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"A manager is trying to decide whether to build a small, medium, or large facility. Demand can be low, average, or high, with the estimated probabilities being 0.25, 0.40, and 0.35, respectively.
A small facility is expected to earn an after-tax net present value of just $18,000 if demand is low. If demand is average, the small facility is expected to earn $75,000; it can be increased to medium size to earn a net present value of $60,000. If demand is high, the small facility is expected to earn $75,000 and can be expanded to medium size to earn $60,000 or to large size to earn $125,000.
A medium-sized facility is expected to lose an estimated $25,000 if demand is low and earn $140,000 if demand is average. If demand is high, the medium-sized facility is expected to earn a net present value of $150,000; it can be expanded to a large size for a net payoff of $145,000.
If a large facility is built and demand is high, earnings are expected to be $220,000. If demand is average for the large facility, the present value is expected to be $125,000; if demand is low, the facility is expected to lose $60,000."

Draw a decision tree for the three options described in the question above. What should management do to achieve the highest expected payoff?



Answer :

0802411

Answer:

Explanation:

To solve this problem, we'll construct a decision tree to visualize the different options and their associated payoffs based on the probabilities of demand being low, average, or high.

Let's denote the options as follows:

- S: Small facility

- M: Medium facility

- L: Large facility

Here's the decision tree:

```

                     / Low (0.25)

                    /

            S ----<---- Average (0.40)

           / \         \

          /   \         \  

     Low /     \ Average \ High

        /       \         \

       /         \         \

  $18,000    $75,000    $75,000

  (S)        (S)        /     \

                        /       \

                  $60,000 (M)  $125,000 (L)

                      (M)       (L)

                     / Low (0.25)

                    /

            M ----<---- Average (0.40)

           / \         \

          /   \         \  

     Low /     \ Average \ High

        /       \         \

       /         \         \

  -$25,000    $140,000   $150,000

    (M)        (M)       /     \

                        /       \

                  $145,000 (L)  $220,000 (L)

                      (L)       (L)

                     / Low (0.25)

                    /

            L ----<---- Average (0.40)

           / \         \

          /   \         \  

     Low /     \ Average \ High

        /       \         \

       /         \         \

  -$60,000   $125,000    $220,000

    (L)        (L)         (L)

```

To achieve the highest expected payoff, management should choose the option with the highest expected value.

Based on the decision tree and the probabilities given:

- Expected payoff for a Small facility: \( 0.25 \times 18000 + 0.40 \times 75000 + 0.35 \times 75000 = 62250 \)

- Expected payoff for a Medium facility: \( 0.25 \times (-25000) + 0.40 \times 140000 + 0.35 \times 150000 = 111750 \)

- Expected payoff for a Large facility: \( 0.25 \times (-60000) + 0.40 \times 125000 + 0.35 \times 220000 = 101500 \)

Thus, management should choose to build a Large facility to achieve the highest expected payoff.

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