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

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.

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