Question

λambda Corp. is analyzing a project which has the following estimates: Sales price per unit: $63 Variable costs per unit: $31.50 Fixed costs: $7,300; Required return: 13% Initial investment: $12,000, with no salvage value Depreciation method: Straight-line Project life: five years. λambda Corp. is a non-profit organization and is not subject to income taxes. |

What sales quantity will result in an NPV of zero? |

Answer #1

Initial investment = $12,000

Sales price per unit = $63

Variable costs per unit = $31.50

Fixed costs = $7,300

Required return = 13%

Depreciation has no consideration in the calculation because there is no tax.

Required : NPV = 0

NPV = Present value of cash inflows - Initial investment

When NPV is 0

Initial investment = Present value of cash inflows

Hence, Present value of cash inflows = $12,000

Present value of cash inflows = [Sales quantity x (Sales price per unit - Variable costs per unit) - Fixed costs] x PVAF (13%, 5 years)

Hence, 12,000 = [Sales quantity x (63 - 31.50) - 7,300] x 3.5172

12,000 / 3.5172 = (Sales quantity x 31.5) - 7,300

3,411.8048 = (Sales quantity x 31.5) - 7,300

3,411.8048 + 7,300 = Sales quantity x 31.5

10,711.8048 / 31.5 = Sales quantity

Sales quantity = 340 units approx.

**Hence, sales quantity of 340 units approx. will result
in an NPV of zero**

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