The LeGou Pen Company is considering development of a new fountain pen line. All their existing lines use cartridge-converter mechanisms and the new line will be a piston-filler.

In year zero, the company will pay for new machinery to produce these piston-filling pens. The total start-up cost of this investment is 20,000. From this initial investment, the company will begin selling black piston-filling pens in year 1. The total stream of free cash flows (including all possible cannibalization of their cartridge-converter lines) is estimated to have a time zero discounted value of 15,000.

Now suppose that the company is considering the possibility of offering their piston-filler pen in additional colors. The investment required to make new pen colors will occur in time one, and cost 8,000. At year zero, there is uncertainty about how popular the company’s piston-filling mechanism will be. Thus, at year one, there is a 50% probability that the additional colors of piston-fillers will produce a time-one discounted free cash flow stream equal to 25,000 (including all cannibalization costs). However, at year one there is also a 50% probability that the additional colors of piston-fillers will produce a time-one discounted free cash flow stream equal to 5,000.

The risk-neutral probability of the piston-fillers being popular is 48%.a

The firm’s cost of capital is 8%.

What is the value of black piston-filling pens as a standalone project?

Suppose the firm commits to investing in additional colors, regardless of market information at time 1. What is the value of the piston-filling line at LeGou Pens?

What would you value LeGou Pens’ piston-filling line to be if you took a strategic options approach?

What is the dollar value of the option?

Please show work and formulas