# Conservation and expected values – Under uncertainty and risk

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• musemma
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Pls can anyone help with an explanation of how the pay off table was derived for question1 of F5 exam for June 2011. I have pasted below. I have looked at the answer but I still do not understand how the values in the table was arrived at. The calculation look ambiguous and confusing. While I understand the parts b and c (expected values and maximin, maximax), it is the part a that I am finding it difficult to understand. I will strongly appreciate if anyone could assist. Below is the question.

Weather Probability Demand
Good 25% 350,000 bags
Average 45% 280,000 bags
Poor 30% 200,000 bags
Each bag of cement sells for \$9 and costs \$4 to make. If cement is unsold at the end of the year, it has to be disposed
of at a cost of \$0·50 per bag.
Cement Co has decided to produce at one of the three levels of production to match forecast demand. It now has to
decide which level of cement production to select.
Required:
(a) Construct a pay off table to show all the possible profit outcomes

acca13
Participant

\$9 is th S.P. and the cost is \$4= you get \$5 profit per bag,
but if the cement is unsold the cost of disposal is \$0.5 + \$4 (the original cost) = overall loss is \$4.5

I will solve the first 3, the rest you can do on your own and match against the answer.

If the supply of bags is 350,000, and the demand too is 350,000 bags in good weather conditions, you would get 350,000 * 5 = \$1750,000

If the supply of bags is 350,000 and the demand is 280,000 bags in average weather condition, you will get 280,000 * 5 = \$1400000 and since 70,000 bags now needs to be disposed of ( 350,000 – 280,000) as there was less demand than the supply, you would get a loss on disposal of \$315000, so the overall profit you would get is: \$1400000 – \$315000 = \$1085000

If the supply of bags is 350,000 and the demand is 200,000 bags in poor weather condition, you would get \$200000 * 5 = 1000,000 and since 150,000 bags are unsold they need to be disposed of ( 350,000 – 200000), you would get a loss on disposal of \$675,000, so the overall profit you would get is \$1000000 – \$675000 = \$325,000.

Now you can solve the rest of the question on your own

musemma
Participant

Thank you so much.

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