8-12. Part 1. NPV assuming no Taxation Cost 30,000,000 WACC (pre-tax) 14% Residual value 10,000,000
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1 10 Correia, Mayall, O Grady and Pang: Solutions to Corporate Financial Management, 2e 11 February 2007 Ch8 Capital Budgeting 8-12 Part 1. NPV assuming no Taxation Cost 30,000,000 WACC (pre-tax) 14% Residual value 10,000, Cost -30,000,000 Residual value 10,000,000 Net Cash Flows 10,000,000 20,000,000 20,000,000 10,000,000 Change in working capital -2,000,000-2,000, ,000,000 2,000,000-32,000,000 8,000,000 20,000,000 22,000,000 22,000,000 PV Factor [1/(1+r) t ] Present Value -32,000,000 7,017,544 15,389,351 14,849,373 13,025,766 NPV [sum of PVs] 18,282,034 IRR 35.8% NPV [Using Excel NPV function] 18,282,034 Conclusion: The NPV is significantly above zero and the IRR exceeds the cost of capital. The company should invest in the project. Workings: Changes in Working Capital Net Working Capital 2,000,000 4,000,000 4,000,000 2,000,000 - Change in Working Capital -2,000,000-2,000,000-2,000,000 2,000,000 Part 2. NPV including the effects of Taxation WACC (after-tax) 11% Cost -30,000,000 Residual value 10,000,000 Cash Flows 10,000,000 20,000,000 20,000,000 10,000,000 Taxation -1,200,000-4,200,000-4,200,000-2,400,000 Change in working capital -2,000,000-2,000, ,000,000 2,000,000-32,000,000 6,800,000 15,800,000 17,800,000 19,600,000 PV Factor [1/(1+r) t ] Present Value -32,000,000 6,126,126 12,823,634 13,015,207 12,911,127 NPV [sum of PVs] 12,876,094 IRR 26.0% NPV [Using Excel NPV function] 12,876,094 Taxation Cash flows 10,000,000 20,000,000 20,000,000 10,000,000 Depreciation 20% -6,000,000-6,000,000-6,000,000-6,000,000 Balancing adjustment 4,000,000 Taxable Income 4,000,000 14,000,000 14,000,000 8,000,000 Taxation 30% -1,200,000-4,200,000-4,200,000-2,400,000 Adjustable Value at the end of the project life Cost 30,000,000 Depreciation to end of Yr4-6,000, ,000,000 Adjustable Value 6,000,000 Residual (market value) at end of Yr4 10,000,000 Adjustable Value -6,000,000 Balancing adjustment 4,000,000
2 Correia, Mayall, O Grady and Pang: Solutions to Corporate Financial Management, 2e 11 February 2007 Ch8 Capital Budgeting Cost -1,320,000 Market value at end of Yr3 1,680,000 Net Rental 87,360 90,854 94,489 Taxation -26,208-27, ,347-1,320,000 61,152 63,598 1,638,142 PV Factor [1/(1+r) t ] Present Value -1,320,000 56,103 53,529 1,264,946 NPV [sum of PVs] 54,578 IRR 10.5% NPV [Using Excel NPV function] 54,578 Taxation Net rental after costs 87,360 90,854 94,489 Gain on sale of property 360,000 87,360 90, ,489 Taxation -26,208-27, ,347 Workings Rental 120,000 Maintenance, rates, admin -36,000 Net rental 84,000 Net rental x (1+g) 84,000 87,360 90,854 94,489 Market value in Yr3 1,680,000 Cost -1,320,000 Profit on sale of Property 360,000
3 12 Correia, Mayall, O Grady and Pang: Solutions to Corporate Financial Management, 2e 11 February 2007 Ch8 Capital Budgeting 8-14 Selling price per unit 30 WACC 14% Production & distribution cost per unit 6 Fixed costs per year 40,000 Contribution per unit 24 Cost of software development 4,000,000 Year Sales (no. of units) 100, ,000 80,000 60,000 No. of units x contribution per unit 2,400,000 2,400,000 1,920,000 1,440, Cost -4,000,000 Net Cash Flows 2,400,000 2,400,000 1,920,000 1,440,000 Fixed costs -40,000-40,000-40,000-40,000 Taxation -108, , , ,000-4,000,000 2,252,000 2,252,000 1,316, ,000 PV Factor [1/(1+r) t ] Present Value -4,000,000 1,975,439 1,732, , , NPV [sum of PVs] 1,176, IRR 30% 3. Payback [years] [Remaining balance at end of Yr1/Net cash flow for Yr2] Determination of payback Cumulative cash flows -4,000,000-1,748, ,000 1,820,000 2,800, Taxation Net cash flows 2,400,000 2,400,000 1,920,000 1,440,000 Cost of software development -2,000,000-2,000,000 Fixed costs -40,000-40,000-40,000-40,000 Taxable Income 360, ,000 1,880,000 1,400,000 Taxation cash flows 30% -108, , , ,000
4 Correia, Mayall, O Grady and Pang: Solutions to Corporate Financial Management, 2e 11 February 2007 Ch8 Capital Budgeting Sales 10,000,000 20,000,000 20,000,000 Operating margin 38% Net Operating cash flows [Margin x Sales] 3,800,000 7,600,000 7,600, Cost -15,000,000 Residual value 6,000,000 Working Capital -10,000,000 10,000,000 Net Cash Flows 3,800,000 7,600,000 7,600,000 Taxation -240,000-1,380,000-1,380,000-25,000,000 3,560,000 6,220,000 22,220,000 PV Factor [1/(1+r) t ] Present Value -25,000,000 3,178,571 4,958,546 15,815, NPV [sum of PVs] -1,047, IRR 10% The firm should not invest in this project as the NPV is negative and the IRR is less than the WACC. Taxation Net cash flows 3,800,000 7,600,000 7,600,000 Depreciation deduction 20% -3,000,000-3,000,000-3,000,000 Balancing adjustment [res. value less adj. value] 0 Taxable Income 800,000 4,600,000 4,600,000 Taxation cash flows 30% -240,000-1,380,000-1,380,000 Adjustable Value at the end of the project life Cost 15,000,000 Depreciation to end of Yr4 3,000, ,000,000 Adjustable Value 6,000,000 Residual value 6,000,000 Adjustable Value -6,000,000 Balancing Adjustment 0
5 14 Correia, Mayall, O Grady and Pang: Solutions to Corporate Financial Management, 2e 11 February 2007 Ch8 Capital Budgeting 8-16 Incremental cash flows Alternatively Fuel savings 74,000 Earnings 144,000 Reduction in claims 60,000 Add: depreciation 30,000 Reduction in cash overheads 40,000 Incremental cash flow 174,000 Incremental cash flow 174, Cost -400,000 Cost savings 174, , , , ,000 Residual value 100, ,000 Taxation -30,000-28,200-28,200-28,200-28,200-88,200 Net Cash flows -330, , , , , ,800 NPV 309,626 IRR 38.8% Taxation Increase in taxable income 174, , , , ,000 Depreciation deduction -80,000-80,000-80,000-80,000-80,000 Loss of depreciation deductions Balancing adjustment 100, ,000 Taxable income 100,000 94,000 94,000 94,000 94, ,000 Tax 30% 30,000 28,200 28,200 28,200 28,200 88,200 Conclusion: The firm should invest in the new trucks as the project's NPV is positive. The IRR of the project is 39% which is significantly higher than the firm's cost of capital.
6 Correia, Mayall, O Grady and Pang: Solutions to Corporate Financial Management, 2e 11 February 2007 Ch8 Capital Budgeting Cost of capital 14% Cost -2,400,000 Cost savings 780, , , , ,000 Residual value 670,000 Proceeds on sale 260,000 Taxation -108, , ,000-90, ,000 Net Cash flows -2,140, , , , ,000 1,159,000 PV factor ,140, , , , , ,948 NPV [Sum of PVs] 413,287 NPV 413,287 IRR 21.1% Taxation Increase in taxable income 780, , , , ,000 Depreciation deduction -480, , , , ,000 Balancing adjustment (Tax value =0) 670,000 Loss of depreciation on current machine 100, , ,000 Balancing adjustment -40,000 Taxable income 360, , , , ,000 Tax 30% 108, , ,000 90, ,000 The firm should invest in the new equipment as the project has a significantly positive NPV. The IRR of 21% is substantially greater than the firm's cost of capital. Note: I do bring to the attention of students whether the old equipment should be sold. The low price of $260000, less the PV of the depreciation deductions if we hold onto the equipment, means that qualitative issues such as having a back-up in case the new machine breaks down, or having spare capacity may result in the value of these options making it worthwhile to hold onto the old equipment. PV cost of holding onto old equipment -260,000-12,000 30,000 30,000 30, ,000 18,000 30,000 30,000 NPV -200,877
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