FCF 9th Edition Chapter 11

Chapter 11Problems 1-32

Input boxes in tanOutput boxes in yellowGiven data in blueCalculations in redAnswers in green

NOTE: Some functions used in these spreadsheets may require that the "Analysis ToolPak" or "Solver Add-In" be installed in Excel.To install these, click on the Office button then "Excel Options," "Add-Ins" and select"Go." Check "Analyis ToolPak" and "Solver Add-In," then click "OK."

NOTE: Some functions used in these spreadsheets may require that the "Analysis ToolPak" or "Solver Add-In" be installed in Excel.

Chapter 11Question 1

Input area:

Variable material cost $ 5.43 Variable labor cost $ 3.13

b. Fixed costs $ 720,000 Production 280,000

c. Sales price $ 19.99 Depreciation $ 220,000

Output area:

a. Total variable cost $ 8.56

b. Total variable cost/year $ 3,116,800

c. Cash breakeven 62,992.13 Accounting breakeven 82,239.72


Input area:

Variable material cost $ 24.86 Variable labor cost $ 14.08 Sales price $ 135.00 Production 120,000 Fixed costs $ 1,550,000 Extra order 5,000

Output area:

Total costs $ 6,222,800 Marginal cost $ 38.94 Average cost $ 51.86 Minimum acceptable revenue $ 194,700 Additional units should be produced only if the costof producing those units can be recovered.


Input area:

Price/unit $ 1,900 Variable cost/unit $ 240 Fixed costs $ 4,800,000 Quantity 95,000 Price accuracy 15%Variable cost accuracy 15%Fixed cost accuracy 15%Quantity accuracy 15%

Output area:

Scenario Unit sales Unit price Unit variable cost Fixed costsBase case 95,000 $ 1,900.00 $ 240.00 $ 4,800,000 Best case 109,250 $ 2,185.00 $ 204.00 $ 4,080,000 Worst case 80,750 $ 1,615.00 $ 276.00 $ 5,520,000


Output area:

An estimate for the impact of changes in price on the profitability of the project can be found from

the NPV at any two different price levels and forming the ratio of the changes in these parameters.Whenever a sensitivity analysis is performed, all other variables are held constant at their base-casevalues

the sensitivity of NPV with respect to price: DNPV/DP. This measure can be calculated by finding

An estimate for the impact of changes in price on the profitability of the project can be found from

the NPV at any two different price levels and forming the ratio of the changes in these parameters.Whenever a sensitivity analysis is performed, all other variables are held constant at their base-case

P. This measure can be calculated by finding


Input area:

Initial cost $ 724,000 Project life 8 Units sales 90,000 Price/unit $ 43.00 Variable cost/unit $ 29.00 Fixed costs $ 780,000 Tax rate 35%Required return 15%

b. New quantity for calculation 95,000 Projected sales change (500)

c. New VC for calculation $ 30.00 Projected VC change $ (1.00)

Output area:

a. Depreciation per year $ 90,500 Accounting breakeven 62,179 DOL 9.619

b. Base OCF $ 343,675 Base NPV $ 818,180.22 New quantity 95,000 OCF $ 389,175 NPV $ 1,022,353.35

$ 40.835 For a sales change of (500)the NPV would change $ (20,417.31)

c. New variable cost $ 30.00 OCF $ 285,175

$ (58,500.00)If variable costs change by $ (1.00)then OCF would change by $ 58,500.00

DNPV/DQ

DOCF/DVC


Input area:

Initial cost $ 724,000 Project life 8 Units sales 90,000 Price/unit $ 43.00 Variable cost/unit $ 29.00 Fixed costs $ 780,000 Tax rate 35%Required return 15%Price uncertainty 10%Quantity uncertainty 10%Variable cost uncertainty 10%Fixed cost uncertainty 10%

Output area:

Annual depreciation $90,500

Scenario Unit sales Unit price Unit variable cost Fixed costsBase case 90,000 $ 43.00 $ 29.00 $ 780,000 Best case 99,000 $ 47.30 $ 26.10 $ 702,000 Worst case 81,000 $ 38.70 $ 31.90 $ 858,000

Best-case OCF $ 939,595.00 Best-case NPV $ 3,492,264.85

Worst-case OCF $ (168,005.00) Worst-case NPV $ (1,477,892.45)


Input area:

Unit price Unit variable cost Fixed costs Depreciation a. $ 3,020 $ 2,275 $ 14,000,000 $ 6,500,000 b. 38 27 73,000 150,000 c. 11 4 1,200 840

Output area:

a. Accounting breakeven 27,517 Cash breakeven 18,792

b. Accounting breakeven 20,273 Cash breakeven 6,636

c. Accounting breakeven 291 Cash breakeven 171


Input area:

Accounting breakeven Unit price Unit variable cost Fixed costs Depreciation a. 112,800 $ 41 $ 30 $ 820,000 ? b. 165,000 ? 43 3,200,000 $ 1,150,000 c. 4,385 98 ? 160,000 105,000

Output area:

a. Depreciation $ 420,800

b. Unit price $ 69.36

c. Unit variable cost $ 37.57


Input area:

Price per unit $ 57.00 Variable cost per unit $ 32.00 Fixed costs $ 9,000 Required return 12%Initial investment $ 18,000 Life 4

Output area:

Accounting breakeven 540 Cash breakeven 360 OCF $ 5,926.22 Financial breakeven 597 DOL 2.519


Input area:

Accounting breakeven 15,500 Cash breakeven 13,200 Life 5 Fixed costs $ 140,000 Variable cost/unit $ 24 Requried return 16%

Output area:

Price $ 34.61 Depreciation $ 24,394 Initial investment $ 121,970 OCF $ 37,250.69

Financial breakeven 16,712


Input area:

Initial output level 65,000 DOL 3.40 New output level 70,000

Output area:

26.15%

The new level of operating leverage islower since FC/OCF issmaller.

DOCF


Input area:

Initial output level 65,000 DOL 3.40 New output level 70,000 Fixed costs $ 130,000 Units 58,000

Output area:

OCF $ 54,167

% change in Q -10.77%

% change in OCF -36.62%

New OCF $ 34,333

New DOL 4.786


Input area:

Fixed costs $ 73,000 Units sold 8,000 OCF $ 87,500 New units sold 8,500

Output area:

Original DOL 1.8343

6.25%

11.46%

New OCF $ 97,531.25

New DOL 1.7485

%DQ

%DOCF

Chapter 11Questions 14,15

Input area:

Initial output 10,000 Initial DOL 2.35 Initial OCF $ 43,000 New output 11,000 New output 9,000

Output area:

Fixed costs = $ 58,050.00 OCF at 11,000 = $ 53,105.00 OCF at 9,000 = $ 32,895.00

DOL at 11,000 = 2.0931 DOL at 9,000 = 2.7647


Output area:

a. IRR = 0% payback = N years

b. IRR = -100% NPV = -I

c. IRR = R% payback < N years NPV = 0

NPV = I[(I/N)(PVIFA R%,N) - 1]

payback = negative

Chapter 11Questions 17-18

Input area:

Initial fixed assets $ 490,000 Life of project (yrs) 4 Price $ 32 Variable costs $ 19 Fixed costs $ 210,000 Quantity sold 110,000 Tax rate 34%Change in quantity 1,000

Output area:

OCF at 110,000 units $ 846,850.00 OCF at 111,000 units $ 855,430.00

$ 8.58

DOL at 110,000 units 1.2480

Accounting break-even 25,576

DOL at 25,576 units 2.7143

DOCF/DQ


Input area:

Initial cost $ 1,700,000 Life 4 Unit sales 190 Price/unit $ 18,000 Variable cost/unit $ 11,200 Fixed costs $ 410,000 Required return 12%Tax rate 35%

a. Unit sales uncertainty 10%Variable cost uncertainty 10%Fixed cost uncertainty 10%

b. New fixed costs $ 420,000

Output area:

Upper bound Lower bounda. Unit sales 209 171

Variable cost/unit $ 12,320 $ 10,080 Fixed costs $ 451,000 $ 369,000

Depreciation $ 425,000

Base case OCF $ 722,050.00 Base case NPV $ 493,118.10

Best case OCF $ 984,832.00 Best case OCF $ 1,291,278.83

Worst case OCF $ 486,932.00 Worst case NPV $ (221,017.41)

b. OCF with fixed costs $ 420,000.00

OCF $ 715,550.00 NPV $ 473,375.32

$ (1.974)For every dollar FC increase, NPV changes by: $ (1.974)

c. Cash breakeven 60

d. Accounting breakeven 123 At this level of output, DOL 1.9647 For every 1% increase in unit sales,OCF will increase by 1.9647%

DNPV/DFC


Input area:

Price per unit $ 750 Variable cost per unit $ 330 Marketing study $ 150,000 Sunk costUnit sales 51,000 High price units lost 11,000 High price club's price $ 1,200 High price club's VC $ 650 Cheap club units gained 9,500 Cheap club's price $ 420 Cheap club's VC $ 190 Fixed costs $ 8,100,000 R&D $ 1,000,000 Sunk costProject cost $ 22,400,000 Net working capital $ 1,250,000 Tax rate 40%Cost of capital 10%

Output area:

Initial cash outlayPlant & Equipment $ (22,400,000)NWC $ (1,250,000)Total $ (23,650,000)

New club sales $ 38,250,000 High-priced sales lost (13,200,000)Cheap sales gained 3,990,000 Total sales $ 29,040,000

New club VC $ (16,830,000)High-priced VC saved 7,150,000 Cheap club VC (1,805,000)Total VC $ (11,485,000)

Total Sales $ 29,040,000 Total VC 11,485,000 Fixed costs 8,100,000 Depreciation 3,200,000 EBIT $ 6,255,000 Taxes 2,502,000 Net income $ 3,753,000

OCF $ 6,953,000

Cash flows

t Cash Flow 0 $ (23,650,000)1 6,953,000 2 6,953,000 3 6,953,000 4 6,953,000 5 6,953,000 6 6,953,000 7 8,203,000

Payback period 3.401 NPV $10,841,563.69

IRR 22.64%


Input area:

Project cost $ 22,400,000 Unit sales 51,000 Price per unit $ 750 Variable cost per unit $ 330 Fixed costs $ 8,100,000 Lost high price units lost 11,000 High price club's price $ 1,200 High price club's VC $ 650 Cheap club units gained 9,500 Cheap club's price $ 420 Cheap club's VC $ 190 Marketing study $ 150,000 Sunk costR&D $ 1,000,000 Sunk costNet working capital $ 1,250,000 Tax rate 40%Cost of capital 10%Uncertainty 10%

Output area:

Best case Worst CaseUnit sales (new clubs) 56,100 45,900 Price (new clubs) $ 825 $ 675 VC (new clubs) $ 297 $ 363 Fixed cost $ 7,290,000 $ 8,910,000 Sales lost (high-priced) 9,900 12,100 Sales gained (cheap) 10,450 8,550


Best case Worst CaseNew club sales $ 46,282,500 $ 30,982,500 High-priced sales lost (11,880,000) (14,520,000)Cheap sales gained 4,389,000 3,591,000 Total sales $ 38,791,500 $ 20,053,500

New club VC $ (16,661,700) $ (16,661,700)High-priced VC saved 6,435,000 7,865,000 Cheap club VC (1,985,500) (1,624,500)Total VC $ (12,212,200) $ (10,421,200)

Total Sales $ 38,791,500 $ 20,053,500 Total VC 12,212,200 10,421,200 Fixed costs 7,290,000 8,910,000 Depreciation 3,200,000 3,200,000 EBIT $ 16,089,300 $ (2,477,700)Taxes 6,435,720 (991,080)Net income $ 9,653,580 $ (1,486,620)

OCF $ 12,853,580 $ 1,713,380

Cash flows

t Cash Flow Cash Flow 0 $ (23,650,000) $ (23,650,000)1 12,853,580 1,713,380 2 12,853,580 1,713,380 3 12,853,580 1,713,380 4 12,853,580 1,713,380 5 12,853,580 1,713,380 6 12,853,580 1,713,380 7 14,103,580 2,963,380

NPV $39,568,058.39 ($14,667,100.92)


Input area:

Project cost $ 22,400,000 Unit sales 51,000 Price per unit $ 750 Variable cost per unit $ 330 Fixed costs $ 8,100,000 Lost high price units lost 11,000 High price club's price $ 1,200 High price club's VC $ 650 Cheap club units gained 9,500 Cheap club's price $ 420 Cheap club's VC $ 190 Marketing study $ 150,000 Sunk costR&D $ 1,000,000 Sunk costNet working capital $ 1,250,000 Tax rate 40%Cost of capital 10%New price $ 800 New quantity 52,000

Output area:


New club sales $ 40,800,000 $ 39,000,000 High-priced sales lost (13,200,000) (13,200,000)Cheap sales gained 3,990,000 3,990,000 Total sales $ 31,590,000 $ 29,790,000

New club VC $ (16,830,000) $ (17,160,000)High-priced VC saved 7,150,000 7,150,000 Cheap club VC (1,805,000) (1,805,000)Total VC $ (11,485,000) $ (11,815,000)

Total Sales $ 31,590,000 $ 29,790,000 Total VC 11,485,000 11,815,000 Fixed costs 8,100,000 8,100,000 Depreciation 3,200,000 3,200,000 EBIT $ 8,805,000 $ 6,675,000 Taxes 3,522,000 2,670,000 Net income $ 5,283,000 $ 4,005,000

OCF $ 8,483,000 $ 7,205,000

Cash flows

t Cash Flow Cash Flow 0 $ (23,650,000) $ (23,650,000)1 8,483,000 7,205,000 2 8,483,000 7,205,000 3 8,483,000 7,205,000 4 8,483,000 7,205,000 5 8,483,000 7,205,000 6 8,483,000 7,205,000 7 9,733,000 8,455,000

NPV $18,290,244.48 $12,068,405.23 $148,973.62

DPrice DQuantity

DNPV/DP

$ 1,226.84 DNPV/DQ


Input area:

Additional purchase price $ 5,450 Total annual cost $ 400 Hybrid mpg 25 Sedan mpg 23

a. Gasoline $ 3.60 Years to keep car 6

b. Miles per year 15,000

c. Interest rate 10%

Output area:

a. Total additional cost $ 7,850 Traditional cost per mile $ 0.156522 Hydrid cost per mile $ 0.144000 Cost savings per mile $ 0.012522 Total miles driven 626,910

Miles per year 104,485

b. Total miles 90,000 Cost savings per mile $ 0.08722

Price per gallon $ 25.08

c. PV of annual cost $ 1,742.10 Total discounted cost $ 7,192.10 Discounted savings $ 574,369.44

Miles driven per year 131,879

Discounted savings $ 0.47947

Savings needed per mile $ 0.110091

Price per gallon $ 31.65


Input area:

Initial cost $ 13,000,000,000 Breakeven sales 249

b. Promised return 20%

c. Years for sales 10

Output area:

a. Cash flow per plane $ 52,208,835

b. Cash flow per year $ 2,600,000,000

Planes per year 49.80

c. Cash flow per year $3,100,795,839

Planes per year 59.39


Input area:

Quantity 85 Sales price $ 40,000 Variable cost $ 20,000 Fixed costs $ 500,000 Operating cash flow $ 1,200,000 Initial investment $ 3,500,000 Tax rate 38%Required return 20%*Depreciation staight-lineover life 5

Output area:

a. From the tax shield definition of OCF:OCF = [(P - V)Q - FC](1 - t) + tD(OCF - tD)/(1 - t) = (P - v)Q - FC{FC + [(OCF - tD)/(1 - t)]} / (P - v) = Q

b. Depreciation $ 700,000 Cash breakeven 25 Accounting breakeven 60 OCF at financial breakeven $ 1,170,328.96 Financial breakeven 98

c. At the accounting breakeven point, net income = 0, so OCF = NI + D = D

= (FC + D)/(P - v) = (FC + OCF)/(P -v)The tax rate has cancelled out in this case.

Qa = [FC + [(D - tD) / (1 - t)]} / (P - v)


Output area:

DOL = %DOCF / %DQ = {[(OCF1 – OCF0)/OCF0] / [(Q1 – Q0)/Q0]}

OCF1 = [(P – v)Q1 – FC](1 – t) + tD; OCF0 = [(P – v)Q1 – FC](1 – t) + tD;

OCF1 – OCF0 = (P – v)(1 – t)(Q1 – Q0)

(OCF1 – OCF0)/OCF0 = (P – v)( 1– t)(Q1 – Q0) / OCF0 ;

[(OCF1 – OCF0)/OCF0][(Q1 – Q0)/Q0] = [(P – v)(1 – t)Q0]/OCF0 =

[OCF0 – tD + FC(1 – t)]/OCF0 ;

DOL = 1 + [FC(1 – t) – tD]/OCF0


Input area:

Quantity 35,000 Initial investment $ 3,200,000 Project life 5 Fixed costs $ 450,000 Variable costs $ 185 Salvage value $ 500,000 Selling price $ 230 Net working capital $ 360,000 Required return 13%Tax rate 38%

b. Initial cost uncertainty 15%Salvage value uncertainty 15%Price uncertainty 10%NWC uncertainty 5%

Output area:

a. Depreciation $ 640,000 Aftertax salvage value $ 310,000 OCF $ 940,700.00 NPV $ 112,308.60

b. Best case Worst case Initial cost $ 2,720,000 $ 3,680,000 Salvage value $ 575,000 $ 425,000 Price $ 253 $ 207 NWC $ 342,000 $ 378,000 Aftertax salvage value $ 356,500 $ 263,500

Best case OCF $ 1,403,320 Best case NPV $ 2,252,918.79

Worst case OCF $ 478,080

Worst case NPV $ (2,028,301.58)


Input area:

Quantity 35,000 Initial investment $ 3,200,000 Project life 5 Fixed costs $ 450,000 Variable costs $ 185 Salvage value $ 500,000 Selling price $ 230 Net working capital $ 360,000 Required return 13%Tax rate 38%New quantity 36,000

Output area:

Depreciation $ 640,000 Aftertax salvage value $ 310,000

Units sold 35,000 OCF $ 940,700 NPV $ 112,308.60


$ 27.90 $ 98.13

You wouldn't want Q to fall below the point whereNPV = 0.

1,144 Minimum Q 33,856

DOCF/DQDNPV/DQ

DQ


Input area:


Output area:




$ 27.90 $ 98.13

Cash breakeven 1,283

Accounting breakeven 24,222

You wouldn't want Q to fall below the point whereNPV = 0.

1,144

DOCF/DQDNPV/DQ

DQ

Financial breakeven 33,856


Input area:


Output area:


DOL 1.03806 Thus, a 1% rise in Q leads to a 1.03806%rise in OCF. If Q rises to 36,000

2.8571%2.9659%

2.9659%

If Q rises by 1,000 units, then OCF will rise by 2.9659%

then DQ =so %DOCF =

From #28, DOCF/OCF

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FCF 9th Edition Chapter 11

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