Imagine that it is 2024 and that supplies of brie from France are about to be cut off. UK sales by a potential monopoly producer of domestic Brie are governed by the inverse demand curve = 68.25 − 5, where Q is the quantity sold and P is the price; the producer must pay a marginal cost for milk, currently estimated at = £12.75. In 2025, this marginal cost will either increase to £28.25 or fall to £5; a cost reduction is twice as likely as a cost increase. The potential UK cheesemaker is considering investing in a factory that would start producing in 2025 (next year). The investment must be made in 2024 and will cost = £125; the plant only operates for one year. The risk-free interest rate is = 5%. Assume that all Brie price risk is diversifiable. You may treat 2024 as the current year.

To aid the evaluation, the firm’s advisor has noticed that stock in the dairy farmers’ cooperative, currently priced at = £30 per share, is perfectly correlated with the potential profits of the new factory. If the cost of milk increases (due to climate change), the cooperative’s stock will fall to=£20 per share If milk becomes cheaper ,the cooperative’s stock will sell for = £50 per share.

a. If the plant would only operate for one year (closing after 2025), should the firm make this investment? What is the associated WACC? [8 marks]

b. What would be the value to the firm of an option to delay the decision until the beginning of 2025 (when the price of milk will be known), assuming that the investment cost rises at half the riskless rate? What portfolio comprised of stock in the cooperative and riskless bonds would replicate the pattern of returns and price the option? [10 marks]

c. What is the value of an option to delay the decision for two years, assuming that no further delay is possible after that? You should assume that the price of milk will rise or fall again in 2026 by the same proportions (compared to 2025) as it did in 2025 (compared to 2024). Also, the cost of building the plant will again rise at half the riskless rate. Identify all decision points and the associated WACCs. [12 marks]