= Value given in problem Given. Solution:

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Clifton Hampton
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1 Instant download and all chapters s Manual Valuation The Art and Science of Corporate Investment Decisions 3rd PROBLEM 2-1 : = Formula/Calculation/Analysis required Discount rate 10% = Qualitative analysis or Short answer required Cash Flow (s) Present Value a. $500 5 $ 310 b. $500 5 $ 1,895 c. $ $ 4,957 d. $ $ 5,000

2 PROBLEM 2-2 = Formula/Calculation/Analysis required a. = Qualitative analysis or Short answer required Initial investment $ 4,000, Annual Cash Flows 500, Project Life 10 : IRR = 4.28% b. Cash Flow 0 $ (4,000,000.00) 1 500, , , , , , , , , , , , , , : IRR = 7.94%

3 PROBLEM 2-3 Growth rate in EBIT for years 1-5 5% EBIT (year 1) $ 100,000 = Formula/Calculation/Analysis required CAPEX for year 0 $ 400,000 = Qualitative analysis or Short answer required Depreciable life of fixed assets 5 years Tax rate 30% New working capital for years % of EBIT EBIT $ 100,000 $ 105,000 $ 110,250 $ 115,763 $ 121,551 Taxes (30,000) (31,500) (33,075) (34,729) (36,465) NOPAT $ 70,000 $ 73,500 $ 77,175 $ 81,034 $ 85,085 Plus: Depreciation 80,000 80,000 80,000 80,000 80,000 Less: CAPEX (400,000) Less: Net working capital needs (See Note 1) (20,000) (1,000) (1,050) (1,103) (1,158) 24,310 Plus: Salvage value of the fixed assets in year 5 - Firm Free Cash Flow (FFCF) $ (420,000) $ 149,000 $ 152,450 $ 156,073 $ 159,876 $ 189,396 Note 1: At the end of year 5 the firm liquidates all of it's investment in net operating working Net Fixed Assets (beginning of the year) $ - $ 400,000 $ 320,000 $ 240,000 $ 160,000 $ 80,000 Plus: CAPEX 400, Less: Depreciation Expense for the - (80,000) (80,000) (80,000) (80,000) (80,000) Net Fixed Assets (end of the year) $ 400,000 $ 320,000 $ 240,000 $ 160,000 $ 80,000 $ -

4 PROBLEM 2-4 Recall that the NFA balance for any year t can be defined using the following equation: NFA(t) = NFA(t-1) + Capex(t) - Depr(t) Solving for Capex(t) Capex(t) = NFA(t) - NFA(t-1) + Depr(t) (i) In this definition for Capex(t) we see that the change in NFA is only part of the Capex. To increase the firm's NFA requires Capex equal to the sum of the change in NFA and depreciation expense. Note too that Capex can be computed from the following relationship: Gross PP&E(t) = Gross PP&E(t-1) + Capex(t) or Capex(t) = Gross PP&E(t) - Gross PP&E(t-1) (ii)

5 PROBLEM 2-5 Sales Expansion percentage 10% Original estimate of FCF (2008) $ 1,383,436,000 Revised estimate of FCF (2008) 1,617,105,293 Assumptions and Forecasts Price/Unit Variable Cost/Unit Constant 1,434,124 39,996,040 Cost of capital 18% Exponent Initial Investment $200,000,000 % 80% 70% Depreciatiable life 5 years Initial Value 8, $ 9, Fixed Cash Operating 50,000,000 $ $ Costs Tax rate 30% Total Market Unit Sales (000) (000) Market Share Price/Unit Cumulative Units ,000 20% 8,000 11,000 $ 27, ,500 20% 5, ,000 20% 4,783 49, ,000 20% 4,249 71, ,500 20% 3,974 88,000 Table 2-1 Market Demand and Revenue Projections for Lexion's LCD Fabricating Plant Projected Lecion Total Market Lecion's Sale Price per Revenue Forecast Cumulative Units Unit Sales (000) Unit Sales (000) Unit (000) (millions) ,000 2,200 17,600,000 2,200 8,000 $ $ 5, ,500 3,300 5,779 19,071, ,000 4,400 4,783 21,044,856 9, ,000 4,400 4,249 18,695,551 14, ,500 3,300 3,974 13,115,102 17,600 Table 2-2 Variable and Fixed Costs per unit Estimates for the Lecion LCD Plant Lecion's Estimated Annual Variable Estimated Fixed Estimated Estimated Annual Variable Operating Cash Operating Cash Operating Depreciation Total Expenses Units Sold (000) Cost per Unit Cost (000) Costs (000) Expense (000) Expenses (000) ,200 $ (9,000) (19,800,000) (50,000) (40,000) (19,890,000) ,300 (5,939) (19,599,741) (50,000) (40,000) (19,689,741) ,400 (4,389) (19,311,937) (50,000) (40,000) (19,401,937) ,400 (3,632) (15,982,466) (50,000) (40,000) (16,072,466) ,300 (3,264) (10,772,094) (50,000) (40,000) (10,862,094) Table 2-3 Estimated Project Free Cash flow for the Lecion LCD Investment Project Free Contribution Revenues (000) Total Expenses (000) NOPAT (000) Depreciation (000) Cash Flows (000) Margin ,600,000 $ (19,890,000) (1,603,000) $ 40,000 $ (1,563,000) -12.5% $ $ -2.8% ,071,263 (19,689,741) (432,935) 40,000 (392,935) ,044,856 (19,401,937) 1,150,044 40,000 1,190, % ,695,551 (16,072,466) 1,836,160 40,000 1,876, % ,115,102 (10,862,094) 1,577,105 40,000 1,617, % Table 2-4 Valuation and Discounting Cash Flows Estimated Project FCF Discount Present Value (000) Factor (000) $ 2003 (200,000) (200,000) 2004 (1,563,000) (1,324,576) 2005 (392,935) (282,200) ,190, , ,876, , ,617, ,852 Project Intrinsic Value $792,075 Initial Capital Expenditure in 2003 $ (200,000) Net Present Value $592,075 Internal Rate of Return 29.98%

6 PROBLEM 2-6 TCM Petroleum Dec-14 Dec-15 Sales $ 12, $ 13, = Formula/Calculation/Analysis required Cost of Goods Sold (9,755.00) (10,591.00) = Qualitative analysis or Short answer required Gross Profit 2, , Selling, General, & Administrative Expense (704.00) (698.00) Operating Income Before Deprec. 1, , Depreciation, Depletion, & Amortization (794.00) (871.00) Operating Profit (NOI) , Interest Expense (265.00) (295.00) Non-Operating Income/Expense Special Items Pretax Income , Total Income Taxes (340.80) (425.60) Net Income $ $ CAPEX estimated as follows: CAPEX = NET PP&E ending + Depreciation - NET PP&E beginning Purchase of PP&E (CAPEX) 875 1,322 Increase in Net Working Capital 102 (430) Increase in Net Working Capital estimated as follows: TCM's average tax rate 40% 40% NWC NWC 2014 a. FCF Calculations for Note that we are calculating only the firm's FCF from its Net Operating Income (NOI) $ 958 $ 1,208 operations. Specifically, in 2014 TCM had nonoperating NOI(1-T) = NOPAT income of $151 million and in in 2015 the firm had Plus: Depreciation Expense nonoperating income plus special items totaling $159 Less: CAPEX (875) (1,322) million. Although these items are not from the firm's Less: Working Capital Investment (102) 430 normal operations, they do constitute cash flows and if we Firm Free Cash Flow $ 392 $ 704 were trying to value the firm we would want to include their value in the analysis (more about this in Chapter 8). b. Estimated FCF for NOI (Growing at 10% per year) $ 1,329 $ 1,462 $ 1,608 $ 1,769 $ 1,945 NOI (1-.40) = NOPAT ,061 1,167 Plus: Depreciation Expense 1,003 1,103 1,203 1,303 1,403 Less: CAPEX (1,000) (1,000) (1,000) (1,000) (1,000) Less: Working Capital Investment (100) (100) (100) (100) (100) Firm Free Cash Flow (FCF) $ 700 $ 880 $ 1,068 $ 1,264 $ 1,470

7 PROBLEM 2-7 Incremental revenue growth for years % Revenues (current) $ 9,000,000 = Formula/Calculation/Analysis required Incremental Revenues $ 900,000 = Qualitative analysis or Short answer required CAPEX for year 0 $ 1,860,000 CAPEX for years 1-5 $ - Maintenance expense for years 1-5 $ 120,000 per year Depreciable life of ovens 5 years Depreciation Expense $ 372,000 Tax rate 30% Discount Rate 9% Incremental Revenues $ 900,000 $ 900,000 $ 900,000 $ 900,000 $ 900,000 Incremental Depreciation (372,000) (372,000) (372,000) (372,000) (372,000) Incremental maintenance expense (120,000) (120,000) (120,000) (120,000) (120,000) Incremental EBIT $ 408,000 $ 408,000 $ 408,000 $ 408,000 $ 408,000 Taxes (122,400) (122,400) (122,400) (122,400) (122,400) NOPAT $ 285,600 $ 285,600 $ 285,600 $ 285,600 $ 285,600 Plus: Depreciation 372, , , , ,000 Less: CAPEX (1,860,000) Less: New working capital needs Project Free Cash Flow (PFCF) $ (1,860,000) $ 657,600 $ 657,600 $ 657,600 $ 657,600 $ 657,600 Net Present Value $ 697,835 Internal Rate of Return 23%

8 PROBLEM 2-8 Initial Investment in software $ (55,000) Technician training cost $ (10,000) = Formula/Calculation/Analysis required Hourly Rate $ = Qualitative analysis or Short answer required Tax Rate 30% Discount Rate 9% Additional Investment per year for $ 15,000 software upgrades % Reduction in hours of technician 25% time for installation Total hours of installation per year 6, Rev $ 37,500 $ 37,500 $ 37,500 $ 37,500 $ 37,500 Upgrade Expense (15,000) (15,000) (15,000) (15,000) (15,000) EBIT $ 22,500 $ 22,500 $ 22,500 $ 22,500 $ 22,500 Less: Taxes (6,750) (6,750) (6,750) (6,750) (6,750) NOPAT $ 15,750 $ 15,750 $ 15,750 $ 15,750 $ 15,750 Plus: DEP Less: CAPEX (65,000) Project Free Cash Flows (PFCF) $ (65,000) $ 15,750 $ 15,750 $ 15,750 $ 15,750 $ 15,750 NPV $ (3,738) IRR 6.76% Payback Period 4.13

9 PROBLEM 2-9 Investment (CAPEX in year 0) $ (600,000) Depreciable life 5 years = Formula/Calculation/Analysis required Initial units for year 1 100,000 = Qualitative analysis or Short answer required Revenue per unit 1.50 Growth Rate per year in units rec 25% Tax Rate 30% Disposal cost per unit $ 0.20 Required Return 15% : Part a Units recycled 100, , , , ,141 Revenues $ 150,000 $ 187,500 $ 234,375 $ 292,969 $ 366,211 Depreciation Expense (120,000) (120,000) (120,000) (120,000) (120,000) EBIT $ 30,000 $ 67,500 $ 114,375 $ 172,969 $ 246,211 Less: Taxes (9,000) (20,250) (34,313) (51,891) (73,863) NOPAT $ 21,000 $ 47,250 $ 80,063 $ 121,078 $ 172,348 Plus: Depreciation expense 120, , , , ,000 Less: CAPEX (600,000) Project Free Cash Flows $ (600,000) $ 141,000 $ 167,250 $ 200,063 $ 241,078 $ 292,348 NPV 63,804 IRR 18.87% : Part b : Part c Units recycled 75,000 93, , , ,105 Revenues $ 112,500 $ 140,625 $ 175,781 $ 219,727 $ 274,658 Depreciation Expense (120,000) (120,000) (120,000) (120,000) (120,000) EBIT $ (7,500) $ 20,625 $ 55,781 $ 99,727 $ 154,658 Less: Taxes 2,250 (6,188) (16,734) (29,918) (46,397) NOPAT $ (5,250) $ 14,438 $ 39,047 $ 69,809 $ 108,261 Plus: Depreciation expense 120, , , , ,000 Less: CAPEX (600,000) Project Free Cash Flows $ (600,000) $ 114,750 $ 134,438 $ 159,047 $ 189,809 $ 228,261 NPV $ (71,978) IRR 10.36% The investment still looks like a good one with a positive NPV and an IRR that exceeds the required return. : Part d Units recycled 100, , , , ,141 Revenues $ 150,000 $ 187,500 $ 234,375 $ 292,969 $ 366,211 Disposal cost (20,000) (25,000) (31,250) (39,063) (48,828) Depreciation Expense (120,000) (120,000) (120,000) (120,000) (120,000) EBIT $ 10,000 $ 42,500 $ 83,125 $ 133,906 $ 197,383 Less: Taxes (3,000) (12,750) (24,938) (40,172) (59,215) NOPAT $ 7,000 $ 29,750 $ 58,188 $ 93,734 $ 138,168 Plus: Depreciation expense 120, , , , ,000 Less: CAPEX (600,000) Project Free Cash Flows $ (600,000) $ 127,000 $ 149,750 $ 178,188 $ 213,734 $ 258,168 NPV (8,613) IRR 14.46% Yes, even including the $0.20 per unit in disposal costs the project appears to be worthwhile.

10 Net Present Value PROBLEM 2-10 Cost of Tester ( 0) $ 250,000 Installation and training costs $ 10,000 = Formula/Calculation/Analysis required CAPEX ( 5) $ 100,000 = Qualitative analysis or Short answer required Annual cost savings $ 70,000 Salvage value $ 5,000 Depreciation Straight Line Project Life 10 years Tax rate 30% Cost of Capital 12% a Investment Outlays Equipment purchases $ (250,000) $ (100,000) Installation costs (10,000) Initial Outlay $ (260,000) After-tax salvage value 3,500 Free Cash Flows Operating Expense Savings $ 70,000 $ 70,000 $ 70,000 $ 70,000 $ 70,000 $ 70,000 $ 70,000 $ 70,000 $ 70,000 $ 70,000 Less: Depreciation Expense (26,000) (26,000) (26,000) (26,000) (26,000) (46,000) (46,000) (46,000) (46,000) (46,000) Additional Operating Income $ 44,000 $ 44,000 $ 44,000 $ 44,000 $ 44,000 $ 24,000 $ 24,000 $ 24,000 $ 24,000 $ 24,000 Less: Taxes (13,200) (13,200) (13,200) (13,200) (13,200) (7,200) (7,200) (7,200) (7,200) (7,200) NOPAT $ 30,800 $ 30,800 $ 30,800 $ 30,800 $ 30,800 $ 16,800 $ 16,800 $ 16,800 $ 16,800 $ 16,800 Plus: Depreciation 26,000 26,000 26,000 26,000 26,000 46,000 46,000 46,000 46,000 46,000 Less: CAPEX (260,000) (100,000) Free Cash Flow $ (260,000) $ 56,800 $ 56,800 $ 56,800 $ 56,800 $ (43,200) $ 62,800 $ 62,800 $ 62,800 $ 62,800 $ 66,300 b. Net Present Value $ 17,590 Internal Rate of Return 13.61% NPV Profile Discount Rates NPV 0% 241,500 2% 188,124 4% 142,825 6% 104,168 8% 71,000 10% 42,391 12% 17,590 14% (4,019) 16% (22,937) 18% (39,577) 20% (54,279) 22% (67,327) 24% (78,955) 26% (89,362) 28% (98,711) 30% (107,144) 32% (114,777) 34% (121,710) 36% (128,030) 38% (133,810) 40% (139,111) NPV Profile 300, , , , ,000 50,000 - (50,000) 0% 10% 20% 30% 40% 50% (100,000) (150,000) (200,000) Discount Rates

11 PROBLEM 2-11 Investment $ (4,000,000) Plant life 5 = Formula/Calculation/Analysis required Salvage value $ 400,000 = Qualitative analysis or Short answer required Variable Cost % 45% This is the solution to part a. of the problem. To Fixed operating cost $ 1,000,000 solve for part b. simply type in 55% in place of Tax rate 38% 45% for the variable cost %. Working capital 10% Change in revenues Required Rate of Return 15% Sales volume $ 1,000,000 $ 1,500,000 $ 3,000,000 $ 3,500,000 $ 2,000,000 Unit Price Revenues 2,000,000 3,000,000 7,500,000 8,750,000 5,000,000 Variable Operating Costs (900,000) (1,350,000) (3,375,000) (3,937,500) (2,250,000) Fixed Operating Costs (1,000,000) (1,000,000) (1,000,000) (1,000,000) (1,000,000) Depreciation Expense (800,000) (800,000) (800,000) (800,000) (800,000) Net Operating Income $ (700,000) $ (150,000) $ 2,325,000 $ 3,012,500 $ 950,000 Less: Taxes 266,000 57,000 (883,500) (1,144,750) (361,000) NOPAT $ (434,000) $ (93,000) $ 1,441,500 $ 1,867,750 $ 589,000 Plus: Depreciation 800, , , , ,000 Less: CAPEX (4,000,000) ,000 Less: Working Capital (200,000) (100,000) (450,000) (125,000) 375, ,000 Free Cash Flow $ (4,200,000) $ 266,000 $ 257,000 $ 2,116,500 $ 3,042,750 $ 2,137,000 NPV $ 419,435 IRR 18% a. The project appears to create value in the amount of its NPV = $419,435 and should be accepted. b. Increasing the variable costs to 55% changes the investment outcome dramatically. The NPV is now negative at ($599,080).

12 PROBLEM 2-12 Machine cost $ 760,000 Depreciation Straight line = Formula/Calculation/Analysis required Annual cost savings 250,000 = Qualitative analysis or Short answer required Machine life 5 Salvage value (before tax) - Tax rate 30% Discount rate 9% Analysis of Cash Flows Additional revenues (cost savings) 250, , , , ,000 Less: Depreciation expense (152,000) (152,000) (152,000) (152,000) (152,000) Additional EBIT $ 98,000 $ 98,000 $ 98,000 $ 98,000 $ 98,000 Less: Taxes (29,400) (29,400) (29,400) (29,400) (29,400) NOPAT $ 68,600 $ 68,600 $ 68,600 $ 68,600 $ 68,600 Plus: Depreciation 152, , , , ,000 Less: Capex (760,000) Less: Change in NWC Project Free Cash Flow $ (760,000) $ 220,600 $ 220,600 $ 220,600 $ 220,600 $ 220,600 Assessment of Project Value NPV $ 98, IRR 13.85% Payback 3.45 years The solution below corresponds to parts a and b. of the problem. To solve for part c. simply substitute $200,000 for the annual cost savings.

13 PROBLEM 2-13 This question asks the student to examine two alternative strategies. The aggressive investment of $1.5 billion and the modest investment of $800 million. The relevant question is then whether it is in Apple s interest to make the $700 million incremental investment in the aggressive strategy relative to the modest strategy. To evaluate this choice, Apple s executives should look at the difference between the cash flows generated by the two strategies and evaluate whether the PV of the difference exceeds the $700 million incremental investment. It should be noted that the more aggressive strategy may be riskier than the modest strategy, implying that the incremental cash flows should be discounted at a rate that exceeds the risk free rate.

2, , , , ,220.21

2, , , , ,220.21 11-7 a. Project A: CF 0-6000; CF 1-5 2000; I/YR 14. Solve for NPV A $866.16. IRR A 19.86%. MIRR calculation: 0 14% 1 2 3 4 5-6,000 2,000 (1.14) 4 2,000 (1.14) 3 2,000 (1.14) 2 2,000 1.14 2,000 2,280.00