We are evaluating a project that costs $848,000, has an eight-year life, and has
ID: 2615047 • Letter: W
Question
We are evaluating a project that costs $848,000, has an eight-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 62,000 units per year. Price per unit is $40, variable cost per unit is $20, and fixed costs are $625,000 per year. The tax rate is 35 percent, and we require a 20 percent return on this project.
Calculate the accounting break-even point.
What is the degree of operating leverage at the accountin g break-even point? (Round your answer to 3 decimal places. (e.g., 32.161))
Calculate the base-case cash flow and NPV. (Round your NPV answer to 2 decimal places. (e.g., 32.16))
What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations and round your answer to 3 decimal places. (e.g., 32.161))
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What is a2-c
We are evaluating a project that costs $848,000, has an eight-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 62,000 units per year. Price per unit is $40, variable cost per unit is $20, and fixed costs are $625,000 per year. The tax rate is 35 percent, and we require a 20 percent return on this project.
Explanation / Answer
Solution: a-1. Break-even point 36,550 units Working Notes: Accounting break-even point = (Annual fixed cost + Depreciation)/Contribution margin per unit Annual fixed cost = $625,000 Depreciation = (initial investment/life) =$848,000/8 =106,000 Contribution margin per unit =selling price per unit - variable cost per unit =$40 - $20 =$20 per unit Accounting break-even point = (Annual fixed cost + Depreciation)/Contribution margin per unit =($625,000 + $106,000)/$20 =$731,000/$20 =36,550 units a-2. Degree of operating leverage 6.896 Working Notes: Degree of operating leverage at the accounting break-even point = Contribution margin /operating income =$731,000/$106,000 =6.8962264 =6.896 Notes: Contribution margin = Contribution margin per units x break even point =$20 x 36,550 =731,000 operating income = Sales - variable cost -fixed cost =36,550 x (40-20) - 625,000 =$731,000 -625,000 =$106,000 b-1. Cash flow $436,850.00 NPV $828,263.26 Working Notes: Operating cash flows base =((price - variable cost) x annual quantity - fixed cost ) x (1- tax rate) +( tax rate x depreciation) =(($40 - $20) x 62,000 - 625,000 ) x (1- 0.35) +( 0.35 x 106,000) =($20 x 62,000 - 625,000 ) x (1- 0.35) +( 0.35 x 106,000) =615,000 x 0.65 + 37,100 =399,750 + 37,100 =$436,850 NPVbase = –Initial investment + operating cash flow x (PVIFA 20%,8) NPVbase = –$848,000 + 436,850 x 3.837159803 NPVbase = –$848,000 + 1,676,263.2599 NPVbase = $828,263.26 PVIFA @ 20% for 1 to 8th is calculated = (1 - (1/(1 + 0.20)^8) ) /0.20 = 3.837159803 b-2. Sensitivity of NPV to changes in the sales figure 49.883 Working Notes: Sensitivity of NPV to changes in the sales figure = Change in NPV/ Change in sales lets take units changes to 65,000 units from 62,000 units Operating cash flows base =((price - variable cost) x annual quantity - fixed cost ) x (1- tax rate) +( tax rate x depreciation) =(($40 - $20) x 65,000 - 625,000 ) x (1- 0.35) +( 0.35 x 106,000) =($20 x 65,000 - 625,000 ) x (1- 0.35) +( 0.35 x 106,000) =($1300,000 - 625,000 ) x (1- 0.35) +( 0.35 x 106,000) =675,000 x 0.65 + 37,100 =438,750 + 37,100 =$475,850 NPVbase = –Initial investment + operating cash flow x (PVIFA 20%,8) NPVbase = –$848,000 + 475,850 x 3.837159803 NPVbase = –$848,000 + 1,825,912.4923 NPVbase = $977,912.4923 PVIFA @ 20% for 1 to 8th is calculated = (1 - (1/(1 + 0.20)^8) ) /0.20 = 3.837159803 Sensitivity of NPV to changes in the sales figure = Change in NPV/ Change in sales =(NPV at 62,000 - NPV at 65,000)/(62,000 -65,000) =($828,263.2599 - $977,912.4923)/-3000 =-149,649.23/-3000 = + 49.88307667 =+49.883 c. sensitivity of OCF to changes in the variable cost figure -40,300 Working Notes: sensitivity of OCF to changes in the variable cost figure = Change in operating cash flow / change in variable cost =OCF at new variable cost - OCF at old variable cost)/(new variable cost - Old variable cost) =($235,350 - $436,850) /($25-$20) =-$201,500/$5 = -40,300 Means increase in $1 of variable cost will decrease OCF by $40,300 or Increases if decrease variable cost per unit by $1. Let new variable cost per unit = $25 per unit OCF at new variable cost $25 per unit Operating cash flows base =((price - variable cost) x annual quantity - fixed cost ) x (1- tax rate) +( tax rate x depreciation) =(($40 - $25) x 62,000 - 625,000 ) x (1- 0.35) +( 0.35 x 106,000) =($15 x 62,000 - 625,000 ) x (1- 0.35) +( 0.35 x 106,000) =($930,000 - 625,000 ) x (1- 0.35) +( 0.35 x 106,000) =305,000 x 0.65 + 37,100 =198,250 + 37,100 =$235,350 Please feel free to ask if anything about above solution in comment section of the question.
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