Question Of The Week

BEC: Expected Value

A company has determined that its sales to residential home builders tend to vary with changes in the prime interest rate. Sales this year will be $5 million. The following information is available:

Prime interest rate	Probability	Sales growth
Increases 2%	15%	(20%)
Increases 1%	40%	3%
Unchanged	35%	5%
Decreases 1%	10%	8%

What amount is the expected value of the company's sales for the coming year's budget?

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		A. $5,037,500
		B. $5,150,000
		C. $5,172,500
		D. $5,337,500

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Explanation

Expected value = ∑ (Probability × Projected sales)

COSO's Enterprise Risk Management (ERM) framework addresses multiple aspects of risk, including prioritizing risk and assessing the severity of that risk. Risk responses are developed based on that assessment. The primary factor in prioritizing risk is calculating the expected value.

Expected value is determined by assigning probabilities to identified risks and combining the likelihoods and amounts of those risks."To find expected value in this scenario, first determine the projected sales amount for each of the interest rate changes using the projected growth rate. Remember, current year sales are given as $5,000,000. For example, if the interest rate increases 2% with a negative sales growth of (20%), projected sales are $4,000,000 [$5,000,000 × (1 − 20%)].

Next, multiply projected sales by the probability of occurrence. Continuing with the same example, the expected value would be $600,000 ($4,000,000 × 15%). Total expected value is $5,037,500, calculated as follows:

Prime interest rate		Sales growth	Projected sales	Probability	Expected value
Increases 2%		(20%)	$4,000,000	15%	$ 600,000
Increases 1%		3%	5,150,000	40%	2,060,000
Unchanged		5%	5,250,000	35%	1,837,500
Decreases 1%		8%	5,400,000	10%	540,000
	Expected value		$5,037,500

Things to remember:
COSO's Enterprise Risk Management (ERM) framework addresses multiple aspects of risk, including prioritizing risk and assessing the severity of that risk. The primary factor in prioritizing risk is calculating the expected value. Expected value assigns probabilities to identified risks and combines the amount of all the risks into a single value.

Lecture References :

BEC 8.03 : Planning, Control & Analysis: Performance Measures

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