Phalaborwa Developmont luxury double storey complex The location provides a spec

ID: 3069842 • Letter: P

Question

Phalaborwa Developmont luxury double storey complex The location provides a spectacular v countryside, including mountains and rivers. PDC plans to pce Corporation (PDC) has purchased land that wil be the site of a new view of the surrounding the individual units between R300 000 and R1 400 000 PDC has c with 30 dopends units preliminary architectural drawings for three different projects one units, one with 60 units and one with 90 units. The financial success of the project upon the size of the complex and the chance event concerning the demand for the The decision problem is stated as follows Select the size of the new complex that wil load to he largest proft given the uncertainty conceming the demand for the units The information for the PDc case (in terms of action and states of nature), including the corresponding payoffs, can be summarised as tollows States of nature probability Decision alternative Strong demand (s.1) Weak demand (s2) 0.2 0.8 Small complex (d 1) Medium complex (d 2) Large complex (d_3) 14 20 -9 The management of PDC is considering a six-month market research study designed to learn more about the potential market's acceptance of the PDC project. Management anticipates that the market research study will provide the following two results: Favourable report a significant number of the individuals contacted express interest in purchasing a PDC unit (1) (2) Unfavourable report very few individuals contacted express interest in purchasing a PDC unit If the market study is undertaken, then P(Favourable report) -0.77 and P(Unfavourable report) 0.23 If the market report is favourable P(strong demand given favourable report)-0.94 P(weak demand given favourable report) 0.06

Explanation / Answer

Answer:

To determine the optimal decision strategy, we will use an approach based on a backward pass through the decision tree, using the following steps:

Step 1: At chance nodes, compute the expected value by multiplying the payoff at the end of each branch by the corresponding branch probabilities;

Step 2: At decision nodes, select the decision branch that leads to the best expected value. This expected value becomes the expected value at the decision node.

Results for Step 1 (first cycle):
The computed expected values for nodes 6 to 14 are:

Marketing Research Study, Favorable Report:
EV(Node 6) = 0.94 x $8M + 0.06 x $7M = $7.94M
EV(Node 7) = 0.94 x $14M + 0.06 x $5M = $13.46M
EV(Node 8) = 0.94 x $20M + 0.06 x -$9M = $18.26M

Marketing Research Study, Unfavorable Report:
EV(Node 9) = 0.35 x $8M + 0.65 x $7M = $7.35M
EV(Node10) = 0.35 x $14M + 0.65 x $5M = $8.15M
EV(Node 11) = 0.35 x $20M + 0.65 x -$9M = $1.15M

No Marketing Research Study:
EV(Node 12) = 0.80 x $8M + 0.20 x $7M = $7.80M
EV(Node 13) = 0.80 x $14M + 0.20 x $5M = $12.20M
EV(Node 14) = 0.80 x $20M + 0.20 x -$9M = $14.20M

Results for Step 1 (second cycle):
The expected value at chance node 2 can be computed as follows:

EV(Node 2) = 0.77 x EV(Node 3) + 0.23 x EV(Node 4)
= 0.77 x $18M + 0.23 x $8.15M = $15.93M

EV(Node 5) = (See Step 1, first cycle) = $14.20M

Results for Step 2 (first cycle):
For decision nodes 3, 4, and 5: Select the branches with the best expected values:

Expected Value at Node 3 = $18.26M

Expected Value at Node 4 = $8.15M

Expected Value at Node 5 = $14.20M

Results for Step 2 (second cycle):
Decision tree with one decision node (node 1) and two branches (node 2 and node 5) Ã Select the branches with the best expected values:

Expected Value at Node 1 = $15.93M

The optimum decision for PDC is to conduct the market research study and then to carry out the following strategy:

2. If the market research is unfavorable, construct the medium condominium complex.

In order to construct the risk profile for the optimal decision strategy, we need to compute the probability for each of the payoffs.

Computing the probabilities for each of the payoffs:

Payoff of V31 = $20M Probability = P(FR) x P(SDFR) = 0.77 x 0.94

= 0.72

Payoff of V32 = $9M Probability = P(FR) x P(WDFR) = 0.77 x 0.06

= 0.05

Payoff of V21 = $14M Probability = P(UR) x P(SDUR) = 0.23 x 0.35

= 0.08

Payoff of V22 = $5M Probability = P(UR) x P(WDUR) = 0.23 x 0.65

= 0.15

As you can see, the use of market research study lowered the probability of the initial $9M loss from 0.20 to 0.05. For the management team of PDC this is a significant reduction of the risk associated with the condominium project and most likely they will pay for a market research study prior to the decision which condominium size to select.