Question

We are evaluating a project that costs $660,000, has a five-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 69,000 units per year. Price per unit is $58, variable cost per unit is $38, and fixed costs are $660,000 per year. The tax rate is 35 percent, and we require a return of 12 percent on this project. a-1 Calculate the accounting break-even point. (Do not round intermediate calculations. Round your answer to the nearest whole number, e.g., 32.) Break-even point units a-2 What is the degree of operating leverage at the accounting break-even point? (Do not round intermediate calculations. Round your answer to 3 decimal places, e.g., 32.161.) DOL b-1 Calculate the base-case cash flow and NPV. (Do not round intermediate calculations. Round your cash flow answer to the nearest whole number, e.g., 32. 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 2 decimal places, e.g., 32.16.) ?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. Do not round intermediate calculations. Round your answer to the nearest whole number, e.g., 32. ) ?OCF/?VC

Answer 1

a-1). Depreciation = $660,000/5 = $132,000

Accounting Breakeven Point = [(Fixed Costs + Depreciation) / (Price per unit - Variable Costs per unit)]

= [($660,000 + $132,000) / ($58 - $38)

= $792,000 / $20 = 39,600 units

a-2). To calculate the accounting breakeven, we must realize at this point (and only this point),

the OCF is equal to depreciation. So, the DOL at the accounting breakeven is:

DOL = 1 + FC/OCF = 1 + FC/D = 1 + [$660,000/$132,000] = 6

b-1). OCF_Base = [(P - VC)Q - FC](1 - T_c) + [T_c x Depreciation]

= [($58 - $38)(69,000) - $660,000][1 - 0.35] + [0.35 x $132,000]

= $468,000 + $46,200 = $514,200

NPV_Base = PV of Cash Inflows - PV of Cash Outflows

= $514,200(PVIFA_12%,5) - $660,000

= [$514,200 x 3.6048] - $660,000 = $1,193,588.16

b-2). To calculate the sensitivity of the NPV to changes in the quantity sold, we will calculate

the NPV at adifferent quantity. We will use sales of 74,000 units. The OCF at this sales level

is:

OCF_new = [(P - VC)Q - FC](1 - T_c) + [T_c x Depreciation]

= [($58 - $38)(74,000) - $660,000][1 - 0.35] + [0.35 x $132,000]

= $533,000 + $46,200 = $579,200

NPV_New = PV of Cash Inflows - PV of Cash Outflows

= $579,200(PVIFA_12%,5) - $660,000

= [$579,200 x 3.6048] - $660,000 = $1,427,900.16

So, the change in NPV for every unit change in sales is:

?NPV/?S = ($1,193,588.16 – $1,427,900.16) / (69,000 – 74,000)

?NPV/?S = -$234,312 / -5,000 = +$46.8624

If sales were to drop by 500 units, then NPV would drop by:

NPV drop = $46.8624(500) = $23,431.20

c). To find out how sensitive OCF is to a change in variable costs, we will compute the OCF at

a variable cost of $39. Again, the number we choose to use here is irrelevant:

We will get the same ratio of OCF to a one dollar change in variable cost no matter what variable cost we use. So, using the tax shield approach, the OCF at a variable cost of $39 is:

OCFnew= [($58 – $39)(69,000) – $660,000](.65) + .35($132,000)

OCFnew= $423,150 + $46,200 = $469,350

So, the change in OCF for a $1 change in variable costs is:

?OCF/?v = ($514,200 – $469,350) / ($38 – $39)

?OCF/?v = $44,850 / -$1 = -$44,850

If variable costs decrease by $1 then OCF would increase by $44,850