Management is currently deciding whether or not to investigate a cost variance that was identified by the accounting system.To help address this question,you have generated the following data:
Possible States of Nature:
1.The underlying operation is in control (i.e. ,is operating normally).
2.The underlying operation is out of control (and therefore is in need of an intervention)
Possible Decisions/Courses of Action:
1.Investigate the variance (to determine its underlying cause(s)).
2.Do not investigate the variance.
Estimated Costs and Probabilities:
1.Cost of investigating the variance = I = $1,500.
2.Cost of correcting an out-of-control process (if the process is found to be out of control)= C = $6,000.
3.Losses from not correcting an out-of-control process = L = $50,000.
4.Probability,p,of the process being out of control = 15%
Required: 1.Given the above information,what is the expected value of investigating the reported variance? (Show calculation. ).
2.Prepare a payoff table that summarizes the states of nature (i.e. ,possible outcomes)and the decision alternatives (i.e. ,management actions).Your table should include cells for combinations of management actions and states of nature,plus cells to represent the expected value of each management action.Which decision is recommended on the basis of information in your payoff table?
3.Given the above information,what is the probability level,p,for an out-of-control process (i.e. ,a nonrandom variance)that would make management indifferent between investigating and not investigating the variance? In what sense can this probability be considered a breakeven probability? (Demonstrate this by calculating the expected value of each management action,based on the break-even probability,p,you calculated. )What is the correct management action of the probability of an out-of-control process is greater than the break-even probability,p? Show all calculations.Round final answers to the nearest whole numbers.
Please see Feedback for answers.

Question

Quizplus · Accepted Answer

Feedback: 1.E(investigate)= [I x (1 - p)] + [(I + C)x p] = [$1,500 x (1 - 0.15)] + [($1,500 + $6,000)x 0.15] = $1,275 + $1,125 =
2.Payoff Table: 11ea6e70_bd43_0551_8f54_a71c5712ceb4_TB1699_00 Since the expected cost of investing the variance < expected cost of not investigating the variance,the variance should be investigated.
3.Break-even probability,p,is defined so as to make management indifferent between the two possible courses of action,investigate and do not investigate.E(investigate)= E(do not investigate).([I x (1 - p)] + [(I + C)x p])= L x p.p = I/(L - C).p = $1,500/($50,000 - $6,000).p = 0.0341 (3.41%)Therefore,if the probability of an out-of-control process,p,is 0.0341,management would be indifferent between investigating and not investigating the variance,because the expected cost under each of these alternatives is the same,as shown below: E(investigate)= (0.9659 x $1,500)+ (0.0341 x $7,500)= $1,449 + $256 = $1,705.E(do not investigate)= (0.9659 x $0)+ (0.0341 x $50,000)= $0 + $1,705 = $1,705.If the probability of an out-of-control process > 0.0341,then the correct decision would be to investigate the variance (as was the case above when the out-of-control probability was 0.15).

Management Is Currently Deciding Whether or Not to Investigate a Cost