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A B D E F G H K L M 1 2 3 4 5 6 1 8 Discounted Cash-Flow Analysis Estimating depreciation of an asset, calculating cash flows, and estimating NPV. Problem 1: Diltz Farms is considering investing in an automated egg-sorting system to increase production for international (web-based) sales of Diltz Farms' products. The new system will cost $3,000 including installation. It will be fully depreciated in 5 yrs. (straight-line) to zero and generate $150 after-tax gain at the end of the projected period (year 6). The initial working captital will be $300 and will be $500 in year one and increase each year thereafter by 5 percent. Revenues generated from the egg-sorter are expected to be $900 in year one, and increase by five percent each year. Expenses are ten percent of revenues. Diltz Farms' opportunity cost of capital is 8.5%. Using the 9 discounted cash-flow analysis, should Diltz Farms invest in the machinery? What is the NPV of the egg-sorter project? 10 11 Finance Concept: When making capital investment decisions we must consider the effect of a change 12 in cash flows. The Excel spreadsheet is extremely useful in calculating cash flows allowing us to 13 compare different assets or depreciation methods (what-if analysis). Step 1: Find the accounting yearly depreciation with the straight line method: Depreciable Basis = Cost of the Asset - Salvage Value 18 SL (Straight-Line) Depreciation = (Initial Cost - Salvage Value) / number of years 19 Hint: Salvage Value for depreciation =0 in cell E22. 20 Cost of Asset 1. Enter values from the problem in cells E20, E21, and E22. 21 Life of Asset in Years 2. In cell E23 enter: = E20-E22 22 Salvage Value 3. In cell E24 enter: =E23/E21 (yearly depreciation] 23 Depreciable Basis 4. Yearly depreciation should be $3,000/5 = $600. 24 Yearly depreciation 5. Salvage Value for year 6 = +150 [from problem] 14 15 16 25 Step 2: Creating a table to calculate the After-Tax Cash Flows and NPV (in millions): 26 27 YEAR: 0 1 2 3 4 5 6 28 Initial Investment 29 Salvage Value 30 Working capital 31 Change in Wk Cap 32 Revenues 33 Expenses 34 Depreciation 35 Pretax profit 36 Tax (35%) 37 Profit after tax 38 CF from operations 39 Cash Flow: 40 CF from capital investments 41 CF from working capital 42 CF from operations 43 Total cash flows 44 Discount factor 45 PV of cash flow 46 Net present value 48 Discount rate 49 50 Completing the spreadsheet is a simple use of Excel mathematical functions. You might want to print the instructions first. 51 Cash Flow From Operations 52 1. In year zero enter the initial investment, the initial wkg capital and the change in wkg cap (0) 2. In year 1[cell F30) enter the new wke cap (500), and calculate the change in wke cap by subtracting vear O from G 1 L N 3. 66 A B D E F H J 50 Completing the spreadsheet is a simple use of Excel mathematical functions. You might want to print the instructions first. 51 Cash Flow From Operations 52 1. In year zero enter the initial investment, the initial wkg capital, and the change in wkg cap (0) 2. In year 1[cell F30] enter the new wkg cap (500), and calculate the change in wkg cap by subtracting year 0 from 53 year 1. In cell F31 enter: =F30-E30. In year two, enter year one's wkg cap*1.05 (G30; =F30*1.05]. Copy the formula through year 5. Also copy chg in 54 wkg cap formula to years 2-6. 55 4. In year one enter revenues. In year two enter year one*1.05 [=F32*1.05] and copy to year 5. 56 5. In year one enter expenses from problem(=F32*10%) and copy across. 57 6. Enter depreciation in year one from the depreciation table and copy (remember $). 58 7. Yearly pretax profit is revenues minus expenses and depreciation. [F35=F32-F33-F34] Copy across. 59 8. Calculate the tax by multiplying pretax profit by the tax rate. (0.35) [F36=F35*35] copy across. 60 9. Subtract the tax from the pretax profit to get the after tax profit [F37=F35-F36] copy across. 61 10. To obtain CF from operations: in year 0:=-initial investment-ch wkg cap [wil be a negative number] 62 11. For years 1-5 add Profit After Tax to Depreciation (F37+F34). Copy across. Year 6 is blank. 63 Calculating the NPV 64 1. Cash Flow from capital investments: enter -E28 in cell E40. 65 2. Cash Flow from working capital: enter -E31 in cell E41 and copy across to J41. 3. Cash Flow from operations in cell F42 enter =F38 and copy across to J42. In cell K41 enter: =-K31+K29. 67 4. Total cash flows: in cell E43 enter =SUM(E40:E42) and copy across to K43. 68 5. Discount rate: enter the required return (085) in E48 6. Discount factor: in cell E44 enter: =1/((1+$E$48) 0) and copy across. Change the exponent in yrs 1-6. 70 7. PV of cash flow: in cell E45 enter =E44*E43 and copy across. 71 8. Net present value: in cell E46 enter = SUM(E45:K45) 72 73 Some check numbers: 74 Year 6 change in working capital = -608 75 Change from wkg cap (K41) = 758 76 Total cash flows for year 5 (J43) = 821 77 78 With a required return of 8.5%, should Diltz Farms go ahead with the new egg-sorter? 79 What is the NPV of the egg-sorter project? 80 What is the IRR of the project? 81 82 What is the NPV if the required return is 9%? 83 84 85 86 Problem 2: Your firm recently purchased an industrial machine costing $555,000. It is classified as a seven-year property under MACRS. What are 87 the annual depreciation allowances and end-of-the-year book values for this machine? 88 89 Finance Concept: For tax purposes, the depreciation expense is computed under MACRS, which was 90 enacted as part of the Tax Reform Act of 1986. The depreciation is larger at the beginning. 69 Beginning Book Value 7 Year MACRS Depreciation Allowance Ending Book Value Year 1 2 3 4 5 92 93 94 95 96 97 98 99 100 101 102 103 104 6 7 8 Solution: Foto tho Dominning Aluefoort 11 02 CO2 A B D E F. G H 1 J K 88 89 Finance Concept: For tax purposes, the depreciation expense is computed under MACRS, which was enacted as part of the Tax Reform Act of 1986. The depreciation is larger at the beginning. 90 Beginning Book Value 7 Year MACRS Ending Book Depreciation Allowance Value Year 1 2 3 4 5 6 7 8 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 Solution: 1 Enter the Beginning Book Value (cost of the machine) in cell E93. 2 Calculate the remaining Beginning Book Values: enter =193 in cell E94 and copy down the column. 3 Calculate the Depreciation Allowance by multiplying $E$93 (Beg Bk V) * F93 (MACRS %). 4 Find the Ending Book Value by subtracting the depreciation from the Beginning Book Value. 5 Copy all your formulas down the columns 6 Year 8 Ending Book Value should equal zero, and beg bk val = depreciation in year 8.. 112 Problem 3: 114 Assume Salvage Value = 0. 119 120 Net Income Year 1-4 121 Sales from problem 122 Variable Costs 25% of Sales 123 Fixed Costs from problem 124 Depreciation from H18 125 EBIT EBIT = Sales-costs-dep 126 Taxes Taxes = EBIT * tax rate 127 Net Income NI = EBIT - taxes 128 129 Operating Cash Flows 130 EBIT 131 + Depreciation 132 - Taxes 133 After-Tax Cash Flow 134 Assume Salvage Value = 0 119 120 Net Income Year 1-4 104 121 Sales from problem 122 490 Variable Costs 25% of Sales 123 Fixed Costs from problem 124 Depreciation from H18 125 EBIT EBIT = Sales-costs-dep 126 Taxes Taxes = EBIT tax rate 127 Net Income NI = EBIT - taxes 128 129 Operating Cash Flows 130 EBIT 131 + Depreciation 132 - Taxes 133 After-Tax Cash Flow 134 Cost of machine as a negative # After-Tax Cash Flows Year's CF 0 1 2 3 4 Equal Cash Flows from cell F133 Required Return Net Present Value Internal Rate of Return