Northfield Bakery: Choosing a Pop-Up Site Under Demand Uncertainty
Northfield Bakery is choosing between two six-week pop-up sites. A city-centre kiosk would have fixed costs of £20,000. A retail-park unit would have fixed costs of £10,000. Both sites sell the same range and earn a contribution of £2.50 per customer.
Demand depends on whether the local economy is buoyant or sluggish. The finance director estimates a 0.55 probability of a buoyant period and a 0.45 probability of a sluggish period. In a buoyant period the city-centre kiosk would attract 14,000 customers, while the retail-park unit would attract 9,000. In a sluggish period the city-centre kiosk would attract 6,000 customers, while the retail-park unit would attract 4,500. The bakery's owner is risk-averse and has said she wants to avoid a loss. A market-research agency offers a survey that would predict the demand state perfectly, for a fee of £2,000.
1. Construct a payoff table for the two sites and calculate the expected value, maximax, maximin and minimax regret decision. Recommend a site under each criterion.
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Payoff table (profit): Buoyant (0.55): City = 14,000 × £2.50 − £20,000 = £15,000; Retail = 9,000 × £2.50 − £10,000 = £12,500. Sluggish (0.45): City = 6,000 × £2.50 − £20,000 = −£5,000; Retail = 4,500 × £2.50 − £10,000 = £1,250.
EV City = 0.55 × £15,000 + 0.45 × (−£5,000) = £8,250 − £2,250 = £6,000. EV Retail = 0.55 × £12,500 + 0.45 × £1,250 = £6,875 + £562.50 = £7,437.50. Retail has the higher EV. Maximax: City £15,000; Retail £12,500 → choose City. Maximin: City −£5,000; Retail £1,250 → choose Retail. Minimax regret: best outcomes are £15,000 (buoyant) and £1,250 (sluggish). Regrets: City buoyant 0, sluggish £6,250; Retail buoyant £2,500, sluggish 0. Maximum regret: City £6,250; Retail £2,500 → choose Retail. So Retail is recommended by EV, maximin and minimax regret; City only by maximax.
2. Calculate the expected value of perfect information (EVPI). Advise whether the bakery should pay £2,000 for the survey.
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With perfect information, choose the best site in each state: City in buoyant (£15,000), Retail in sluggish (£1,250). Expected payoff = 0.55 × £15,000 + 0.45 × £1,250 = £8,250 + £562.50 = £8,812.50. EVPI = £8,812.50 − £7,437.50 = £1,375. The survey is worth at most £1,375 in expected-value terms, so at £2,000 it destroys value. Do not buy it on financial grounds. Caveats: the survey may reduce risk, not just raise expected profit; if the owner is highly risk-averse, she might value the information differently. Also the probabilities and payoffs are estimates, and the survey may be imperfect.
3. Discuss the limitations of expected value for this decision and explain how the owner's risk aversion might change the recommendation. Include two non-financial factors.
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EV assumes risk neutrality, linear payoffs, known probabilities and a repeated decision. Here it is a one-off decision; the city site can lose £5,000, which may threaten cash flow. A risk-averse owner may prefer retail despite a lower EV if it avoids loss and has lower maximum regret. Expected value also ignores the distribution of outcomes and the owner's utility.
Non-financial factors could include: the city-centre site may build brand awareness and future catering contracts; the retail park may have easier parking, lower staffing risk, or a shorter lease. Other factors include weather, competitor reaction, availability of staff, and the strategic value of establishing a city presence.