Question

A beauty product company is developing a new fragrance named Happy Forever. There is a probability of 0.46 that consumers will love Happy Forever, and in this case, annual sales will be 1.00 million bottles; a probability of 0.36 that consumers will find the smell acceptable and annual sales will be 174,000 bottles; and a probability of 0.18 that consumers will find the smell unpleasant and annual sales will be only 52,000 bottles. The selling price is $39, and the variable cost is $8 per bottle. Fixed production costs will be $1.05 million per year, and depreciation will be $1.20 million. Assume that the marginal tax rate is 40 percent. What are the expected annual incremental after-tax free cash flows from the new fragrance?

Answer 1

Expected sales (units) = [Probability(i) * Units(i)]

=1

= [0.46 * 1,000,000] + [0.36 * 174,000] + [0.18 * 52,000]

= 460,000 + 62,640 + 9,360

= 532,000

Expected pre-tax profit ($) = Expected Revenue - Expected variable costs - Fixed costs - Depreciation

= (532,000 * $39) - (532,000 × $8) - $1,050,000 - $1,200,000

= $20,748,000 - $4,256,000 - $1,050,000 - $1,200,000

= $14,242,000

Expected after-tax profit ($) = Expected pre-tax profit * (1 - tax rate)

= $14,242,000 * (1 - 0.4)

= $8,545,200

Expected after-tax free cash flow ($) = Expected after-tax profit + Depreciation (Since it's non-cash expense)

= $8,545,200 + $1,200,000

= $9,745,200