We are evaluating a project that costs $800,000, has an eight-year life, and has
ID: 2737952 • Letter: W
Question
We are evaluating a project that costs $800,000, 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 60,000 units per year. Price per unit is $40, variable cost per unit is $20, and fixed costs are $800,000 per year. The tax rate is 35 percent, and we require a return of 10 percent on this project. a. Calculate the accounting break-even point. (Do not round intermediate calculations and round your final answer to nearest whole number (e.g., 32).) Break-even point 45000 units b-1 Calculate the base-case cash flow and NPV. (Do not round intermediate calculations and round your NPV answer to 2 decimal places (e.g., 32.16).) Cash flow $ 295000 NPV $ 773796 b-2 What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations and round your final answer to 3 decimal places (e.g., 32.161).) NPV/Q $ 295000 b-3 Calculate the change in NPV if sales were to drop by 500 units. (Enter your answer as a positive number. Do not round intermediate calculations and round your answer to 2 decimal places (e.g., 32.16).) NPV would by $ c. What is the sensitivity of OCF to changes in the variable cost figure? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your final answer to nearest whole number (e.g., 32).) OCF/VC $
Explanation / Answer
a.
Annual depreciation = $800,000/8 years = $100,000
Total fixed costs = $800,000 + $100,000 = $900,000
Contribution margin per unit = Selling price per unit – Variable cost per unit = $40 - $20 = $20 per unit
Accounting breakeven point = Fixed costs/Contribution margin per unit = $900,000/$20 per unit = 45,000 units
b.
Total contribution margin = $20 * 60,000 units = $1,200,000
Net income after taxes = (Contribution margin – Fixed costs)*(1-Tax rate) = ($1,200,000 - $900,000) * (1 – 0.35) = $195,000
Annual Operating cash flows = Net income after taxes + Depreciation = $195,000 + $100,000 = $295,000
Present value of annuity of $1 = {1-(1+r)-n}/r
Present value of annual operating cash flows = $295,000*(1-1.10-8)/0.10 = $295,000 * 5.3349 = $1,573,795.50
Net present value for base case = -$800,000 + $1,573,803.23 = $773,795.50
Say Q = 70,000 units
New contribution margin = 70,000 units * $20 = $1,400,000
Net income after taxes = ($1,400,000 - $900,000)*(1-0.35) = $325,000
New operating cash flows = $325,000 + $100,000 = $425,000
Present value of operating cash flows = $425,000*5.3349 = 2,267,332.50
New NPV = -$800,000 + $2,267,332.50 = $1,467,332.50
Sensitivity of NPV to changes in sales = DNPV/DS = ($1,467,332.50 - $773,795.50)/(70,000 - 600,000) = $65.3537
If sales were to drop by 500 units, then NPV would drop by = $65.3537 * 500 units = $34,676.85
c.
Say, variable cost = $19 per unit
New contribution margin = ($40-$19)*60,000 units = $1,260,000
New net income after taxes = ($1,260,000-$900,000)*(1-0.35) = $234,000
New operating cash flows = $234,000 + $100,000 = $334,000
Sensitivity of OCF to changes in the variable cost figure = DOCF/DVC = ($295,000 – $334,000)/($20 – $19) = –$39,000
If variable costs fell by $1 then, OCF would rise by $39,000
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