Question

A project has the following estimated data: price = $80 per unit; variable costs = $28.80 per unit; fixed costs = $5,500; required return = 10 percent; initial investment = $8,000; life = seven years. Ignore the effect of taxes. a. What is the accounting break-even quantity? b. What is the cash break-even quantity? c. What is the financial break-even quantity? d. What is the degree of operating leverage at the financial break-even level of output?

Answer 1

Solution:

a)Calculation of accounting break-even quantity

Accounting break even quantity=Fixed cost for each period/Contribution per unit

Fixed cost include annual depreciation,that is;

=Initial investment/Life of the project

=$8000/7=1142.86

Total Fixed cost=$5500+$1142.86=$6,642.86

Accounting break even quantity=$6,642.86/($80-$28.80)

=$6642.86/$51.20

=129.74 units or 130 units

b)Calculation of cash break-even quantity

Cash break-even quantity=Cash fixed cost/Contribution per unit

=$5500/$51.20

=107.42 units or 107units

c)At financial break-even,the project will have Zero NPV.Therefore,Sum of present value cash flows of the project shall be equal to its initial cost.Thus operating cash flows of the project is calculated as follow;

Initial cost=Operating cash flows*Present value of annuity factor@10% for 7 years

$8,000=Operating cash flows*4.86842

Operating cash flows=$8,000/4.86842

=$1643.24

Now,financial break even point is;

=[$5500+$1643.24]/($80-$28.80)

=$7,143.24/$51.20

=139.52 units or 140 units

d)Degree of operating leverage(DOL)

DOL=1+($5500/$1643.24)

=4.35