Chap 020

CHAPTER 20 CAPITAL BUDGETING QUESTIONS 20-1

The three major steps in capital budgeting decisions are: project identificat identification ion and definition, evaluation and selection, and monitoring and review. r eview.

20-2

Firms make capital investments to improve efficiency and productivity and to 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 compute and report periodic net incomes and that reported periodic incomes 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 that will be reported when they consider capital investments.  Although net income is a measure on the outcome of a capital investment, overemphasizing the importance of net income can lead to erroneous capital investment decisions because of the requirement to conform with the generally accepte accepted d account accounting ing princi principle ples s when when comput computing ing periodic periodic net incom income e which, which, among others, mandate the use of an accrual basis in all process. In contrast, capital investment decisions use cash flow data. The periodicity reporting requirement and the arbitrary process involved in 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 chose to use. With a different, yet equally acceptable, accounting method the net income of a period can be substantially different.

20-3

Cash inflows: • Fees from patients • Proceeds from disposal of equipment no longer needed • Investment tax credits. Cash outflows: Salary, Salary, wages, wages, and benef benefits its for for additi additiona onall profess profession ional al medica medicall • staffs including: ♦ Physicians ♦ Technicians ♦ Nurses ♦ Clerks Operating expenses of the scanner such as: • ♦ Utilities ♦ Supplies ♦ Maintenance expenses

Solutions Manual

20-4  After 20 years of operation, oper ation, a chemical company needs to ensure that there is no

residual effect on the environment before abandoning the factory. Restoration of  the site to remove any environmental effect to the neighborhood the factory might have caused over the years is the most critical critical step the firm needs to take. Very likely it is also among the most expensive processes. 20.5 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 effects in acquiring a new factory can include: • acquisition or construction cost of the factory building, • purchase costs for machinery and equipment needed for the factory, working capital for additional materials, payrolls, and operating expenses, • • cash receipts from selling the products, proce proceeds eds from from sale sales s of the the old old fact factory ory,, mach machin iner ery, y, and and equi equipme pment nt • replaced. 20-6

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: • decreases in taxes because of the depreciation expenses of the new factory • increases increases in tax payments for gains or decreases decreases in tax payments for losses on disposal of the replaced factory, machinery, or equipment or the abandonment of the investment at the end of its useful life • increases increases in tax payments for gains from operations operations or decreases decreases in tax payments for losses on operations • investment tax credit

20-7  A book value by itself is irrelevant in capital budgeting since it has no effect on

cash flow. However, a capital capital budgeting budgeting decision decision often involves disposal of one 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 affect the tax payment of the firm, which, in turn, affect the cash flows of the firm. c onsider an 20.8 Among the limitations of the payback period technique are its failure to consider investment project’s total profitability and the time value of money. The present value payback period technique considers the time value of  money. It fails, however, to consider an investment project’s total profitability. 20-9

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 and and incl includ udes es in its its comp computa utati tion on meas measure ures s that that are resul results ts of the the arbit arbitrar rarilily y selected accounting procedures the firm chooses to follow. 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 rate of return over the project’s entire useful years.

Blocher, Chen, Cokins, Lin: Cost Management, 3e

2

©The McGraw-Hill Companies, Inc., 2005

20-10 The 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 investment. Furthermore, a higher NPV signals a better capital investment. The IRR method uses a different decision criterion for evaluating capital 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 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, or a rate that the firm sets for the investment. 20-11 DCF 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  impo importa rtant nt fact factors ors rele releva vant nt to a capi capita tall inve invest stme ment nt such such as effe effect cts s of the the investment on the firm’s strategic position, competitive advantage, community in which the firm locates or serves, or relationships with unions. 20-12  A sound capital investment decision needs to consider both quantitative and

quali qualita tati tive ve fact factors ors.. Unfo Unfort rtuna unate tely ly,, quali qualita tati tive ve fact factors ors ofte often n are diff diffic icult ult or  imposs impossibl ible e to quanti quantify fy.. Decisi Decision-ma on-maker kers s may leave leave out the impact impacts s of nonnonquanti quantitat tative ive factor factors s in invest investmen mentt decisi decisions ons because because there there are no number numbers s attached to these factors.  Among cost-benefit features that are often left out are effects on strategic positi position, on, compet competiti itive ve advanta advantage ge of the firm, firm, commun communit ity, y, enviro environme nment, nt, and relationships with unions. r equire careful analyses and evaluations. evalu ations. Availability of funds for  20-13  All investments require 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 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 the investment well. With limited funds available for investment, the firm also needs to compare relative returns of competing investment opportunities, strategic direction of the firm, additional demands on management’s time, impacts on community, among others. 20-14  Among important behavioral factors that might affect capital investment decisions

are: Desir Desires es of mana manage gers rs to grow grow thro through ugh acqui acquisi siti tion ons s and and new new investments. Tendency to escalate commitments commitments • • Effects of prospects on capital investment decisions. Prope Propens nsit ity y of not not want wantin ing g to spend spend addit additio iona nall time time and and effo effort rt • needed to secure capital investments. • Intolerance of uncertainty. •

Solutions Manual

20-15 NPV method and IRR method may yield conflicting results when two investment

projects differ in: • size of initial investment timing of net cash inflows • • pattern of net cash inflow length of useful life • 20-16 The 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 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 capital investments. 20-17 The 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 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 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 returns over a longer period of time than that of a late dollar. 20-18 Depreciation expenses affect capital investment decisions in two ways:

1. Depreci Depreciati ation on expenses expenses decrea decrease se periodic periodic net inco incomes mes from from inves investme tment nt and, thereby, reduce tax payments. 2. Depreci Depreciati ation on expens expenses es decreas decrease e the book book value of of the inve investm stmen entt and, and, 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 of  the investment. 20-19 The desired rate of return of a firm may change from one year to the next

because of changes in, among others: 1. investment investment opportunities opportunities available available to the firm, firm, 2. bank bank or loan loan inte interest rest rates, rates, 3. marke markett situ situat atio ion, n, 4. priori priority ty of of the the firm firm.. firm can expect to earn earn a higher higher return than than the cost of funds funds needed needed for  20-20 a. The firm the investment if the internal rate of return is 11 percent and the cost of capital is 10%. b. A capital capital project project that has has a net present value of $148,000 $148,000 computed computed based on 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.

Blocher, Chen, Cokins, Lin: Cost Management, 3e

4

©The McGraw-Hill Companies, Inc., 2005

20-21  A firm that chooses to build often faces many uncertainties, uses evolving

technologies, and traverses in environments that are not familiar to management and can change rapidly. Capital budgeting processes in these firms are often less formal, formal, rely less on formal formal analyses, analyses, use more nonfinancia nonfinanciall and nonquantifiab nonquantifiable le data data such such as mark market et share share pote potent ntia iall and and compe competi tito tors rs’’ acti action ons, s, and and appl apply y subjective criteria in evaluating capital investment projects. These firms are likely 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 marke market. t. As a result result,, its its capit capital al budget budgetin ing g proces processes ses are more more like likely ly to be formalized. Most data needed for capital investment decisions are quantifiable and financial in nature. Its required payback period tends to be short and the hurdle rate high. 20-22 1. Capital

budge dgeting is a proc rocess ess of asse ssessin sing pro projects that hat requ requir ire e commitments of large sums of funds and generate benefits stretching well into the future. Among uses of capital budgeting are assessments of purchasing new equipme equipment, nt, acquiri acquiring ng new facili facilitie ties, s, developi developing ng and introdu introducin cing g new products, and expanding into new sales territories. 2. Diff Differ eren ence ces s betwe between en payba payback ck and and net net presen presentt value value meth method ods s of capi capita tall budgeting include recognition of time value of money, decision criterion for  sele select ctin ing g the the best best inve invest stme ment nt,, and and numb number er of perio periods ds cons consid idere ered. d. The The 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  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 prese present nt value value meth method od is the the amou amount nt of net net prese present nt valu values. es. A supe superio rior  r  investment is the one with the highest net present value. In addition, the payback period method considers only cash flows needed to recover the initial investment. Cash flows after the payback period are not included in evaluations of capital investments when using a payback period method. In contrast, a net present value method includes all cash flows. 3. The cost cost of capital capital of a firm is the the weighted weighted average average of the cost cost of the funds funds that comprise the firm’s capital structure. 4. Financ Financial ial account accounting ing data data often often are not suitab suitable le for use in capital capital budgetin budgeting g because: a. finan financia ciall account accounting ing uses accrual accrual accounti accounting ng in all of its measureme measurements nts.. The The net net inco income me of a peri period od may may incl includ ude e reve revenu nues es not not yet yet paid paid by customers and exclude payments made to suppliers for future deliveries. Receivables included in the revenues of the period are not available to the firm for payments. The amount of cash paid is no longer available for other  payments, even though the payment is not an expense of the period. b. finan financia ciall accounti accounting ng data often often are not suitab suitable le also because because of the need to use arbitrary accounting procedures in financial accounting data.

Solutions Manual

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% =

Net effect on cash outflow

Blocher, Chen, Cokins, Lin: Cost Management, 3e

6

$34,000

©The McGraw-Hill Companies, Inc., 2005

20.24 Basic Capital Budgeting Techniques (10 min)

a. Project A:

 Payback  Period  =

$5,000 $1,800

=

2.78 years

Or, 2 years and 10 months b. Year 1 2 3 4

Net

Cumulative

Cash Inflow

Net Cash Inflow  

$ 500 1,200 2,000 2,500

$ 500 1,700 3,700

Project B: Payback period:

 Payback  Period 

=

3+

($5,000

−

$3,700 )

$2,500

=

3.52 years

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:

 Payback  Period 

=

$5,000

Or, 2 years and 5 months

Solutions Manual

$2,125

=

2.35  years

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

0 1 $ 500 2 1,200 3 2,000 4 2,500 5 2,000 Net Present Value Project C:

Present Value

.926 .857 .794 .735 .681 $2,125 x 3.993 - $5,000 =

Project D: Present value of cash inflows: Year 1 through 4 ($1,200 + $900) x 3.312 = Year 5 (2,100 + $500) x 0.681 = Present value of cash inflows Initial investment 5,000 Net present value

Blocher, Chen, Cokins, Lin: Cost Management, 3e

8

463 1,028 1,588 1,838 1,362 $1,279 $3,485

$6,955 1,771 $8,726 $3,726

©The McGraw-Hill Companies, Inc., 2005

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 or Rate of Dividend Expected Book Value Rate Return Bond $5,000,000 9% 5.73% Preferred Stock 5,000,000 10% 10.00% Common Stock 500,000 20.00% Total $10,500,000

Solutions Manual

Weighted Total Average Market Cost of   Value Weight Capital $ 5,500,000 0.275 1.58% 6,000,000

0.300

3.00%

8,500,000 $20,000,000

0.425 1.000

8.50% 13.08%

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. b.

FV (0.015, 1200, 0, 24, 0) = $1,378,675,128 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

Blocher, Chen, Cokins, Lin: Cost Management, 3e

10

©The McGraw-Hill Companies, Inc., 2005

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 Year Book Value Expense Depreciation 0 1 $60,000 $30,000 $30,000 2 30,000 15,000 45,000 3 15,000 7,500 52,500 4 7,500 7,500 60,000

Ending Book Value $60,000 30,000 15,000 7,500 0

Net 30% After-tax 10% Cash Depreciation Taxable Income Net Cash Discount Present Year Inflow Expense Income Taxes Inflow Factor Value 0 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

Solutions Manual

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 25% 25%2.362

Discount Factor  2.362

?

2.230

30% Difference

5%

2.166 ?

0.196

0.132

Internal rate of return: 25 %

0.132 +

0.196

× 5% =

Blocher, Chen, Cokins, Lin: Cost Management, 3e

28 .37 %

12

©The McGraw-Hill Companies, Inc., 2005

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 Depreciation expense $500,000 ) 10 = Increase in net income

$120,000 50,000 $ 70,000

(a) On initial investment:

$70,000 ) $500,000 =

14%

(b) On average investment:  Average investment: Book rate of return:

($500,000 + 0) ) 2 = $250,000 $70,00 ÷ $250,000 = 28%

c. NPV: Present value of net cash inflows: $120,000 x 5.65 = $678,000 Initial investment Net present value $178,000

Solutions Manual

20-28 (Continued-1)

d. Present value payback period: Year

Present Value of  Net cash inflow

Cumulative Cash Flow





1

107,160

< 392,840>

2 3

95,640

< 297,200>

85,440

< 211,760>

76,320

< 135,440>

68,040

<

67,400>

60,840

<

6,560>

0

4 5 6 7

6  years +

54,240

$6,560 $54,240

47,680

= 6.12  years (6  years 2 months)

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

 Internal   Rate of  Return = 20% +

Blocher, Chen, Cokins, Lin: Cost Management, 3e

$503,040 - $500,000 $74,520

14

×

=

5% = 20.20%

©The McGraw-Hill Companies, Inc., 2005

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 investment, $678,027 - $500,000 = $178,027

initial

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 Solutions Manual

20.29 Basic Capital Budgeting Techniques: Uneven Net cash inflow with Taxes (40 min)

1. a. Payback period: Year

Net Cash Inflow

Depreciation Expense

Saving or  on Income Tax

Taxable Income

0



1

50,000



0

2

80,000



30,000

3

120,000



4

200,000

5

Net Aftertax Income

Net After-tax Cash Inflow

Cumulative Net  After-tax cash inflow

0

50,000





21,000

71,000



70,000



49,000

99,000





150,000



105,000

155,000



240,000



190,000



133,000

183,000

58,000

6

300,000



250,000



175,000

225,000

7

270,000



220,000



154,000

204,000

8

240,000



190,000



133,000

183,000

9

120,000



70,000



49,000

99,000

10

40,000





3,000



43,000

Total



1,160,000

 Payback  Period  = 4  years +

Blocher, Chen, Cokins, Lin: Cost Management, 3e

0



812,000

$125,000 = 4.68  years $183,000

16

©The McGraw-Hill Companies, Inc., 2005

20-29 (Continued-1)

b. Average net income of the investment period: $812,000/10 = Book rate of return: a. On initial investment: $81,200/$500,000 = b. On average investment:  Average investment: ($500,000 + 0)/2 = $250,000 Book rate of return: $81,200/$250,000 = c. Net present value: Year 1 2

Net After-tax cash inflow

Discount Factor at 12%

Present Value of  Net cash inflow

$50,000

0.893

$44,650

0.797

56,587

3

71,000 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

0.404

73,932

9

183,000 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

$81,200 16.24% 32.48%

20-29 (Continued-2)

d. Internal rate of return: Net After- 18% PV of Net 20% PV of Net Year  tax cash Discount cash inflow Discount cash inflow at inflow Factor  at 18% Factor  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%: PV of net cash inflows at 20%: Difference in PV with 2% difference in discount rate

$540,042 $497,623 $ 42,419

Internal rate of return =

18% +

$540,042 - $500,000 $42,419

Blocher, Chen, Cokins, Lin: Cost Management, 3e

18

×

2% = 19.89%

©The McGraw-Hill Companies, Inc., 2005

20-29 (Continued-3)

2.

 A

B

C

D

1

Year

Net Cash Inflow

Depreciation Expense

Taxable Income

2

0



3

1

50,000



4

2

80,000

5

3

6

E Saving or  on Income Tax

F Net Aftertax Income

0

0

0

50,000



30,000



21,000

71,000

120,000



70,000



49,000

99,000

4

200,000



150,000



105,000

155,000

7

5

240,000



190,000



133,000

183,000

8

6

300,000



250,000



175,000

225,000

9

7

270,000



220,000



154,000

204,000

10

8

240,000



190,000



133,000

183,000

11

9

120,000



70,000



49,000

99,000

12

10

40,000







43,000

13

Total

Solutions manual



19

1,160,000

3,000

812,000

G Net Aftertax Cash Inflow

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 @IRR (.1, f2:f12) = .1988

Blocher, Chen, Cokins, Lin: Cost Management, 3e

20

©The McGraw-Hill Companies, Inc., 2005

20-30 Basic Capital Budgeting Techniques: Uneven Net cash inflows with MACRS (40 min)

1. Payback period: Year 

Net Cash Flow Return

Taxable Income

Depreciation Expense

Income Tax  After-tax Net  After-tax Net Expense Income cash inflow

Cumulative  After-tax Net cash inflow

0



1

50,000





15, 000



65,000



2

80,000





24,000



104,000



3

120,000



24,000



16,800

112,800



4

200,000



142,400



99,680

157,280

< 60,920>

5

240,000



182,400



127,680

185,280

124,360

6

300,000



271,200



189,840

218,640

7

270,000

0

270,000



189,000

189,000

8

240,000

0

240,000



168,000

168,000

9

120,000

0

120,000



84,000

84,000

10

40,000

0

40,000



28,000

28,000

1,160,000



812,000

1,312,000

Total



 Payback  Period  = 4  years +

Solutions manual

21

$60,920 $185,280

= 4.33  years

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  Depreciation End of    Average the Year  the Year  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 Book rate of return:

$81,200/$114,920 =

Blocher, Chen, Cokins, Lin: Cost Management, 3e

22

70.66%

©The McGraw-Hill Companies, Inc., 2005

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

 Internal  Rate of  Return = 20% +

Blocher, Chen, Cokins, Lin: Cost Management, 3e

24

$27,875 $37,602

×

2% = 21.48%

©The McGraw-Hill Companies, Inc., 2005

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 =

Tax rate

3,000 x

Income taxes

40% $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 =

Total

$23,493

Initial investment

30,600

NPV

Solutions manual

378



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) =

Tax saving on depreciation expense

$600 x 0.35 = +

Total 1.Payback

$780 210 $990

period :

$6,000 = 6.06   years $990 2.

Operating income in each of the 10 years: Sales

$1,200

Depreciation

600

Operating income before taxes

$ 600

Taxes

210

Operating income

$ 390

 Book  rate of  return = 3. 4.

$390 $6,000

= 6.5%

$990 x 5.019 = $4,969

Required net after-tax annual cash inflow: $6,000 ) 5.019 = Tax saving on depreciation expense

$1,195 -

Required net after-tax annual cash revenue 1 - tax rate

Blocher, Chen, Cokins, Lin: Cost Management, 3e

$985 )

Before-tax annual cash revenue needed

26

210 0.65 $1,515

©The McGraw-Hill Companies, Inc., 2005

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. Factor  AccuDril Operating Cost 1 Overhaul cost Tax savings on depreciation 2 Other Expenses 3 Year 1 Year 2 Year 3 Year 4 Year 5 Total PV

Discount Present Value 0

Buy RoboDril 1010K Equipment Purchase4 Operating Cost 5 Tax saving on depreciation 6 Other expenses7 Salvage value8 Total PV

1

.893 .797 .712 .636 .567

< 56,533> < 50,498> < 45,020>

1.000 3.605



3.605 3.605 .567

69,216 17,010

2

28

Overhaul











4

4

16

16

16







19.2 19.2 19.2



PV of the difference in cash flow between the alternatives RoboDril

Blocher, Chen, Cokins, Lin: Cost Management, 3e

Cash Flows in ‘000 3 4 5



19.2



19.2 30



$402,441 - $359,259 = $ 43,182 in favor of 

©The McGraw-Hill Companies, Inc., 2005

20-34 (Continued-1) 1

Years 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

2

Years 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 Overhaul cost Total amount to be depreciated Number of years Depreciation expense per year Tax Rate Tax savings on depreciation

3

$ 20,000 100,000 $120,000 3 ÷ $ 40,000 x 40% $ 16,000

$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 Tax Rate Tax savings on depreciation

$240,000 ÷ 5 Years =

7

$55,000 x (1 - Tax Rate 40%) = $33,000

8

$50,000 x (1 - Tax Rate 40%) = $30,000

Solutions manual

29

$48,000 x 0.40 $19,200

20-34 (Continued-2)

2. Year 0

Cash Flow AccuDril RoboDril $0

Difference in Cash Flow

Cumulative Difference

1





63,200



2





163,200

< 13,600>

3





41,600

 Payback  period = 2  years +

$13,600 $41,600

= 2.33  years

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 • Differences in product qualities manufactured by the two machines

Blocher, Chen, Cokins, Lin: Cost Management, 3e

30

©The McGraw-Hill Companies, Inc., 2005

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:

$43,182 1.914

= $22, 561

Before-tax,

$22,56 1 0.6 

= $37,602

$3 7  ,602 = 47% $80,000 For the replacement decision to be in error financially, the overhaul of   AccuDril X10 needs to improve the operating efficiency by at least 53%.

Solutions manual

31

20-35 (Continued-1)

2. Discount Factor

Present Value

0

Cash Flows in '000 2 3 4

1

Overhaul in 2 years Tax savings from depreciation Overhaul cost

4 .893 .797 .712 .636 .567

3,572 11,392 10,176 9,072

PV of overhaul in 2 years Overhaul now and again in 2 years Overhaul cost Savings from Improved efficiency1 Tax savings on depreciation2 1.000 .893 .797 .712 .636 .567

16

16 16 16

9.6 24

32

16



9.6 24

4

4

4

33.6 3.6

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.

Blocher, Chen, Cokins, Lin: Cost Management, 3e

16

4

30,005 2,869 2,848 2,544 2,268

4

5

©The McGraw-Hill Companies, Inc., 2005

4 4 4

20-35 (Continued-2) 1

Savings from the improved productivity $10 per hour x 8,000 hours x 20% = Taxes on the saving

$16,000 x 40% tax rate =

$16,000 -

6,400

Net after Tax savings 2

$9,600

Years 1 and 2: Book value at the time of overhaul:

$10,000 x 2 + $20,000 =

Overhaul cost

$ 40,000 +

Total amount to be depreciated

80,000 $120,000

Number of years

2

÷

Depreciation expense per year

$60,000

Tax Rate

x

Tax savings on depreciation

0.40 $24,000

Years 3, 4, and 5: Overhaul cost

$30,000

Number of years

÷

Depreciation expense per year

3 $10,000

Tax Rate

x

Tax savings on depreciation

0.40 $ 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.

Solutions manual

33

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.

Blocher, Chen, Cokins, Lin: Cost Management, 3e

34

©The McGraw-Hill Companies, Inc., 2005

20-36 (Continued-1)

3.

$995,000  Payback  Period = = 2.43 years $410,000 4. Average investment = ($995,000 + $195,000)/2 = $595,000  Average net income = $210,000 Book 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 = $ Year 4: $605,000 x 0.592 = + Total present value net cash inflows $1,310,180 Initial investment NPV $ 6.

PV of cash flows at 25%: $410,000 x 1.952 + $605,000 x 0.410 PV of cash flows at 30% $410,000 x 1.816 + $605,000 x 0.350 Changes in PV of cash flows  Internal  rate of  return = 25% +

$1,0 48,370 - $995,000 $92,060

952,020 358,160 995,000 315,180

$1,048,370 $ 956,310 $ 92,060 ×

5% = 27. 90%

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 =

Solutions manual

35

$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 Proceeds from disposal Taxes on gains on disposal Cash outflow

$3,000 < 600>

Year 1-4 Operating cost using the current machine ($40,000 + 10,000 + 10,000) x 0.8 = Operating cost using the SP1000 ($30,000 + 2,000 + 1,000) x 0.8 = Savings in operating cost with the new machine Savings in taxes on depreciation expense Depreciation expense $100,000 ÷ 5 = $20,000 Tax rate x 20% Net cash inflows in each of Years 1-4 Year 5  After-tax cash inflow from savings in operating costs  After-tax cash inflow from disposed of the investment $5,000 x 0.8 = Total cash inflow in year 5 2. PV of cash inflow in each of years 1-4: $25,600 x 3.465 = PV of cash inflow in year 5: $29,600 x 0.747 = Total PV of cash inflow Less: Initial investment NPV

2,400

$48,000 26,400 $21,600 4,000 $25,600 $25,600 4,000 $29,600 $ 88,704 22,111 $110,815 < 97,600> $ 13,215

3. Payback period = $97,600 ÷ $25,600 = 3.81 years

Blocher, Chen, Cokins, Lin: Cost Management, 3e

36

©The McGraw-Hill Companies, Inc., 2005

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 0.089  Internal  rate of  return = 8% + × 1% = 8.86% 0.103

5. Year

Cash Inflow

1 2 3 4 5

$20,000 22,000 25,000 30,000 40,000 Interest Rate 10% 10% ? 12% 2% ?

Discount factor at 10% 0.909 0.826 0.751 0.683 0.621

PV at 10%

Discount factor at 12%

$ 18,180 18,172 18,775 20,490 24,840 $100,457

0.893 0.797 0.712 0.636 0.567

PV at 12% $17,860 17,534 17,800 19,080 22,680 $94,954

PV of Net cash inflows $100,457 $100,457 97,600 94,954 $5,503 $2,857

 Internal  rate of  return = 10% +

$2,857  $5,503

×

2% = 11.04%

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 Solutions manual

37

min)

 After-tax net cash inflows Before Tax Cash Flow Depreciation Net Income Year Return Expense Income Tax (24%) 1 $ 9,000 $15,000

After Tax Cash Flow Return $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

1. Year 0

After Tax Cash Flow Return

$51,080 Cumulative After Tax Net cash inflow

1

10,440

< 34,560>

2

12,000

< 22,560>

3

13,560

<

9,000>

4

8,280

<

720>

5

6,800

 Payback   period  = 4  years +

Blocher, Chen, Cokins, Lin: Cost Management, 3e

38

$720 $6,800

= 4.11  years

©The McGraw-Hill Companies, Inc., 2005

20-38 (Continued)

2.

After Tax Cash Year Flow Return 1 $10,440

Discount Present Value of Cumulative Factor (10%) After Tax Net cash inflow .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 = 3.

Net Cash Year Inflow 1 $10,440

PV Factor At 6% 0.943

PV at 6% $ 9,845

PV Factor at 4% 0.962

PV at 4% $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 Discount Rate 4%

4%

PV of Net Cash Inflows $45,867

$45,867

? 6% 2%

$45,867

45,000 43,553

?

$ 2,314

$

 Internal  rate of  return = 4% +

867

$867  $2,314

×

2% = 4.75%

20-39Working Backward: Determine Initial Investment Based on Book Rate of Return (5 min)

Solutions manual

39

Let Y = Cost of the new machine Then,

($6,750

−

Y 

) × (1 − 0.20) 10 Y 

=

0.10

($6,750 – .1 Y ) x 0.8 = 0.1 Y  ∴Initial investment = $30,000

Blocher, Chen, Cokins, Lin: Cost Management, 3e

40

©The McGraw-Hill Companies, Inc., 2005

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

Solutions manual

41

20-41 Determine Periodic Cash Flow Based on Book Rate of Return (5 min)

Let Y be the firm's after-tax operating income

 y $60,000

= 0.15

∴y = $9,000

Operating income before taxes = $9,000 ) (1 - 0.25) = $12,000 Total cash inflow before taxes:

Blocher, Chen, Cokins, Lin: Cost Management, 3e

$12 ,000 +

42

$60,000 5

= $24 ,000

©The McGraw-Hill Companies, Inc., 2005

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 Depreciation ($5,000 - $600)/11

New ($8,000 - $400)/10

= $400

Difference

= $760

$360

Operating expense



Difference in net income Book value: Year 0



Old $5,000 - $400 = $4,600

New $8,000

600

400

$2,600

$4,200

Year 10  Average Investment (book Value)

Incremental average investment on new machine = $4,200 - $2,600 = $1,600

 Accounting  rate of  return =

$390 $1,600

= 24.3 8%

c. NPV = $750 x 5.650 – ($8,000 - $3,000) - ($600 - $400) x 0.322 = $4,237.50 - $5,000 - $64.40 =

Solutions manual

43

20-42 (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% +

166  226 

×

1% = 7.73%

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 y = $896.35 Maximum required savings

Blocher, Chen, Cokins, Lin: Cost Management, 3e

44

©The McGraw-Hill Companies, Inc., 2005

Value of Accelerated Depreciation (5 min)

20-43

1. Year 1

PV Depreciation Method Difference Factor PV of  SYD S-L Amount Tax Effect at 8% Tax Effect $40,000 $25,000 $15,000 $6,000 .926 $ 5,556

2

30,000

25,000

3

20,000

25,000

4

10,000

5,000

2,000

< 5,000>

25,000

.857

1,714

.794



.735

$100,000 $100,000 2. Year 1

$1,272

PV Depreciation Method Difference Factor PV of  DD S-L Amount Tax Effect at 8% Tax Effect $50,000 $25,000 $25,000 $10,000 .926 $9,260

2

25,000

25,000

3

12,500

25,000

4

12,500 $100,000

3. Year 1

-0-

25,000

-0-



.857

-0-

.794

< 3,970>

.735



$100,000

$1,615

PV Depreciation Method Difference Factor PV of  DD S-L Amount Tax Effect at 8% Tax Effect $33,330 $25,000 $8,330 $3,332 .926 $3,085

2

44,450

25,000

3

14,810

25,000

4

7,410 $100,000

Solutions manual

19,450

25,000 $100,000

7,780



.857

6,667

.794 < 3,236 > .735

$1,345

45

20-44 Capital Budgeting with Sensitivity Analysis (15 min)

1. Expected annual net cash inflows ($600,000 + $100,000) Income taxes at 30%  After-tax net cash inflows

$700,000 210,000 $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.

3.

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 Year Depreciation 1 .2 P 2 .32 P 3 .192 P 4 .1152P 5 .1152P 6 .0576P

Tax Effect .06 P .096 P .0576 P .03456P .03456P .01728P

PV Factor 0.893 0.797 0.712 0.636 0.567 0.507

Present Value .05358 P .076512 P .0410112P .0219801P .0195955P .0087609P .2214397P

P = $2,434,320 + .2214397P .7785603P = $2,434,320 P = $3,126,694

Blocher, Chen, Cokins, Lin: Cost Management, 3e

46

©The McGraw-Hill Companies, Inc., 2005

20-45Cash Flow Analysis and NPV (15 min)

Item & Description a. Foregone rent ($5,000 x 12 x 0.6) b. All are irrelevant c. Remodeling Depreciation

PV Factor 3.433 0.877 0.769 0.675 0.592 0.519

CASH FLOWS IN YEAR (in '000) PV 0 1 < 100,000> 14,032 7,382 3,888 2,557 2,242

d. Investment in inventory and receivables < 600,000> Recovery 0.519 311,400 e. Irrelevant f. Sales ($900 x 0.6) 3.433 1,853,820 Operating expenses ($500 x 0.6) 3.433 g.Sales Promotion ($100 x 0.6) < 60,000> h. Termination ($50 x 0.6) 0.519 < 15,570> NPV $ 266,263



2

3

4



16 9.6 5.76 4.32 4.32 600 540

540

540

540









47

540

< 60>

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.

Solutions manual

5

< 30>

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 = Present value of operating costs: $1,800,000 x (1 - 0.45) x 2.577 = Present value of salvage value: $50,000 x (1 - 0.45) x 0.794 = Present value of costs with the original equipment

$724,781 21,835

Present value of the costs with the new machine Initial outlay Present value of tax savings on depreciation: Beginning Depreciation Tax Tax Discount Year Book Value Expense Rate Saving Factor 1 $2,000,000 $1,333,333 x 0.45 = $600,000 x 0.926 2 666,667 444,445 x 0.45 = 200,000 x 0.857 3 222,223 222,223 x 0.45 = 100,000 x 0.794 Cash proceeds from sale of the old machine Tax saving of loss on disposal of the old machine ($1,875,000 - $300,000) x 0.45 = Present value of operating costs $1,000,000 x (1 - .45) x 2.577 = Total cost at present value

Present Value = $ 555,600 = 171,400 = 79,400 300,000 708,750

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.

Blocher, Chen, Cokins, Lin: Cost Management, 3e

48

©The McGraw-Hill Companies, Inc., 2005

20-47 Equipment Replacement (15 min)

1.a.

Selling price Variables cost: Direct materials Direct labor Indirect costs Contribution margin per unit

$30.00 $0.25 x 8 = $8.00 x 2 =

$2.00 16.00 0.30

18.30 $11.70

b.

$0.3 +

$25,000 100,000

= $0.55

c. Current fixed costs Increase in equipment depreciation: New equipment ($100,000 - $10,000) ÷ 10 = $9,000 Current 2,000 Total fixed costs

$25,000 7,000 $32,000

Total overhead = $32,000 + $0.40 per unit x Units manufactured d.

$32,000 100,000

+ $0.4 0 = $0.72

e. Selling price Variables cost: Direct materials Direct labor ($8 per hour x 1 hour) Indirect costs Contribution margin per unit

Solutions manual

49

$30.00 $2.00 8.00 0.40

10.40 $19.60

20-47 (Continued)

f. Purchase price Proceeds from selling the old saw Tax savings from loss on disposal: Book value Selling price Loss on sales Tax rate Net additional investment required

$100,000 $4,000 $20,000 4,000 $16,000 0.40

6,400

10,400 $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.

Blocher, Chen, Cokins, Lin: Cost Management, 3e

50

©The McGraw-Hill Companies, Inc., 2005

20-48 Equipment Replacement with MACRS (15 min)

1. Contribution margins of the additional units: Sales price per unit Current manufacturing cost Current contribution margin per unit  Additional saving with the new machine Contribution margin per unit of the additional units

$3,500 - 2,450 $1,050 + 150 $1,200

Net cash inflows: Present Discount Value Factor 2007

Item Description 2008 2009 2010 Purchase cost Installation 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 VacuTech can expect to have a negative net present value of  $70,497 if it purchases the new pump.

Solutions manual

51

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 • Competitors’ reaction

Blocher, Chen, Cokins, Lin: Cost Management, 3e

52

©The McGraw-Hill Companies, Inc., 2005

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.

Solutions manual

53

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.

Blocher, Chen, Cokins, Lin: Cost Management, 3e

54

©The McGraw-Hill Companies, Inc., 2005

20-51Sensitivity Analysis (5 min)

1. 15 years: 12 years :

$600,000 x 6.142 = $3,685,200 Yes $600,000 x 5.66 = $3,396,000 No

2. 600,000 x A n, 14% = $3,500,000 Solving for A n, 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.

Solutions manual

55

20-52 Uneven Cash Flows (5 min)

Present value of net cash inflows: Year 2

$1,000,000 x .797 =

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 =

Total present value of net cash inflows

$

797,000

6,992,811 $10,091,811

Initial investment

15,000,000

NPV

$

Blocher, Chen, Cokins, Lin: Cost Management, 3e

56

©The McGraw-Hill Companies, Inc., 2005

20-53 Environment Cost Management (20 min)

1. Solvent System

Initial investment  After-tax Operating cost Depreciation Tax saving on depreciation Net after-tax cost Discount factor (12%) Present value Total cost Powder System Initial investment  After-tax Operating cost Depreciation Tax saving on depreciation Net after-tax cost Discount factor (12%) PV Total cost Difference in total cost

Solutions manual

Present Value $400,000

1,191,075 $1,591,075

Year 1

Year 2

Year 3

Year 4

Year 5

Year 6

Year 7

Y

$228,000 40,000 16,000

$228,000 $228,000 $228,000 $228,000 $228,000 $228,000 $2 72,000 57,600 46,080 36,880 29,480 26,200 28,800 23,040 18,432 14,752 11,792 10,480

212,000 0.893 189,316

199,200 0.797 158,762

$240,000 120,000 48,000

$240,000 $240,000 $240,000 $240,000 $240,000 $240,000 $2 216,000 172,800 138,240 110,640 88,440 78,600 86,400 69,120 55,296 44,256 35,376 31,440

204,960 0.712 145,932

209,568 0.636 133,285

213,248 0.567 120,912

216,208 0.507 109,617

217,520 0.452 98,319

2

$1,200,000

1,064,182 $2,264,182 $673,107

192,000 0.893 171,456

153,600 0.797 122,419

57

170,880 0.712 121,667

184,704 0.636 117,472

195,744 0.567 110,987

204,624 0.507 103,744

208,560 0.452 94,269

2