Page 225 - BA2 Integrated Workbook STUDENT 2018

Risk 2: Probability

Example:

ABC is a furniture retailer. It offers a customer loan facility. If a new customer
requests a loan then ABC either: refuses it, gives a high loan limit, or gives a low loan
limit. From years of past experience, ABC estimates that the probability that a new
customer makes a full repayment of a loan is 0.95, whilst the probability of non-
repayment is 0.05 (these probabilities being independent of the size of loan limit).
The average profit on the loans, per customer is given by the following table.

Loan limit – High Loan limit – Low
Full repayment $50 $20
Non-repayment ($200) ($30)

A decision tree representing this information is shown below.

Repay 0.95
$50
A

High Not repay 0.05
loan ($200)

C
Refuse

Repay 0.95
$20
Low B
loan
Not repay 0.05
($30)

From this the expected value can be calculated at the outcome points A and B:

Expected value at point A: (0.95 × 50) + (0.05 × (200)) = 37.5

Expected value at point B: (0.95 × 20) + (0.05 × (30)) = 17.5

At decision point C compare the EVs of $37.5 and $17.5.

Recommendation: if a customer requests a loan give him/her a high loan limit.

Illustrations and further practice

Now try TYU 8

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