QMDM – APR 2023 – L2 – Q2 – Decision Tree for Construction Contract

Explain EMV, draw decision tree, recommend contractor based on probabilities and payoffs.

Question

Taaboa a manufacturing firm has decided to capitalize on its existing success by building an extension to its production plant to come on stream by 2028. The firm has evaluated the decision and calculated that its profitability will improve by GHS 650,000.00 if the extension is completed on time. If, however, the extension is delayed then, because of contractual production commitments, the firm stands to lose some GHS 350,000.00. The firm has invited tenders for the construction work and two contractors have been shortlisted. Contractor A has indicated that they would undertake all the work themselves and that they have a track record such that 75 % of previous jobs have been completed on time. Contractor B, on the other hand, has a track record of 95 % of jobs being completed on time where Contractor B has done all work. However, Contractor B occasionally subcontracts work to other companies – some 30% of their jobs have a subcontract element in them. Their completion rate on jobs involving subcontractors is less impressive, with 40% of such jobs not being completed on time.

(a) Explain (in your own words) the term expected monetary value to the manager of Taaboa. [5 Marks]

(b) Draw a decision tree for the situation Taaboa faces. [15 Marks]

Answer

(a) Expected Monetary Value (EMV) is a decision-making tool that calculates the average outcome of a uncertain event by weighting possible payoffs by their probabilities. For Taaboa’s manager, it means multiplying each potential profit or loss (e.g., GHS 650,000 gain if on time, GHS 350,000 loss if delayed) by the likelihood of occurrence and summing them. This provides a single figure representing the ‘expected’ financial impact, helping compare risky options like contractors, though it ignores risk aversion—useful in banking for loan approvals where EMV assesses default risks against returns.

(b) The decision tree starts with a decision node: Choose Contractor A or B.

For A: All self-work. Branch to On Time (prob 0.75, payoff +650,000) or Delayed (0.25, -350,000). EMV_A = (0.75650,000) + (0.25(-350,000)) = 487,500 – 87,500 = 400,000.
For B: First, subcontract decision (implicit in track record): No Sub (prob 0.70), then On Time (0.95, +650,000) or Delayed (0.05, -350,000). Sub (0.30), then On Time (0.60, since 40% not on time so 60% on time) or Delayed (0.40, -350,000).
- EMV_NoSub = (0.95650,000) + (0.05(-350,000)) = 617,500 – 17,500 = 600,000.
- EMV_Sub = (0.60650,000) + (0.40(-350,000)) = 390,000 – 140,000 = 250,000.
- Overall EMV_B = (0.70600,000) + (0.30250,000) = 420,000 + 75,000 = 495,000.
  Tree structure: Decision square to A or B branches; probability circles for outcomes; endpoints with payoffs. (In practice, draw with lines; here described for clarity.)

To arrive at EMV: Use the formula EMV = Σ (Payoff_i * Probability_i). For A, straightforward. For B, conditional on subcontract: overall prob on time for B = (0.700.95) + (0.300.60) = 0.665 + 0.18 = 0.845; delayed 0.155. But tree uses nested.

(c) Recommend Contractor B, as EMV_B = GHS 495,000 > EMV_A = GHS 400,000, indicating higher expected profitability. In Ghanaian banking context, similar to choosing investments with higher EMV under BoG risk guidelines, but consider variance if risk-averse, as B has more variability due to subcontracting.

Tags: contractor selection, Decision tree, Expected Monetary Value, Probability, Uncertainty
Level: Level 2

Uploader: Samuel Duah