Kurt’s Interiors is considering a project with a sales price of $11, variable cost per unit of $8.50, and fixed costs of $134,500. The tax rate is 35 percent and the applicable discount rate is 14 percent. The project requires $224,000 of fixed assets that will be worthless at the end of the 4-year project. What is the present value break-even point in units per year?

The present value break-even point is 89,048 units

Explanation:

In order to calculate the present value break-even point in units per year we have to calculate first the annual cash flows using the following formula:

Annual cash flows, C = [(Sale Price per unit - Variable cost per unit) x Quantity - Fixed costs - Depreciation] x (1 - Tax rate) + Depreciation = [(11 - 8.50) x Q - 134,500 - 224,000 / 4] x (1 - 35%) + 224,000 / 4 = 1.625Q -67,825

This annual cash flow will occur as annuity over n = 4 years.

The Discount rate, r = 14%

Hence, PV of annual cash flows = C / r x [1 - (1 + r)-n] = Initial investment for cash flow break even

Hence, (1.625Q - 67,825) / 14% x [1 - (1 + 14%)-4] = 224,000

Or. (1.625Q - 67,825) x  2.9137 = 224,000

Hence, 1.625Q = 224,000 /  2.9137 + 67,825 =  144,702.87

Hence, Q =  144,702.87 / 1.625 =  89,048

Hence, the break even quantity is Q =  89,048

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