Question

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

Answer 1

Let the sales units be X

Particulars	Amount ($)
Sales (Selling price per unit * Units)	28.8X (28.8 * X)
Variable cost (Variable cost per unit * Units)	8.1X (8.1 * X)
Contribution (Sales - Variable cost)	20.7X
Fixed cost	420,000
Depreciation (1,550,000 / 6)	258,333
PBT (Contribution - Fixed cost - Depreciation)	20.7X - 678,333
Tax @ 25% (PBT * 25%)	5.175X - 169,583.25
PAT (PBT - Tax)	15.525X - 508,749.75
Add: Depreciation	258,333
Annual cash flow	15.525X - 250,416.75
PVIFA @ 14% for 6 years	3.889
PV of cash flow (Annual cash flow * PVIFA)	60.38X - 973,870.74

Financial break-even point =>

PV of cash flow = Initial investment

60.38X - 973,870.74 = 1,550,000

60.38X = 1,550,000 + 973,870.74

X = 2,523,870.74 / 60.38

X = 41,799.78 (approx.)

Therefore, the exact answer is $41,804.