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QUESTION 1 Decision Analysis
Show all calculations to support your answers. You may follow the methods shown in the mp4 on Decision Analysis for a way to do part (b) of this question if you wish.
(a) Distinguish between decision making under certainty and decision making under uncertainty. To what aspects of the decision does the uncertainty refer? What other possible sources of uncertainty are there in decision making?
(b) Joe Black runs a manufacturing business. Because of competition in his market Joe is considering purchasing one of three new types of equipment, A, B or C. The conditional profits from each given favourable or unfavourable markets are as follows:
(i) If Joe is an optimist which type of equipment should he buy?
(ii) If Joe is a pessimist which type of equipment should he buy?
(iii) Following the criterion of regret which type of equipment should he buy?
(iv) If Joe believes that there is a 70% chance of the market being favourable which type of equipment should he buy?
(c) The management of Wildcat Drilling N.L. is considering the purchase of an oil exploration lease over a parcel of land, for $200,000. If the lease is purchased a test well could be drilled at a cost of $1,500,000. If the test well proved dry the lease would be abandoned. If the well brought in oil the lease could be sold immediately for $18,000,000. On known information the probability that the well would prove dry is assessed at 0.95.
The manager has absolute faith in the ability of a mystic, Bill Diviner, who for a fee of $500,000 can give a perfect prediction as to whether the well would be a success or dry.
Draw a decision tree showing the choices available to the manager of Wildcat and the merits of each. What should the management do?
QUESTION 2 Value of information
Show all calculations to support your answers. You may follow the methods shown in the mp4 on Value of info for a way to answer this question if you wish.
A firm is considering the marketing of a new product which will either be a success or a failure. The prior probability of success is judged to be 0.3. If the product is marketed and is a success the firm expects to earn $500,000, while a failure is expected to lead to a loss of $300,000.
(i) Should the product be marketed? Why?
(ii) What is the expected value of perfect information about the success or failure of the product?
The firm is considering a market survey whose results can be classified as favourable, neutral or unfavourable (meaning that you will have to prepare 3 lots of revisions of probability, one for each signal). Some of the conditional probabilities are:
p(favourable|success) = 0.6
p(neutral|success) = 0.3
p(neutral|failure) = 0.2,
p(unfavourable|failure) = 0.7.
(iii) What is the posterior probability of success given a favourable survey result?
(iv) What is the maximum the firm should be willing to pay for the market survey?
QUESTION 3 Simulation
This is a work integrated assessment item. The tasks are similar to what would be carried out in the workplace.
The Bandicoots Football Club gains significant revenue from ticket sales at each game played at home during the season. The sale of programs for these games also adds to profitability. Each program costs $2.00 to produce and sells for $5.00. Any programs unsold at the end of any game are sent to a recycling centre and do not produce any revenue.
Records of the programs sold for each game show the following:
Number of Programs Sold
(a) Your manager has asked you as the management accountant for the club to determine the profitability of program production. In particular you have been asked to investigate two strategies where the number of programs to be printed are either 2500 or 2600. You decide to use Excel to simulate the sale of programs at 10 games in a season together with the profit or loss on programs for each game when (1) 2500 and (2) 2600 programs are printed. Include a calculation of the total profit/loss for the season and the average profit/loss per game.
Hints: Your model should have 8 columns: Game #, RN Sales, Demand, Production #, Sales Units, Sales Revenue, Production Costs, Profit/Loss. The model must be completely formula driven - there must be no data in the model or the model formulas – all data should be in a data input section above the model. An IF or MIN function is required in the formulas in the Sales Units column. After completing the model you can vary the results by pressing F9 (recalculate) a number of times to view such variations resulting from changes in the random numbers generated.
Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts must show row and column numbers and be copied from Excel into Word. See Spreadsheet Advice in Interact Resources for guidance.
(b) To check on hour simulation conclusions use marginal analysis to determine the optimum number of programs to print.
(c) Write a report to your manager explaining which of the two production strategies you would recommend and why. You may support your report by including reference to the profits under each strategy, noting any limitations to the methods you have adopted to analyse the situations.
The report must be dated, addressed to the Manager and signed off by you.
(Word limit: No more than 150 words)
QUESTION 4 Regression Analysis and Cost Estimation
Acme Company is trying to estimate the behaviour of overhead costs. Data for the last 10 months has been collected, together with possible cost drivers, as follows (DLH = direct labour hours, MH = machine hours):
(a) Using the High-Low method of cost estimation and DLH as the cost driver, what would be the overhead cost equation?
(b) Using Excel, perform three regression analyses to regress overhead cost against DLH, then MH, then against both of them simultaneously. State the cost equation from each. Analyse and comment on the results of each regression as you perform it and determine the best one to use as a basis for future use.
(c) If the simple regression using DLH were adopted, what would be the predicted overhead in a month when there were 400 DLH and 500 MH used?
QUESTION 5 CVP Analysis
(a) CVP Ltd has a monthly sales volume of $75,000 for its only product. Variable costs are $45,000 and monthly fixed costs are $7,500.
i. Monthly breakeven point in sales dollars.
ii. The required level of sales to yield a monthly profit of $25,000 before tax.
iii. The profit before tax expected in a month in which sales of $80,000 are realised.
iv. The unit sales volume required to earn an after-tax monthly profit of $42,000 given a sales price of $20 per unit and a company tax rate of 30c in the dollar.
(b) A company makes two products, X and Y. At present the sales mix is 1 unit of X to 3 units of Y. Fixed costs per period are $20,000. Selling prices and variable costs per unit for each product are:
Unit selling price $18 $15
Unit variable cost $10 $11
i. Given this sales mix, how many units of each product must be sold in a period to make a profit of $15,000 before tax?
ii. If in a period the sales mix changed to 2 units of X to 2 units of Y, and the total number of units sold in the period were 8,000, how much profit would be earned in the period?
(c) Alpha Company produces a single product, Beta, which has the following unit selling price and costs:
Selling price per unit $2000
Variable costs per unit $1500
Fixed costs per annum $2 000 000
Prices and costs are certain, but annual demand is uncertain. It is thought that annual demand is normally distributed with expected sales of 6000 units and a standard deviation of 1000 units.
i. Calculate expected annual profit.
ii. What is the standard deviation of expected profit?
iii. Calculate the probability of at least breaking even using the probability distribution of profits.
This assessment task covers: Decision analysis: uncertainty and risk, Decision analysis: value of information, Simulation for complex decisions. Correlation and regression analysis and Cost-volume-profit analysis. It has been designed to ensure that you continue to engage with the subject content on a regular basis. More specifically, it seeks to assess your ability to:
apply decision theory and probability concepts to business situations
use simulation to analyse decisions
understand statistical hypothesis testing to interpret the significance of regression coefficients
apply CVP analysis to product mix decisions