076> .794 < 3,236 > 4 7,410 25,000 <17,590> <7,036> .735 <5,171 > $100,000 $100,000 $1,345 Solutions manual 45
20-44 Capital Budgeting with Sensitivity Analysis (15 min)
1. Expected annual net cash inflows ($600,000 + $100,000) $700,000
Income taxes at 30% 210,000
After-tax net cash inflows $490,000
Let P denotes the maximum price the buyer would be willing to pay: P = $490,000 x A.12, 8 + (P/8 x 0.3) x A.12, 8
P = $490,000 x 4.968 + P/8 x 0.3 x 4.968 P = $2,434,320 + 0.1863P
0.8137P = $2,434,320 P = $2,991,668
2. Let S denotes the minimum price Meidi can accept
S = $460,000 x A.10, 8 + (S - 800,000 - 0.05S) x 0.4 + 0.05S
S = $460,000 x 5.335 + 0.38S - 320,000 + 0.05S S = $2,454,100 + 0.43S - $320,000
0.57S = $2,134,100 S = $3,744,035
3. Year Depreciation Tax Effect PV Factor Present Value
1 .2 P .06 P 0.893 .05358 P 2 .32 P .096 P 0.797 .076512 P 3 .192 P .0576 P 0.712 .0410112P 4 .1152P .03456P 0.636 .0219801P 5 .1152P .03456P 0.567 .0195955P 6 .0576P .01728P 0.507 .0087609P .2214397P P = $2,434,320 + .2214397P .7785603P = $2,434,320 P = $3,126,694
20-45Cash Flow Analysis and NPV (15 min)
PV CASH FLOWS IN YEAR (in '000)
Item & Description Factor PV 0 1 2 3 4 5 a. Foregone rent
($5,000 x 12 x 0.6) 3.433 <$123,588> <36> <36> <36> <36> <36> b. All are irrelevant
c. Remodeling < 100,000> <100> Depreciation 0.877 14,032 16 0.769 7,382 9.6 0.675 3,888 5.76 0.592 2,557 4.32 0.519 2,242 4.32 d. Investment in inventory and receivables < 600,000> <600> Recovery 0.519 311,400 600 e. Irrelevant f. Sales ($900 x 0.6) 3.433 1,853,820 540 540 540 540 540 Operating expenses ($500 x 0.6) 3.433 <1,029,900> <300> <300> <300> <300> <300> g.Sales Promotion ($100 x 0.6) < 60,000> < 60> h. Termination ($50 x 0.6) 0.519 < 15,570> < 30> NPV $ 266,263
2. The positive net present value $266,263, suggests that, compared to the leasing alternative it is financially advantageous to convert the facility into a factory outlet. The net present value from converting into the factory outlet is also better then the alternative of selling the warehouse for $200,000.
20-46 Machine Replacement with Tax Considerations (15 min) Present Value of Costs with the Original Equipment
Present value of tax savings on depreciation:
$2,500,000 ÷ 4 x 0.45 x 2.577 = $724,781
Present value of operating costs:
$1,800,000 x (1 - 0.45) x 2.577 = <2,551,230> Present value of salvage value:
$50,000 x (1 - 0.45) x 0.794 = 21,835 Present value of costs with the original equipment <$1,804,614> Present value of the costs with the new machine
Initial outlay <$2,000,000>
Present value of tax savings on depreciation:
Beginning Depreciation Tax Tax Discount Present Year Book Value Expense Rate Saving Factor Value
1 $2,000,000 $1,333,333 x 0.45 = $600,000 x 0.926 = $ 555,600 2 666,667 444,445 x 0.45 = 200,000 x 0.857 = 171,400 3 222,223 222,223 x 0.45 = 100,000 x 0.794 = 79,400 Cash proceeds from sale of the old machine 300,000 Tax saving of loss on disposal of the old machine
($1,875,000 - $300,000) x 0.45 = 708,750 Present value of operating costs
$1,000,000 x (1 - .45) x 2.577 = <1,417,350> Total cost at present value <$1,602,200> Savings from using the new machine:
$1,804,614 - $1,602,200 = $202,414
The total cost of the new machine, including the purchase cost and the operating cost in each of the three years, is $202,414 below the total cost of continuing with the original equipment. Financially purchase of the new machine is a good investment.
20-47 Equipment Replacement (15 min)
1.a. Selling price $30.00
Variables cost:
Direct materials $0.25 x 8 = $2.00 Direct labor $8.00 x 2 = 16.00
Indirect costs 0.30 18.30
Contribution margin per unit $11.70 b.
$0.55
=
100,000
$25,000
+
$0.3
c. Current fixed costs $25,000
Increase in equipment depreciation:
New equipment ($100,000 - $10,000) ÷ 10 = $9,000
Current 2,000 7,000
Total fixed costs $32,000
Total overhead = $32,000 + $0.40 per unit x Units manufactured d. $0.72 = 0 $0.4 + 100,000 $32,000 e. Selling price $30.00 Variables cost: Direct materials $2.00
Direct labor ($8 per hour x 1 hour) 8.00
Indirect costs 0.40 10.40
Contribution margin per unit $19.60
20-47 (Continued)
f. Purchase price $100,000
Proceeds from selling the old saw $4,000 Tax savings from loss on disposal:
Book value $20,000
Selling price 4,000
Loss on sales $16,000
Tax rate 0.40 6,400 10,400
Net additional investment required $89,600 g. Increase in contribution margin per unit
$19.60 - 11.70 = $ 7.90
Number of units x 100,000
Increase in total contribution margin before taxes $790,000 Increase in income taxes ($790,000 x 40%) - 316,000 Increase in total contribution margin after taxes $474,000 Additional tax savings from depreciation $7,000 x 0.4 = 2,800 Expected additional net cash inflow per year $476,800 2. With over forty percent of the households in the community having at least one member working for the firm, the firm is a major employer of the community. Unless alternative employment opportunities can be created, a fifty percent reduction in its workforce will definitely have a major impact on the economy of the community.
To remain competitive the firm needs to upgrade its equipment. However, the shareholders and the management should not be the only beneficiaries from the additional net cash inflows. Although the firm may be able to ease the pain of layoffs by not filling positions vacated through retirement or resignation, a reduction of one-half of its employment will definitely be a major blow to the community. The firm needs to use the additional net cash inflows to create new job opportunities for the labor force to be reduced.
20-48 Equipment Replacement with MACRS (15 min) 1. Contribution margins of the additional units:
Sales price per unit $3,500
Current manufacturing cost - 2,450
Current contribution margin per unit $1,050 Additional saving with the new machine + 150 Contribution margin per unit of the additional units $1,200 Net cash inflows:
Present Discount
Item Description Value Factor 2007 2008 2009 2010 Purchase cost <$608,000>
Installation <12,000> Net proceeds from
disposing old 30,000 Contribution margin Per unit $1,200 $1,200 $1,200 $1,200 Additional units 30 50 50 70 CM from additional units (‘000) $ 36 $ 60 $ 60 $ 84 Efficiency saving (‘000) 125 125 125 125 Total increase in CM before taxes (‘000) $161 $185 $185 $209 Income taxes (‘000) 64.4 74 74 83.6 Total after tax increase
In CM before
depreciation (‘000) $96.60 $111 $111 $125.4 After tax proceeds from
disposal ($80,000 x .6) 48
Tax saving from
depreciation (‘000) 81.84 111.60 37.20 17.36 Total net cash inflow 153,815 .862 $178.44
165,392 .743 222.60
94,996 .641 148.20
105,300 .552 190.76
Net Present Value <$70,497>
VacuTech can expect to have a negative net present value of $70,497 if it purchases the new pump.
20.48 (Continued)
2. Other factors the firm needs to consider include:
• Maintenance costs of the machines • Reliability of the machines
• Changes and timing of newer machine
• Effects on production workers
• Learning effect on using the new machine • Changes in market
20-49Joint Venture (5 min)
Present value of net cash inflows:
$900,000 x 0.8 x 4.192 = $3,018,240 Initial investment 3,000,000
NPV $ 18,240
Yes. The group can expect a positive NPV of $18,240.
20-50 Risk and NPV (5 min)
1. PV at 12%: $275,000 x 6.194 = $1,703,350 Yes, because $1,703,350 > $1,500,000
2. PV at 16%: $275,000 x 5.197 = $1,429,175 No, because $1,429,175 < $1,500,000
3. Many firms raise discount rate in evaluating capital investments in view of uncertainties underlying the investment. This approach allows managers to factor in risks and uncertainties. The higher the risk or uncertainty a project has, the higher the discount rate.
However, managers should use a direct approach whenever possible in dealing with risk or uncertainty. For example, if a firm considers that revenues from an investment are likely to differ from the projected figures, the firm should adjust the projected revenues. If the expenses are likely to be higher, adjusting the projected expenses would allow the firm to be aware of the need for a higher amount of cash outflows. Using a direct approach whenever possible is better than simply using a higher discount rate.
20-51Sensitivity Analysis (5 min)
1. 15 years: $600,000 x 6.142 = $3,685,200 Yes 12 years : $600,000 x 5.66 = $3,396,000 No 2. 600,000 x An, 14% = $3,500,000
Solving for An, 14% : An, 14% = 5.833
The discount factor at 14% for 13 years is 5.842
Therefore, the number of years needed for the Seattle facility to earn at least a 14% return is approximately 13 years.
20-52 Uneven Cash Flows (5 min) Present value of net cash inflows:
Year 2 $1,000,000 x .797 = $ 797,000 Year 3 $1,000,000 x .712 = 712,000 Year 4 $2,500,000 x .636 = 1,590,000 Years 5-10 $3,000,000 x 4.111 x .567 = 6,992,811 Total present value of net cash inflows $10,091,811
Initial investment 15,000,000