Week 8 Practice Set_RB

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Apr 3, 2024

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Week 8 – Practice Set Name: Rachel Brewer Please type a numerical solution to the problems below: Using the spreadsheet provided, please run the following sensitivities: 1. Please take sales up to $630,000 and down to $570,000 (up by 5% and down by 5%) and record the new net present value numbers. For Sales increased to $630,000: Total cash flow: (Total Sales Revenue - Total Operating Expenses = Total Operating Cash Flow) ($800,000) $132,800 $132,800 $132,800 $132,800 $132,800 $132,800 $132,800 $632,800 Present Value: (Future Value / (1 + (ROI / number of times the amount is compounded)) $941,732 Net Present Value: (Total Cash Flow – Present Value) $141,732 For Sales decreased to $570,000: Total cash flow: ($800,000) $106,880 $106,880 $106,880 $106,880 $106,880 $106,880 $106,880 $606,880 Present Value: $803,451 Net Present Value: $3,451 2. Returning to the original numbers, please take disposition value up to $525,000 and down to $475,000 (up by 5% and down by 5%) and record the new net present value numbers. For the disposition value increased to $525,000: Total cash flow: ($800,000) $119,840 $119,840 $119,840 $119,840 $119,840 $119,840 $119,840 $625,840 Present Value: $884,254 Net Present Value: $84,254 For the disposition value decreased to $475,000: Total cash flow: ($800,000) $119,840 $119,840 $119,840 $119,840 $119,840 $119,840 $119,840 $575,840 Present Value: $861,689 Net Present Value: $61,689 3. Returning to the original numbers, please take variable costs up for all years to 42% and down to 38% (up by 5% and down by 5%) and record the new net present value numbers. For variable costs increased to 42%: Total cash flow: ($800,000) $111,840 $111,840 $111,840 $111,840 $111,840 $111,840 $111,840 $611,840 Present Value: $887,497 Net Present Value: $87,497 For variable costs decreased to 38%: Total cash flow: ($800,000) $127,840 $127,840 $127,840 $127,840 $127,840 $127,840 $127,840 $627,840

Present Value: $918,685 Net Present Value: $118,685 When variable costs increase, it reduces the net cash flows available for the project, leading to a lower NPV. Conversely, when variable costs decrease, it increases the net cash flows avail- able for the project, resulting in a higher NPV. The changes in NPV reflect the impact of vary- ing variable costs on the profitability of the project. 4. Returning to the original numbers, please take fixed costs up for all years to $231,000 and down to $209,000 (up by 5% and down by 5%) and record the new net present value numbers. For fixed costs increased to $231,000: Total cash flow: ($800,000) $99,840 $99,840 $99,840 $99,840 $99,840 $99,840 $99,840 $599,840 Present Value: $830,339 Net Present Value: $30,339 For fixed costs decreased to $209,000: Total cash flow: ($800,000) $121,840 $121,840 $121,840 $121,840 $121,840 $121,840 $121,840 $621,840 Present Value: $914,844 Net Present Value: $114,844 When fixed costs increase, it reduces the net cash flows available for the project, resulting in a lower NPV. Conversely, when fixed costs decrease, it increases the net cash flows available for the project, resulting in a higher NPV. This is because higher fixed costs lead to higher ex- penses, thereby reducing the profitability of the project, while lower fixed costs have the op- posite effect. 5. Returning to the original numbers, please take the tax rate to up to 29.4% and down to 26.6% (up by 5% and down by 5%) and record the new net present value numbers. For tax rate increased to 29.4%: Total cash flow: ($800,000) $104,458 $104,458 $104,458 $104,458 $104,458 $104,458 $104,458 $604,458 Present Value: $671,214 Net Present Value: $67,214 For tax rate decreased to 26.6%: Total cash flow: ($800,000) $106,989 $106,989 $106,989 $106,989 $106,989 $106,989 $106,989 $606,989 Present Value: $684,969 Net Present Value: $77,969 When the tax rate increases, it decreases the after-tax income, which in turn reduces the net cash flows available for the project, resulting in a lower NPV. Conversely, when the tax rate decreases, it increases the after-tax income, leading to higher net cash flows and a higher NPV. The changes in NPV reflect the impact of varying tax rates on the profitability of the project.

6. Returning to the original numbers, please take the weighted average cost of capi- tal for this project up to 10.5% and down to 9.5% (up by 5% and down by 5%) and record the new net present value numbers. For WACC increased to 10.5%: Total cash flow: ($800,000) $119,840 $119,840 $119,840 $119,840 $119,840 $119,840 $119,840 $619,840 Present Value: $672,807 Net Present Value: $52,807 For WACC decreased to 9.5%: Total cash flow: ($800,000) $127,174 $127,174 $127,174 $127,174 $127,174 $127,174 $127,174 $627,174 Present Value: $720,229 Net Present Value: $93,055 The Weighted Average Cost of Capital (WACC) represents the minimum return that a com- pany must earn on its existing assets to maintain its market value and attract funds. When the WACC increases, it raises the discount rate used to calculate the present value of future cash flows, resulting in lower present values and thus a lower NPV. Conversely, when the WACC decreases, it decreases the discount rate, leading to higher present values and a higher NPV. Therefore, the changes in NPV reflect the sensitivity of the project's profitability to variations in the weighted average cost of capital. 7. From the answer to the prior six problems using the resulting range of outcome after making the 5% changes to the variables, which variable has the greatest in- fluence on the net present value of this project? Based on the results of the prior six problems where we made 5% changes to various vari- ables, including sales, disposition value, variable costs, fixed costs, tax rate, and weighted av- erage cost of capital (WACC), we can determine which variable had the greatest influence on the Net Present Value (NPV) of the project. From the provided results, it appears that the vari- able with the greatest influence on the NPV of the project is indeed Sales. 8. Please go back to the original spreadsheet numbers the original net present value is $72,591. Please run a net present value breakeven using this original data and record the net present value level of sales here ___________. Prior to beginning this project, the company can increase the initial outlay by $150,000. This addi- tional upfront acquisition stage cost would lower the variable costs to 30% of sales and increase the disposition value to $550,000. What is the new net present value____________, and the new net present value breakeven level of sales___________, and would this be a good move for the company? To perform the net present value (NPV) breakeven analysis and assess the impact of the pro- posed changes, let's first recalculate the NPV with the adjusted initial outlay, variable costs, and disposition value. Then, I’ll determine the breakeven level of sales. Original NPV: $72,591 Adjusted assumptions: Initial outlay increased by $150,000: New initial outlay = $950,000 Variable costs reduced to 30% of sales

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Disposition value increased to $550,000 Now, let's calculate the new NPV: New NPV = Total Present Value of Cash Flows - Initial Outlay Here are the calculations: Total Present Value of Cash Flows: = Present Value of Operating Stage Cash Flows + Present Value of Disposition Stage Cash Flow = $872,591 (original present value) + $550,000 (present value of disposition stage cash flow) = $1,422,591 New NPV = $1,422,591 - $950,000 (new initial outlay) New NPV = $472,591 The new NPV is $472,591. To find the breakeven level of sales, we need to determine the level of sales at which the NPV becomes zero. This can be calculated by setting up the equation: NPV = 0 = Total Present Value of Cash Flows - Initial Outlay Total Present Value of Cash Flows = Initial Outlay Let X be the breakeven level of sales. X = Initial Outlay / Present Value of Operating Stage Cash Flows X = $950,000 / ($872,591 + Present Value of Disposition Stage Cash Flow) X= ($872,591+Present Value of Disposition Stage Cash Flow) X= $950,000 / ($872,591+$550,000) X= $950,000 / $1,422,591 X ≈ $568,503 So, the breakeven level of sales is approximately $568,503. Now, let's analyze the impact of these changes and determine if it would be beneficial for the company: After increasing the initial cash outlay by $150,000, decreasing variable cost to sales ratio to 30%, and increasing the disposition value to $550,000, the new NPV is $176,385. To breakeven using the new data, the annual sales must be at $534,400 or a NPV of total sales of $2,850,985. Overall, this new move will be good for the company because the breakeven point in sales is lower and thus easier to reach. Once the breakeven point is reached and sur- passed, profitability is achieved in a shorter timeframe. 9. Please go back to the original spreadsheet numbers. As an alternative, before be- ginning this project, the company can reduce the initial outlay by $300,000. This would increase the variable costs to 50% of sales and decrease the disposition value to $400,000. What is the new net present value____________, and the new net present value breakeven level of sales___________, and would this be a good move for the company?

To analyze the impact of reducing the initial outlay by $300,000, increasing the variable cost to sales ratio to 50%, and decreasing the disposition value to $400,000, let's recalculate the net present value (NPV) and determine the new breakeven level of sales. Original NPV: $72,591 Adjusted assumptions: Initial outlay reduced by $300,000: New initial outlay = $500,000 Variable costs increased to 50% of sales Disposition value decreased to $400,000 Now, let's calculate the new NPV: New NPV = Total Present Value of Cash Flows - Initial Outlay Here are the calculations. Total Present Value of Cash Flows: = Present Value of Operating Stage Cash Flows + Present Value of Disposition Stage Cash Flow = $872,591 (original present value) + $400,000 (present value of disposition stage cash flow) = $1,272,591 New NPV = $1,272,591 - $500,000 (new initial outlay) New NPV = $772,591 The new NPV is $772,591. To find the breakeven level of sales, we need to determine the level of sales at which the NPV becomes zero. This can be calculated by setting up the equation: NPV = 0 = Total Present Value of Cash Flows − Initial Outlay Total Present Value of Cash Flows = Initial Outlay X be the breakeven level of sales. X = Initial Outlay / Present Value of Operating Stage Cash Flows X = $500,000 / ($872,591 + Present Value of Disposition Stage Cash Flow) X = $500,000 / ($872,591+Present Value of Disposition Stage Cash Flow) X = $500,000 / ($872,591 + $400,000) X = $500,000 / $1,272,591 X ≈ $550,290 So, the breakeven level of sales is approximately $550,290. After decreasing the original cash outlay by $300,000, increasing variable cost to sales ratio to 50%, and decreasing the disposition value to $400,000, the new NPV is $95,475. To breakeven using this newer data, the annual sales must be $550,290 or a NPV of total sales of $2,935,757. Overall, this will be a good move for the company (compared to the original data) because this has also led to a lower breakeven point in sales.

10. Going back to the prior two problems, which of these alternatives is better for the company? The original method, the modification suggested in problem 8, or the modification in problem 9? Why? I believe the modifications in problem 8 is the best alternative for the company because it has led to the highest NPV at $176,385. This also means that the breakeven point in sales is much lower, and thus easier achieved.

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