Suria Packaging: Plant Size, EMV and the Value of a Forecast
Suria Packaging must choose plant capacity before demand is known. Demand will be high, medium or low with probabilities 0.35, 0.45 and 0.20 respectively. The payoffs, in RM million, are:
| Plant | High | Medium | Low |
|---|---|---|---|
| Small | 8 | 5 | 2 |
| Medium | 14 | 7 | -1 |
| Large | 22 | 4 | -8 |
The finance director advocates the large plant because it has the highest expected monetary value. The operations director prefers the small plant because its worst outcome is the least damaging. A consultant offers a perfectly reliable demand forecast for RM1.5 million. The board is unsure whether the forecast is worth buying and whether the expected-value criterion should settle the decision. No other costs are relevant.
1. Calculate the expected monetary value of each plant size and recommend a choice on that criterion. Comment on the strength of the recommendation.
Read the worked answer
EMV(Small) = 0.35(8) + 0.45(5) + 0.20(2) = 2.80 + 2.25 + 0.40 = RM5.45m.
EMV(Medium) = 0.35(14) + 0.45(7) + 0.20(-1) = 4.90 + 3.15 - 0.20 = RM7.85m.
EMV(Large) = 0.35(22) + 0.45(4) + 0.20(-8) = 7.70 + 1.80 - 1.60 = RM7.90m.
On EMV, choose Large, but only by RM0.05m (RM50,000) over Medium. That is tiny relative to the size of the payoffs and to uncertainty in the probabilities. Large also produces an RM8m loss in the low state, while Medium's worst case is only -RM1m. A risk-neutral firm can justify Large on EMV, but the recommendation is weak; a risk-averse board could reasonably choose Medium, giving up almost nothing in expected value for a much smaller downside.
2. Compute the expected value of perfect information. Advise whether the consultant's perfect forecast at RM1.5 million is worth buying.
Read the worked answer
With perfect information, the best payoff in each state is chosen: High: max(8,14,22) = 22 Medium: max(5,7,4) = 7 Low: max(2,-1,-8) = 2
Expected payoff with perfect information = 0.35(22) + 0.45(7) + 0.20(2) = 7.70 + 3.15 + 0.40 = RM11.25m.
EVPI = 11.25 - 7.90 = RM3.35m.
The EVPI is an upper bound on what any information is worth. A truly perfect forecast at RM1.5m would leave a net gain of RM1.85m, so the price is below the upper bound. However, real forecasts are imperfect, and the value of an imperfect forecast is below EVPI. The probabilities are also subjective. The consultant's offer is worth negotiating, but EVPI alone does not prove it should be bought; the board should ask for the forecast's reliability and value it as imperfect information.
3. Evaluate the operations director's maximin proposal. Explain how the disagreement with the finance director should be resolved.
Read the worked answer
Maximin looks at the worst payoff for each plant: Small: min(8,5,2) = 2 Medium: min(14,7,-1) = -1 Large: min(22,4,-8) = -8
Maximin chooses Small, because its worst outcome is the least bad. Maximax would choose Large, with best payoff 22.
The disagreement is about risk attitude, not arithmetic. EMV is appropriate if the firm can absorb the RM8m loss and expects to face many similar decisions. Maximin is appropriate if an RM8m loss would be catastrophic or if the firm is strongly risk-averse. Medium is a practical compromise: it is almost tied with Large on EMV and has a much smaller worst-case loss. The board should decide using its risk tolerance, financing constraints and confidence in the probabilities, not by treating one criterion as universally correct.