8/13/2015 Solution Chapter: Problem: 11 Estimating Cash Flows and Analyzing Risk 18 Webmasters.com has developed a powerful new server that would be used for corporations' Internet activities. It would cost $10 million at Year 0 to buy the equipment necessary to manufacture the server. The project would require net working capital at the beginning of each year in an amount equal to 10% of the year's projected sales; for example, Nwc, = 10% (Sales.). The servers would sell for $24,000 per unit, and Webmasters believes that variable costs would amount to $17,500 per unit. After Year 1, the sales price and variable costs will increase at the inflation rate of 3%. The company's nonvariable costs would be $1 million at Year 1 and would increase with inflation. The server project would have a life of 4 years. If the project is undertaken, it must be continued for the entire 4 years. Also, the project's returns are expected to be highly correlated with returns on the firm's other assets. The firm believes it could sell 1,000 units per year. The equipment would be depreciated over a 5-year period, using MACRS rates. The estimated market value of the equipment at the end of the project's 4-year life is $500,000. Webmasters' federal-plus-state tax rate is 40%. Its cost of capital is 10% for average-risk projects, defined as projects with a coefficient of variation of NPV between 0.8 and 1.2. Low-risk projects are evaluated with a WACC of 8%, and high-risk projects at 13%. a. Develop a spreadsheet model, and use it to find the project's NPV, IRR, and payback. Key Results: NPV = IRR Payback = $3,463 21.19 2.90 Input Data (in thousands of dollars) Equipment cost Net operating working capital/Sales First year sales (in units) Sales price per unit Variable cost per unit (excl. depr.) Nonvariable costs (excl. depr.) Market value of equipment at Year 4 Tax rate WACC Inflation in prices and costs Estimated salvage value at year 4 $10,000 1096 1,000 $24.00 $17.50 $1,000 $500 40% 1096 3.09 $500 b. Now conduct a sensitivity analysis to determine the sensitivity of NPV to changes in the sales price, variable costs per unit, and number of units sold. Set these variables' values at 10% and 20% above and below their base- case values. Include a graph in your analysis. % Deviation from Base Case -2096 -10% 0961 1096 2096 SALES PRICE Base NPV $24.00 $3,463 $19.20 $21.60 $24.00 $3,463 $26.40 $28.80 Note about data tables. The data in the column input should NOT be input using a cell reference to the column input cell. For example, the base case Sales Price in Cell B95 should be the number $24.00 you should NOT have the formula =D28 in Ithat cell. This is because you'll use D28 as the column input cell in the data table and if Excel tries to iteratively replace Cell D28 with the formula =D28 rather than a series of numbers, Excel will calculate the wrong answer. Unfortunately, Excel won't tell you that there is a problem, so you'll just get the wrong values for the data table! % Deviation from Base Case -20% -10% 096 VARIABLE COST Base NPVI $17.50 % Deviation 1st YEAR UNIT SALES from Base NPV Base Case 1,000 -20% -10% 096 10% 10% 2096 20% $0 Deviation NPV at Different Deviations from Base from Sales Variable Base Case Price Cost/Unit Units Sold -20% $0 $0 -10% $0 $0 $0 096 $0 $0 $0 10% $0 $0 $0 20% $0 $0 $o Range c. Now conduct a scenario analysis. Assume that there is a 25% probability that best-case conditions, with each of the variables discussed in Part b being 20% better than its base-case value, will occur. There is a 25% probability of worst-case conditions, with the variables 20% worse than base, and a 50% probability of base-case conditions. Sales Price Scenario Unit Sales Variable Costs Probability NPV Best Case Base Case Worst Case 25% 50% 2596 $28.80 $24.00 $19.20 1,200 1,000 800 $14.00 $17.50 $21.00 Expected NPV = Standard Deviation = Coefficient of Variation = Std Dev / Expected NPV = d. If the project appears to be more or less risky than an average project, find its risk-adjusted NPV, IRR, and payback. 0.8 to 1.2 CV range of firm's average-risk project: Low-risk WACC = 896 WACC = 10% High-risk WACC = 13% Risk-adjusted WACC = Risk adjusted NPV = IRR = Payback = e. On the basis of information in the problem, would you recommend that the project be accepted? 0 1 1,000 $24.00 $17.50 1,000 $24,000 $2,472 2 1,000 $24.72 $18.03 1,030 $24,720 $2,546 3 1,000 $25.46 $18.57 1,061 $25,462 $2,623 4 1,000 $26.23 $19.12 1,093 $26,225 $0 Intermediate Calculations Units sold Sales price per unit (excl. depr.) Variable costs per unit (excl. depr.) Nonvariable costs (excl. depr.) Sales revenue Required level of net operating working capital Basis for depreciation Annual equipment depr. rate Annual depreciation expense Ending Bk Val: Cost - Accum Depirn Salvage value Profit (or loss) on salvage Tax on profit (or loss) Net cash flow due to salvage $2,400 $10,000 20.00% $2,000 $8,000 32.00% $3,200 $4,800 19.20% $1,920 $2,880 $10,000 11.5296 $1,152 $1,728 $500 -$1,228 -$491 $991) 0 Cash Flow Forecast Sales revenue Variable costs Nonvariable operating costs Depreciation (equipment) Oper. income before taxes (EBIT) Taxes on operating income (40%) Net operating profit after taxes Add back depreciation Equipment purchases Cash flow due to change in NOWC Net cash flow due to salvage Net Cash Flow (Time line of cash flows) 1 $24,000 17,500 1,000 2,000 $3,500 1,400 $2,100 2,000 Years 2 $24,720 18,025 1,030 3,200 $2,465 986 $1,479 3,200 3 $25,462 18,566 1,061 1,920 $3,915 1,566 $2,349 1,920 4 $26,225 19,123 1,093 1,152 $4,858 1,943 $2,915 1,152 -$10,000 -$2,400 -$72 -$74 -$76 $2,623 $991 $7,681 -$12,400 $4,028 $4,605 $4,193 Key Results: Appraisal of the Proposed Project Net Present Value (at 1096) = IRR = MIRR = Payback = Discounted Payback = $3,463 21.09% 16.9996 2.90 3.34 8/13/2015 Solution Chapter: Problem: 11 Estimating Cash Flows and Analyzing Risk 18 Webmasters.com has developed a powerful new server that would be used for corporations' Internet activities. It would cost $10 million at Year 0 to buy the equipment necessary to manufacture the server. The project would require net working capital at the beginning of each year in an amount equal to 10% of the year's projected sales; for example, Nwc, = 10% (Sales.). The servers would sell for $24,000 per unit, and Webmasters believes that variable costs would amount to $17,500 per unit. After Year 1, the sales price and variable costs will increase at the inflation rate of 3%. The company's nonvariable costs would be $1 million at Year 1 and would increase with inflation. The server project would have a life of 4 years. If the project is undertaken, it must be continued for the entire 4 years. Also, the project's returns are expected to be highly correlated with returns on the firm's other assets. The firm believes it could sell 1,000 units per year. The equipment would be depreciated over a 5-year period, using MACRS rates. The estimated market value of the equipment at the end of the project's 4-year life is $500,000. Webmasters' federal-plus-state tax rate is 40%. Its cost of capital is 10% for average-risk projects, defined as projects with a coefficient of variation of NPV between 0.8 and 1.2. Low-risk projects are evaluated with a WACC of 8%, and high-risk projects at 13%. a. Develop a spreadsheet model, and use it to find the project's NPV, IRR, and payback. Key Results: NPV = IRR Payback = $3,463 21.19 2.90 Input Data (in thousands of dollars) Equipment cost Net operating working capital/Sales First year sales (in units) Sales price per unit Variable cost per unit (excl. depr.) Nonvariable costs (excl. depr.) Market value of equipment at Year 4 Tax rate WACC Inflation in prices and costs Estimated salvage value at year 4 $10,000 1096 1,000 $24.00 $17.50 $1,000 $500 40% 1096 3.09 $500 b. Now conduct a sensitivity analysis to determine the sensitivity of NPV to changes in the sales price, variable costs per unit, and number of units sold. Set these variables' values at 10% and 20% above and below their base- case values. Include a graph in your analysis. % Deviation from Base Case -2096 -10% 0961 1096 2096 SALES PRICE Base NPV $24.00 $3,463 $19.20 $21.60 $24.00 $3,463 $26.40 $28.80 Note about data tables. The data in the column input should NOT be input using a cell reference to the column input cell. For example, the base case Sales Price in Cell B95 should be the number $24.00 you should NOT have the formula =D28 in Ithat cell. This is because you'll use D28 as the column input cell in the data table and if Excel tries to iteratively replace Cell D28 with the formula =D28 rather than a series of numbers, Excel will calculate the wrong answer. Unfortunately, Excel won't tell you that there is a problem, so you'll just get the wrong values for the data table! % Deviation from Base Case -20% -10% 096 VARIABLE COST Base NPVI $17.50 % Deviation 1st YEAR UNIT SALES from Base NPV Base Case 1,000 -20% -10% 096 10% 10% 2096 20% $0 Deviation NPV at Different Deviations from Base from Sales Variable Base Case Price Cost/Unit Units Sold -20% $0 $0 -10% $0 $0 $0 096 $0 $0 $0 10% $0 $0 $0 20% $0 $0 $o Range c. Now conduct a scenario analysis. Assume that there is a 25% probability that best-case conditions, with each of the variables discussed in Part b being 20% better than its base-case value, will occur. There is a 25% probability of worst-case conditions, with the variables 20% worse than base, and a 50% probability of base-case conditions. Sales Price Scenario Unit Sales Variable Costs Probability NPV Best Case Base Case Worst Case 25% 50% 2596 $28.80 $24.00 $19.20 1,200 1,000 800 $14.00 $17.50 $21.00 Expected NPV = Standard Deviation = Coefficient of Variation = Std Dev / Expected NPV = d. If the project appears to be more or less risky than an average project, find its risk-adjusted NPV, IRR, and payback. 0.8 to 1.2 CV range of firm's average-risk project: Low-risk WACC = 896 WACC = 10% High-risk WACC = 13% Risk-adjusted WACC = Risk adjusted NPV = IRR = Payback = e. On the basis of information in the problem, would you recommend that the project be accepted? 0 1 1,000 $24.00 $17.50 1,000 $24,000 $2,472 2 1,000 $24.72 $18.03 1,030 $24,720 $2,546 3 1,000 $25.46 $18.57 1,061 $25,462 $2,623 4 1,000 $26.23 $19.12 1,093 $26,225 $0 Intermediate Calculations Units sold Sales price per unit (excl. depr.) Variable costs per unit (excl. depr.) Nonvariable costs (excl. depr.) Sales revenue Required level of net operating working capital Basis for depreciation Annual equipment depr. rate Annual depreciation expense Ending Bk Val: Cost - Accum Depirn Salvage value Profit (or loss) on salvage Tax on profit (or loss) Net cash flow due to salvage $2,400 $10,000 20.00% $2,000 $8,000 32.00% $3,200 $4,800 19.20% $1,920 $2,880 $10,000 11.5296 $1,152 $1,728 $500 -$1,228 -$491 $991) 0 Cash Flow Forecast Sales revenue Variable costs Nonvariable operating costs Depreciation (equipment) Oper. income before taxes (EBIT) Taxes on operating income (40%) Net operating profit after taxes Add back depreciation Equipment purchases Cash flow due to change in NOWC Net cash flow due to salvage Net Cash Flow (Time line of cash flows) 1 $24,000 17,500 1,000 2,000 $3,500 1,400 $2,100 2,000 Years 2 $24,720 18,025 1,030 3,200 $2,465 986 $1,479 3,200 3 $25,462 18,566 1,061 1,920 $3,915 1,566 $2,349 1,920 4 $26,225 19,123 1,093 1,152 $4,858 1,943 $2,915 1,152 -$10,000 -$2,400 -$72 -$74 -$76 $2,623 $991 $7,681 -$12,400 $4,028 $4,605 $4,193 Key Results: Appraisal of the Proposed Project Net Present Value (at 1096) = IRR = MIRR = Payback = Discounted Payback = $3,463 21.09% 16.9996 2.90 3.34