CHAPTER 20: CAPITAL BUDGETING

STUDENT SOLUTIONS MANUAL

STUDENT SOLUTIONS MANUALSTUDENT SOLUTIONS MANUAL

CHAPTER 20: CAPITAL BUDGETING

EXERCISES

20-34Basic Capital Budgeting Techniques (45 min)

a. Project A:

Or, 2 years and 10 months

b. Project B:

After-tax Cumulative

YearCash Inflows

After-tax Cash Inflows

1

$ 500 $ 500

2

1,200

1,700

3

2,000

3,700

4

2,500

Or, 3 years and 7 months

c.Project 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

Or, 2 years and 5 months

20-34 (Continued)d.Project D:

(1)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

Operating income after taxes

$1,200

Book rate of return = ADVANCE \d 7

ADVANCE \u 7$1,200 ( $5,000 = 24.00%

(2) Average book value = ($5,000 + $500) ( 2 = $2,750

Book rate of return = $1,200 ( $2,750 = ADVANCE \d 7

ADVANCE \u 743.64%e.Net Present Values (@8%), rounded:

Project A:($1,800 x 3.993) $5,000 =

$7,187 $5,000 = $2,187

Project B:

After-tax 8% Discount Present

Year Cash Flows

Factor

Values

0

1

$ 5000.926463

2

1,2000.8571,028

3

2,0000.7941,588

4

2,5000.7351,838

5

2,0000.681 1,362

Net Present Value (NPV) =$1,279

Project C: ($2,125 x 3.993) $5,000 =

$8,485 $5,000 = $3,485

Project D:

Present value of cash inflows:

Years 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

Net present value (NPV)

=

$3,726

20-36Future and Present Values Using Excel (20 min)

A.To calculate future values, use the following Excel function:

FV(rate,nper,pmt,pv,type)

1. Between January 1, 1701 and December 31, 2007 there are 614 six-month periods (nper). Thus, at the end of year 2007, at an annual interest rate of 6% compounded semiannually, the $24.00 will have grown to $1,829,225,347, as follows:

FV(0.06/2,614,0,-24,0)

2. FV(0.08/2,614,0,-24,0) = $$689,733,898,953

3.a. FV(0.06/4,1228,0,-24,0) = $2,091,756,483

b.FV(0.08/4,1228,0,-24,0) = $873,418,055,163

4. FV(0.08/2,12,0,-9500000000,0) = $15,209,806,076

B. To calculate present values, use the following Excel function:

PV(rate,nper,pmt,fv,type)

1. For a stream of ten (10) end-of-year payments of $25,200,000 (ordinary annuity) and a discount rate of 12%, we have:

PV(0.12,10,-25200000,0,0) = $142,385,620

2.If the first payment is received the day the contract is assigned (annuity due), we have:

PV(0.12,10,-25200000,0,1) = $159,471,895

3. Given an income-tax rate of 45%, the after-tax cost of (1) above is:

PV(0.12,10,-25200000*0.55,0,0) = $78,312,091.17

20-38 Basic Capital Budgeting Techniques: Uniform Net cash inflows, No Income Taxes, Non-MACRS-Based Depreciation (45 min)

a.Unadjusted Payback Period: As shown above, the payback period occurs between years 4 and 5. Alternatively, the payback period = $500,000 ( $120,000/year = 4.17 years (about 4 years and 2 months)

b.Book (accounting) rate of return:

As indicated above, the average increase in net income over the ten-year period = $700,000/10 years = $70,000/year. Thus, the ARR

(1) On initial investment: $70,000/$500,000 =14.00%

(2)On average investment:

Average investment: ($500,000 + 0)/2 =

$250,000

Book rate of return:$70,000 ( $250,000 =28.00%20-38 (Continued)

c.NPV: using the PV factors from Table 2 (p. 871), NPV = $178,120

Based on the NPV function of Excel, the NPV = $178,027 (the difference in NPV estimates is due to rounding that takes place when using the PV factors provided in the Table 2 rather than the built-in NPV function)

d. Present value payback period: as indicated in the above schedule, the present value payback period is 6-plus years; this is the time it takes for the present value of future cash inflows to cover the original investment outlay of $500,000

e. Internal rate of return: as indicated in the above schedule, we can use the built-in function in Excel to estimate the IRR for this proposed investment; IRR = 20.18%Alternatively, we can estimate the IRR as follows. We are looking for an interest/discount rate that provides for a NPV = $0 (i.e., a rate that provides a present value of future cash inflows equal in amount to the original investment outlay, $500,000). Thus,

PV of net cash inflows:

At 20% (i.e., a rate too low): $120,000 x 4.192 =$503,040

At 25% (i.e., a rate too high): $120,000 x 3.571 = 428,520

Difference in PV with 5% difference in discount rate = $ 74,520 ADVANCE \u1220-40 Basic Capital Budgeting Techniques: Uneven Net Cash Inflows, Income Taxes, and MACRS Depreciation (60 min)

1. Payback period: as shown by the above schedule, the payback period is between 4 and 5 years. Using a linear interpolation, we estimate the payback period as

20-40 (Continued)

2. Book rate of return (ARR):Average after-tax operating income/year: $812,000/10 = $81,200Book (accounting) rate of return (ARR):

a.On initial investment: $81,200/$500,000 = 16.24%b. On average investment:

Computation of Simple Average Annual Investment:

YearBook Value, Beginning-of-YearDepreciation

Expense for the YearBook Value, End-of-YearAverage BV During the Year

1$500,000$100,000$400,000$450,000

2400,000160,000240,000320,000

3240,00096,000144,000192,000

4144,00057,60086,400115,200

586,40057,60028,80057,600

628,80028,800014,400

7000

8000

9000

10000

Totals$500,000$1,149,200

Average investment: $1,149,200/10 = $114,920

Book rate of return (ARR): $81,200/$114,920 = 70.66%3. Net Present Value (NPV): as indicated in the above schedule, the NPV of the proposed investment is $229,821 (based on PV factors from Table 1, p. 870). Based on the built-in NPV function in Excel, the estimated NPV is $229,743. The difference in estimates is due to the rounding that is embodied in the PV factors taken from Table 1.

4.Internal Rate of Return (IRR): as indicated in the above schedule, we can use the built-in function in Excel to estimate the IRR for this proposed investment; IRR = 21.46%. Alternatively, we can use a linear interpolation procedure to estimate the projects IRR, as follows: we are looking for an interest/discount rate that produces a PV of cash inflows equal to the net original investment outlay ($500,000). Thus,

PV of net cash inflows at 20% (a rate that is too low): $527,875

PV of net cash inflows at 22% (a rate that is too high): $490,273Difference in PV with 2% difference in discount rate: $ 37,602

Thus,

20-42 Capital Budgeting with Tax, Non-MACRS Depreciation, and Sensitivity Analysis (35 min)

Annual after-tax net cash inflow:

Cash revenue

$1,200 x (1 0.35) =$780

Tax saving on depreciation expense($6,000/10) x 0.35 = 210

Total

$990

1. Payback period:

2. Estimated Operating Income per year:

Sales

$1,200

Depreciation

600

Operating income before taxes$ 600

Taxes

210

Operating income

$ 390

Therefore,

3. The maximum initial investment is such that the project at this level of investment would yield a NPV = $0 (i.e., a situation where PV of cash inflows = PV of cash outflows). The appropriate annuity factor for 10 years, 15% is 5.019. Let X = maximum initial investment, then:

X = $990 x 5.019 = $4,969 4. Required annual (pre-tax) cash revenue:

Given an initial investment outlay of $6,000, the after-tax annual cash flow needed per year to generate a return of 15% = $6,000/5.019 =

$1,195

Less: Annual Tax savings on depreciation expense =

210

Required after-tax annual cash revenue

$985

( (1 t)

( 0.65

Annual (pre-tax) cash revenue needed$1,51520-42 (Continued)5.

NPV Calculations under different assumptions regarding the discount rate (required rate of return) and annual after-tax net cash inflows. Assume a ten-year life and an initial investment outlay of $6,000.

DiscountPV AnnuityAnnual Net After-Tax Cash Flow

RateFactor$500$1,000$2,000

10%6.145($2,928)$145$6,290

15%5.019($3,491)($981)$4,038

20%4.192($3,904)($1,808)$2,384

PROBLEMS

20-44 Equipment Replacement Decision; Strategy (60 min)

1. & 3. PV/

Annuity Present After-tax Cash Flows (000s)

Factor Value 0 1 2 3 4 5

Overhaul AccuDrilOperating Cost1

(48.0)(48.0)(38.4)(38.4)(38.4)

Overhaul cost

(100.0)

Tax savings on deprec.2 4.0 4.0

16.0

16.0

16.0

Other Expenses3

(57.0)(57.0)(57.0)(57.0)(57.0)Net after-tax cash flows:

Year 1 0.893 ($90,193)(101.0)

Year 2 0.797 (160,197)

(201.0)

Year 3 0.712 ( 56,533)

(79.4)

Year 4 0.636 ( 50,498)

(79.4)

Year 5 0.567 ( 45,020)

(79.4)

Total PV

($402,441)Buy RoboDril 1010K

Net Equip. Purchase4 1.000 ($240,000)(240.0)

Operating Cost5 3.605 (86,520)

(24.0)

(24.0)(24.0)(24.0)(24.0)

Tax savings on depr.6 3.605 69,216 19.2 19.2 19.2 19.2 19.2

Other expenses7 3.605 (118,965)

(33.0) (33.0) (33.0) (33.0)(33.0)

Salvage value8 0.567 17,010

30.0

Total PV ($359,259) PV difference in cash flow between alternatives= $402,441 $359,259 = $43,182 in favor of RoboDril20-44 (Continued-1)NOTES

1Years 1 and 2: $10 per hour x 8,000 hours x (1 t) =

$48,000

Years 3, 4, and 5: $48,000 x (1 20%) =

$38,400

2Years 1 and 2:

Depreciation expense per year (SL basis):

($120,000 $20,000) ( 10 =

$10,000

Income Tax Rate (t)

x 0.40

Tax savings on depreciation, Years 1 and 2

$ 4,000 Years 3, 4, and 5:

Book value before overhaul (end of original useful life)

$ 20,000

Overhaul cost, Year 3

100,000

Total amount to be depreciated

$120,000

Number of years

( 3

Depreciation expense per year

$ 40,000

Income Tax Rate (t)

x 40%

Tax savings on depreciation, Years 3, 4, and 5

$ 16,0003 $95,000 x (1 t) = $95,000 x 0.60 = $57,0004 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/hour x 4,000 hours) x (1 t) = $40,000 x 0.60 =

$24,0006 Depreciation expense per year: $240,000 ( 5 Years =

$48,000

Income Tax Rate (t)

x 0.40

Annual Tax savings on depreciation deduction

$19,2007 $55,000 x (1 t) = $55,000 x 0.60 =

$33,0008 ($50,000 - $0) x (1 t) = $50,000 x 0.60 =

$30,00020-44 (Continued-2)2.

Net After-tax Cash Flows Difference in Cumulative

Year AccuDril RoboDril Cash Flows 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

Thus, the payback period for investing in the new machine is 2-plus years. Using a linear interpolation method, we estimate the payback period as:

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

20-46

Comparison of Capital Budgeting Techniques; Sensitivity Analysis (50 min)

1. Effects of the new equipment on operating income after tax:

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

Times: Number of units x 10,000

Total cost of goods sold

1,350,000

Gross margin

$ 600,000

Operating Expenses:

Variable marketing: Cost per unit $ 10

Number of units x 10,000$100,000

Additional fixed marketing cost + 200,000 300,000 Operating income before taxes

$300,000

Income taxes (@30%)

90,000 Operating income after tax

$210,000Thus, the company will increase its after-tax operating income by $210,000 each year.

2.

Years

1 to 3 Year 4 After-tax operating income

$210,000$210,000

Add: increased depreciation expense

200,000200,000

After-tax cash inflow from disposal of equipment

195,000 Total cash inflow

$410,000$605,000The new machine will increase cash inflows by $410,000 in each of the first three years and $605,000 in Year 4.

3.4.

Average investment = ($995,000 + $195,000)/2 = $595,000

Average after-tax operating income = $210,000

Book rate of return (ARR) based on average investment =

$210,000/$595,000 = 35.29%20-46 (Continued-1)

5.

Using PV and Annuity Tables:

PV of after-tax cash inflows (@14%):

Years 1 through 3: $410,000 x 2.322 =$ 952,020

Year 4 ($410,000 + $195,000): $605,000 x 0.592 = 358,160 Total present value future after-tax cash inflows =$1,310,180

Less: Initial investment outlay

995,000

NPV of the proposed investment

$ 315,180

Using the NPV Function in Excel:

Thus, the estimated NPV of the investment = $315,078 (note the rounding error that occurs when using the PV and annuity factors)

6. Trial-and-Error Approach (initial investment outlay = $995,000):

PV of cash flows @ 25%:

($410,000 x 1.952) + ($605,000 x 0.410) $1,048,370

PV of cash flows @ 30%:

($410,000 x 1.816) + ($605,000 x 0.350)$ 956,310

Difference in PV of after-tax cash inflows$ 92,060

Thus, the estimated IRR for this investment is:

Based on the built-in function in Excel, the estimated IRR of this project = 27.80%, as follows:

20-46 (Continued-2)

7. a.Based on an estimated NPV of $315,078 (part 5, above), the PV of any after-tax increase in variable costs associated with units produced by the new machine = $315,078. Thus, the annual after-tax increase that would be permissible = $315,078/2.914 = $108,126.

To convert this annual cost to a pre-tax basis, we would have to divide by the quantity (1 t), where t = the income-tax rate (30.0%). Thus, the maximum increase in pre-tax variable cost = $108,126/0.70 = $154,466.

Therefore, the variable cost per unit can increase by a maximum of $154,466/10,000 units = $15.45 per unit. At this increase, the new equipment would generate a rate of return of exactly 14%its cost of capital.

b.The maximum pre-tax decrease in selling price = $154,466 (see (a) above). On a per-unit basis, for all units sold, the maximum decrease in unit selling price is therefore equal to $7.72 (rounded), that is, $154,466/20,000 units. This would represent a decrease of approximately 4% ($7.72/$195.00).20-48Capital Budgeting with Sum-of-the-Years-Digits Depreciation; Spreadsheet Application (25 min)

20-50 Determine Initial Investment Based on Internal Rate of Return (10 min)

Let C be the cost of the machine. Then,

after-tax cash flow per year x annuity factor for 6 years, 10% = C

[$20,000 (($20,000 C/6) x 0.20)] x 4.355 = C

[$20,000 $4,000 + 0.03333C] x 4.355 = C

$69,680 + 0.14517C = C

C = $69,680/0.8548 = $81,51620-52 Machine Replacement and Sensitivity Analysis without Taxes

(40 - 50 min)

Net additional cash outlay for the new machine (@ March 5, 2008):

$8,000 $3,000 = $5,0001. 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 (cash)

($750)

Difference in annual pre-tax income (reduction in expenses)

$390

Loss on trade-in of existing asset (at March 5, 2008) =

book value of asset trade-in value = ($5,000 $400) $3,000

= $1,600 (this loss complicates the determination of ARR, but not

NPV or IRR for the proposed investment)

Book values: Old New

3/5/2008 ($5,000 $400 deprec.) $4,600$8,000

3/5/2018

600 400

Average Investment (Book Value)

$2,600$4,200

Therefore, the incremental average investment on the new machine

= $4,200 - $2,600 = $1,600

The average incremental income, including recognition of the loss on disposal of the

existing machine, is $130, as follows:

Ten-Year Difference in Pre-tax Income = 10 x $390 = $3,900

Less: Loss on disposal of existing asset = $4,600 - $3,000 = ($1,600)

Total income difference in favor of new machine = $2,300

Average annual income difference = $230Thus, under the specified treatment of the loss on disposal of the existing machine, the ARR of the proposed replacement decision is slightly over 14%, as follows:

20-52 (Continued)

Students should be alerted to other possible treatments for the loss and to the fact that this is a good example of one of the ambiguities associated with the use of the ARR for capital investment decision-making.

c.NPV= ($750 x 5.650) ($8,000 $3,000) [($600 - $400) x 0.322]

= $4,237.50 $5,000.00 $64.40 = ($826.90) d.Given a negative NPV, we know that the IRR must be less than the discount rate (12%). We are looking for a discount rate that produces a PV of future cash inflows = $5,000 (net investment outlay for the new machine). We try, somewhat arbitrarily, 7% and 8%, as follows:

PV of net cash inflows at 7% = ($750 x 7.024) ($200 x 0.508)= $5,166

PV of net cash inflows at 8% = ($750 x 6.710) ($200 x 0.463)= 4,940

Difference = $ 226

( the estimated IRR = 7.73%, as follows:

2.No, because NPV < $0 (NPV is $826.90). Note that the decision based on the ARR is ambiguous.

3.Because the expected NPV of the project is negative, the firm would have to realize operating cost savings greater than those originally assumed. Let the required pre-tax annual savings = Y. Then, to make NPV = $0, we must have:

PV of Cash Savings = Original Investment Outlay

5.650Y - ($200 x 0.322) = $5,000

5.650Y = $5,064.40

Y = $896.35

(That is, the maximum savings per year before the decision not to invest is changed. This revised amount represents a change of approximately 19.5% above the current estimate of $750. Note that at annual cash savings of $896.35, the IRR on the proposed investment would exactly equal 12%, the companys cost of capital.)20-54Capital Budgeting with Sensitivity Analysis (45 min)

1.Expected annual net cash inflows ($600,000 + $100,000)=

$700,000

Income taxes at 30%

=

210,000After-tax net cash inflows

=

$490,000

The buyer is essentially purchasing an eight-year stream of after-tax rental incomes and income-tax savings associated with the depreciation deduction. Thus, a rational purchase price would be the PV of these future cash flows, using 12% as the discount rate. Note, however, that the depreciation deduction is a function of the purchase price, which we are trying to estimate. Therefore, let P denote the maximum price the buyer would be willing to pay. The amount is approximately $3 million, as follows:

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=$2,991,6682.From Meidis perspective, the selling price should be set such that it would cover three things: (1) the PV of the after-tax rental incomes she is foregoing, (2) capital gains taxes she would have to pay on the sale of the real estate, and (3) the sales commission (5%) she has to pay the real estate broker. Thus, if this is the case,

Let S denote the minimum price Meidi would be willing to accept

S=[$460,000 x A.10, 8] + [(S $800,000 0.05S) x 0.40] + 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=$3,744,0353.MACRS depreciation increases to the buyer the PV of the depreciation write-offs (compared to the use of the SL method, as in (1) above). Thus, to the extent the buyer could realize these tax savings, the buyer would be willing to pay a higher price for the property.

As in (1) above, we represent the maximum price the buyer would be willing to pay as the sum of two components: the PV of after-tax rental incomes ($2,434,320) plus the PV of the tax savings due to the depreciation deductions over the life of the property. This second component is represented as 0.2214397P (where P represents the purchase price, and therefore depreciable cost, of the property), as follows:

20-54 (Continued)

(1)

MACRS (2) (3)

(2) x (3)

Year Depreciation1 Tax Effect2PV Factor Present Value

1 0.2000P0.06000P0.8930.0535800P

2 0.3200P0.09600P0.7970.0765120P

3 0.1920P0.05760P0.7120.0410112P

43 0.1152P0.03456P0.6360.0219801P

5 0.1152P0.03456P0.5670.0195955P

6 0.0576P0.01728P0.5070.0087609P

0.2214397P

Notes:

1See text, Exhibit 20.6 for MACRS depreciation rates, 5-year property

2Assuming a 30% marginal income-tax rate.

3First year of switching to SL depreciation method.

Thus, the maximum amount that a rational buyer would be willing to pay has increased to $3,126,694, as follows:

P= $2,434,320 + 0.2214397P

0.7785603P= $2,434,320

P= $3,126,694 (an increase of $135,026 over the amount calculated above in (1))

20-56 Machine Replacement with Tax Considerations (30 - 45 min)Present Value of Costs with the Original Equipment:

Present value of tax savings from depreciation deductions:

($2,500,000 ( 4) x 0.45 x 2.577 =

($724,781)

Present value of cash 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 = $1,804,614Present value of Costs with the New Machine:

Initial outlay cost

$2,000,000Present value of tax savings from depreciation deductions:

Beginning Depreciation TaxTax Discount

YearBook Value Expense1 Rate Savings Factor

1

$2,000,000 $1,333,333x 0.45 = $600,000 x 0.926=

($555,600)

2

666,667 444,445x 0.45 = 200,000 x 0.857=

(171,400)

3

222,223 222,223x 0.45 = 100,000 x 0.794=

(79,400)

Cash proceeds from sale of the old machine

($300,000)

Tax savings related to loss on disposal of the old machine:

($1,875,0002 $300,000) x 0.45 = ($708,750)

Present value of cash operating costs: $1,000,000 x (1 0.45) x 2.577 = $1,417,350

Present value of costs with the new machine$1,602,200

Notes:

1DDB depreciation charges were calculated using the VDB function in Excel, as follows:

20-56(Continued)

2Book value of old asset at time of sale =

Original cost accumulated depreciation =

$2,500,000 [($2,500,000/4) x 1 year] =

$2,500,000 $625,000 = $1,875,000

PV of savings from using the new machine:

$1,804,614 $1,602,200 = $202,414The total cost of the new machine, including the purchase cost and the cash operating cost in each of the three years, is in present value terms $202,414 below the total cost of continuing with the original equipment. Therefore, from a purely financial standpoint, the purchase of the new machine is a good investment.

20-58Equipment Replacement with MACRS Depreciation (35 - 45 min)

1.Per-unit profit margin of the additional units:

Sales price per unit

$3,500

Current manufacturing cost

- 2,450Current gross margin per unit

$1,050

Cost savings per unit with the new machine

+ 150Gross margin (cash flow) per unit for the additional units

$1,200

Net cash inflows:

Present Discount

Item Description Value Factor 2010 2011 2012 2013 Purchase cost($608,000)

Installation cost($12,000)

After-tax proceeds from disposing old $30,000

Gross margin/unit (above)

$1,200$1,200$1,200$1,200

Additional units

30 50 50 70Pre-tax cash flow from additional units (000)

$ 36$ 60$ 60$ 84

Efficiency savings (000)

125 125 125 125Total increase in pre-tax incomes/cash flow (000)

$161$185$185$209

Income taxes (000)

64.4 74 74 83.6Increase in after-tax cash flow before depreciation (000)

$96.60$111$111$125.4

After-tax proceeds from disposal ($80,000 x 0.6)

48

Tax savings from depreciation (000)

81.84 111.60 37.20 17.36After-tax cash inflows

$155,2430.870 $178.44

$168,286 0.756

222.60

$97,5160.658

148.20

$109,115 0.572

190.76

Net Present Value (NPV)

($59,840)VacuTech can expect to have a negative NPV of $59,840 if it purchases the new pump.

20-58 (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

Competitor reaction

20-60Risk and NPV (45 min)

1. PV of future cash inflows @ 12% = $275,000 x 6.194 = $1,703,350

Less: Initial investment outlay, year 0 = $1,500,000

Net present value (NPV) =

$ 203,350

Since the NPV > $0, the project should be accepted.

2. PV of future cash inflows @ 15% = $275,000 x 5.421 = $1,490,775

Less: Investment outlay, year 0 = $1,500,000

Net present value (NPV) = $(9,225)

Since the NPV < $0, the project should not be accepted.

3.The break-even initial investment outlay is the amount that would produce a NPV = $0, given the annual after-tax flows of $275,000 and a discount rate of 15.00%. We can use Excel to solve, in two steps, for this break-even amount = $1,490,670:

Step 1: Estimate the Projects NPV (compare with 2 above)

20-60 (Continued)

Step 2: Complete the following goal seek dialog box: 4.Many firms raise the discount rate in evaluating a particular capital investment 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.

An alternative is to use a direct approach 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. Some believe that using a direct approach (if possible) is better than simply using a higher discount rate. In any case, the topic of risk adjustments is handled more completely in financial management textbooks.

20-62 Uneven Cash Flows (40 min)

1.Present value of net cash inflows:

Year 1

-0-

Year 2

$1,000,000 x 0.797 =$ 797,000

Year 3

$1,000,000 x 0.712 = 712,000

Year 4

$2,500,000 x 0.636 =1,590,000

Years 5-10($3,000,000 x 4.111) x 0.636 =7,843,788

Present value of net cash inflows $10,942,788

Less: Initial investment outlay, year 0

15,000,000 NPV (@12%)

$(4,057,212)

Alternatively, the built-in functions in Excel can be used to estimate the NPV and the IRR of this project, as follows:

2. The maximum purchase price the seller would be willing to offer, given a discount rate of 12% and the indicated cash flows, would be slightly less than $11,000,000, as follows:

20-62 (Continued)

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Blocher, Stout, Cokins, Chen, Cost Management, 4/e 20-1 The McGraw-Hill Companies, 2008Blocher, Stout, Cokins, Chen, Cost Management, 4/e 20-4 The McGraw-Hill Companies, 2008Blocher, Stout, Cokins, Chen, Cost Management, 4/e 20-5 The McGraw-Hill Companies 2008

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