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.

   

a-1	Calculate the accounting break-even point.

  

Break-even point

units

   

a-2	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))

   

DOL

   

b-1	Calculate the base-case cash flow and NPV. (Round your NPV answer to 2 decimal places. (e.g., 32.16))

  

Cash flow	$
NPV	$

  

b-2	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))

  

?NPV/?Q

$

  

c.	What is the sensitivity of OCF to changes in the variable cost figure? (Negative amount should be indicated by a minus sign.)

  

?OCF/?VC

$    What is a2-c

Answer 1

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.