Question

We are evaluating a project that costs $788,400, has a nine-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 75,000 units per year. Price per unit is $52, variable cost per unit is $36, and fixed costs are $750,000 per year. The tax rate is 21 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 and round your answer to the nearest whole number, e.g., 32.)
a-2.	What is the degree of operating leverage at the accounting break-even point? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)
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.)
b-2.	What is the sensitivity of NPV to changes in the quantity sold? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c.	What is the sensitivity of OCF to changes in the variable cost figure? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32. )

Answer 1

Answer a (1):

Annual Fixed cost = $750,000

Depreciation = Cost of project /useful life = 788400 / 9 =$87,600

Contribution per unit = sales price - variable cost per unit = $52 - $36 = $16

Contribution margin ratio = 16/52 = 30.76923%

Accounting break-even in units = Total Fixed costs / Contribution per unit = (750000 +87600) / 16 = 52350 units

Accounting break-even in dollar sales = break-even in units * sales price = 52350 * 52 = $2,722,200

Accounting break-even in units = 52350 units

Accounting break-even in dollar sales = $2,722,200

Answer a(2):

At accounting break-even, operating cash flow (OCF) is equal to Depreciation.

Degree of operating leverage (DOL) = 1 + FC / OCF = 1 + 750000 / 87600 = 9.562

Degree of operating leverage (DOL) = 9.562

Answer b(1):

Base case cash flow (for year 0 and for years 1 to 9) and NPV are calculated and given below (highlighted)

Answer b(2):

Sensitivity of NPV to changes in the quantity sold:

Change in NPV for change per unit of quantity = Contribution per unit * (1 - Tax rate) * PV factor for annuity

= 16 * (1 - 21%) * 5.328250

= $67.35

Sensitivity of NPV to change of per unit in the quantity sold = $67.35

Answer c:

If variable cost increases contribution decreases.

Sensitivity of OCF to changes in the variable cost = - Variable cost * Quantity *(1 - Tax rate) = - $1* 75000 * 79% = - $59,250

Sensitivity of OCF to change per $ in the variable cost = - $59,250

(when variable cost increases by $1, OCF decreases by $59,250)