Reto S. A. Question 1: Since we are initially ignoring the effects of taxes and do not know the required return, (we initially know only that debt costs 8% but are not provided any information regarding equity costs) the only available option is to use either a non-time value based evaluation or the internal rate of return: Cash Flow Time Amount Equipment Cost 0 SFr -600000 Revenue 1-10 2000000 Less Commissions-15% -300000 Less Materials -600000 Less Labor -900000 Before Tax Cash Flow SFr 200000 Internal Rate of Return 31. 11% Question 2:
Introducing taxes to the problem will change the annual cash flows although they remain an annuity since the depreciation is assumed to be an equal amount each year: Cash Flow Time Amount Equipment Cost 0 SFr -600000 Revenue 1-10 2000000 Less Commissions-15% -300000 Less Materials -600000 Less Labor -900000 Less Depreciation -60000 Before Tax Profit SFr 140000 Less Taxes at 45% -63000 After Tax Profit 77000 Add Back Depreciation 60000 Annual Cash Flow 137000 Internal Rate of Return 18. 732% Question 3: Knowing that Torgler wants a return of 12% permits the use of the NPV approach to the problem.
We know it will be a positive NPV since Question 2 indicated a IRR greater than 12%, but it would still be interesting to know the actual number. Using the cash flow data from the previous question and a discount rate of 12% yields a NPV of SFr 174,080. 56 which is the Present Value of the Inflows = SFr 774,080. 56 less the Present Value of the Outflows (Initial Investment) = SFr 600,000. We could also break apart the two component parts of the total cash flow into the after tax operating cash flow and the depreciation tax shield: Time Outflow Operating Profit After-Tax Depreciation Depreciation Cash Flow Present
Operating Profit Tax Shelter Value 0 -600000 -600000. 00 1 200000 110000 60000 27000 137000 122321. 43 2 200000 110000 60000 27000 137000 109215. 56 3 200000 110000 60000 27000 137000 97513. 89 4 200000 110000 60000 27000 137000 87065. 98 5 200000 110000 60000 27000 137000 77737. 48 6 200000 110000 60000 27000 137000 69408. 46 7 200000 110000 60000 27000 137000 61971. 84 8 200000 110000 60000 27000 137000 55332. 00 9 200000 110000 60000 27000 137000 49403. 57 10 200000 110000 60000 27000 137000 44110. 33 NPV 174080. 55 Question 4:
Reworking the analysis to reflect the new depreciation methodology is much easier to accomplish when the two components of the cash flow are separated as above: Time Outflow Operating Profit After-Tax Depreciation Depreciation Cash Flow Present Operating Profit Tax Shelter Value 0 -600000 -600000. 00 1 200000 110000 200000 90000 200000 178571. 43 2 200000 110000 80000 36000 146000 116390. 31 3 200000 110000 40000 18000 128000 91107. 87 4 200000 110000 40000 18000 128000 81346. 31 5 200000 110000 40000 18000 128000 72630. 64 6 200000 110000 40000 18000 128000 64848. 8 7 200000 110000 40000 18000 128000 57900. 70 8 200000 110000 40000 18000 128000 51697. 05 9 200000 110000 40000 18000 128000 46158. 08 10 200000 110000 40000 18000 128000 41212. 57 NPV 201863. 75 Question 5: Working capital is a relevant cash flow and can dramatically impact the NPV even though the total cash flows of investing in working capital will have no aggregate effect except for the loss of the time value: Time Outflow Operating Profit After-Tax Depreciation Depreciation Cash Flow Present Operating Profit Tax Shelter Value 0 -900000 -900000. 00 200000 110000 200000 90000 200000 178571. 43 2 200000 110000 80000 36000 146000 116390. 31 3 200000 110000 40000 18000 128000 91107. 87 4 200000 110000 40000 18000 128000 81346. 31 5 200000 110000 40000 18000 128000 72630. 64 6 200000 110000 40000 18000 128000 64848. 78 7 200000 110000 40000 18000 128000 57900. 70 8 200000 110000 40000 18000 128000 51697. 05 9 200000 110000 40000 18000 128000 46158. 08 10 200000 110000 40000 18000 428000 137804. 55 NPV -1544. 28 Investing SFr 300,000 at time zero (outflow) and recovering it at the end of year 10 will result in a negative NPV for the project.
The time values associated with the working capital indicates a time value adjusted present value of –SFr 203,408. 03. (The present value of recovering SFr 300,000 ten years from now at 12% is SFr 96,591. 71). This negative amount pulls the project present value from a strong positive level to a slightly negative amount. Question 6: Selling the old equipment will reduce the investment required for the new equipment both due to the cash received from the sale and the tax savings associated with selling it for less than book value.
Time Outflow Operating Profit After-Tax Depreciation Depreciation Cash Flow Operating Profit Tax Shelter 0 -710000 1 400000 220000 253333 113999. 85 333999. 9 2 400000 220000 93333 41999. 85 261999. 9 3 400000 220000 26667 12000. 15 232000. 2 5 400000 220000 26667 12000. 15 232000. 2 6 400000 220000 26667 12000. 15 232000. 2 7 400000 220000 26667 12000. 15 232000. 2 8 400000 220000 26667 12000. 15 232000. 2 9 400000 220000 26667 12000. 15 232000. 2 10 400000 220000 66667 30000. 15 250000. 2 NPV 721,634. 85 Question 7: Losing the salvage from the old machine will increase the cost of acquiring he new machine. TimeOutflowOperating ProfitAfter-Tax DepreciationDepreciationCash Flow Operating ProfitTax Shelter 0-820000-820000 1400000220000253333113999. 85333999. 9 24000002200009333341999. 85261999. 9 34000002200002666712000. 15232000. 2 44000002200002666712000. 15232000. 2 54000002200002666712000. 15232000. 2 64000002200002666712000. 15232000. 2 74000002200002666712000. 15232000. 2 84000002200002666712000. 15232000. 2 94000002200002666712000. 15232000. 2 104000002200006666730000. 15250000. 2 NPV611634. 85 The resulting net present value would cause Torgler to still pursue the investment opportunity.
