In order to answer this question it is necessary to start by calculating the new profit figures at an increase of 30%, then 20% and finally 10%.

Once these figures have been calculated the expected value of profits can be calculated by applying the three probabilities of 35% (good sales manager), 45% (average one) and 20% (bad one.)

Once the expected profit figure has been calculated the salary cost of a new manager then needs to be deducted from it.

Then, this expected net profit figure can be compared to the existing profit figure of $180,000 to then decide whether the manager should be employed. Hence, the calculations are as follows:

New profit figures before salary paid:
Good manager: $180,000 x 1.3 = $234,000
Average manager: $180,000 x 1.2 = $216,000
Poor: $180,000 x 1.1 = $198,000

Expected value of profits = (0.35 x $234,000) + (0.45 x $216,000) + (0.2 x $198,000) = $81,900+
$97,200 + $39,600 = $218,700.

Deduct salary cost and expected net profit with manager = $178,700
Since the company’s current profits are $180,000, the decision is therefore that the manager should not be employed as his employment would cause profits to fall by $1,300. So, the answer is A.

Distractor B would be selected by candidates who have forgotten to deduct manager’s costs from the expected profit of $218,700. With this omission, they would therefore advise the company to employ manager as profits will then increase by $38,700.

Distractor C would be selected by candidates who calculated an expected value based on profits of $140,000 instead of $180,000 i.e. they incorrectly deducted the manager’s costs at the start. Therefore their calculations would be as follows:

Good manager: $140,000 x 1.3 = $182,000
Average manager: $140,000 x 1.2 = $168,000
Poor manager: $140,000 x 1.1 = $154,000

Expected value of profits = (0.35 x $182,000) + (0.45 x $168,000) + (0.2 x $154,000) = $63,700+
$75,600 + $30,800 = $170,100.
Deduct salary cost and expected net profit with manager = $140,100
Therefore employ manager as profits will increase by $100 if comparing to the $140,000.

Distractor D is similar to C and would be selected by candidates who compared the $140,100 to $180,000 and advised the company not to employ the manager as it would cause profits to fall by $39,900.