Question

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?

I have found an answer with very confusing formulas and am unsure if it can be simplified. Previous questions from this assignment did not require the use of multiple formulas to find an answer, and I am not sure if I am making my answer more involved than needed. Thank you in advance!

Answer 1

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

=[(2.5)*Q -190500)]*0.65+56000

=[(2.5Q -190500)]*0.65 +56000

=1.625Q - 123825+56000

= 1.625Q - 67,825

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

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

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

Q =  144,702.87 / 1.625 =  89,048

The break even quantity is Q =  89,048