Question

# Grace P. has compiled this information related to a new project: Initial investment: \$1,550,000; Fixed costs:...

Grace P. has compiled this information related to a new project: Initial investment: \$1,550,000; Fixed costs: \$420,000; Variable costs: \$8.10 per unit; Selling price: \$28.80 per unit; Discount rate: 14 percent; Project life: 6 years; Tax rate: 25 percent. Fixed assets are depreciated using straight-line depreciation over the project's life. What is the financial break-even point?

 38,522 39,211 40,286 41,804 42,374

Solution

Initial investment =\$15,50,000

Selling price =\$28.80 per unit

Variable cost =\$8.10 per unit

Contribution per unit = \$28.80-\$8.10= \$20.70

Fixed cost =\$4,20,000

Project life = 6 years

Tax rate = 25%

Depreciation = 15,50,000/6= \$2,58,333

Tax saving on depreciation = \$2,58,333*0.25 = \$64,583

Financial break even point :-

Initial investment = present value of ( sales - variable cost - fixed cost) (1- tax rate) + present value of tax saving on depreciation

Assume number of units sold be X

15,50,000 = [(28.80 - 8.10) *X * 0.75]* PVAF ( 14%, 6 years) - 4,20,000*0.75*PVAF (14%,6 years) + 64,583* PVAF (14%,6 years)

15,50,000 = 60.37156X - \$12,24,930 + \$2,51,142

X =( 15,50,000 + 12,24,930 - 2,51,142) / 60.37156

X = 25,23,78/60.37156= 41,804

Financial break even point = 41,804

Option d is correct i.e. 41,804