Help with Shadow Pricing question

Ssheha11y ago

I have a question from Kaplan exam kit that I need help with. Product A and B are made of the same raw materials. Product A : Selling price $20 Materials $6 Labour $4 VOH $2 Contribution per unit $8 Product B: Selling Price $18 Materials $5 Labour $3 VOH $1.50 COntribution per unit $ $8.50 The maximum demand for A is 500 units per week and unlimited for product B per week. What would the shadow price of these materials be if the material were limited to 2000kg per week? Ans: $3.40 per kg However, I couldnt understand how in the answer sheet, it was simply done by optimising the production of B and then divide the contribution per unit bu the number of kg B uses for one unit.

John MoffatTutor11y ago#1

It would have helped if you had typed out the full question - you have not said how many kg of material is used by each of the products!!!! However, firstly, B is better than A because the contribution per kg is higher for B that for A. So....because there is unlimited demand for B, you would use all 2,000 kg making product B. The shadow price is the most extra you would be prepared to pay to get 1 extra kg of material. I am guessing that product B uses 2.5 kg of material and is currently paying $2 per kg. In which case, B is currently generating a contribution of $8.50 / 2.5 = $3.40 per kg. If we have to pay extra to get more kg's of B, then for every extra $1 we will make $1 less contribution per kg, so we are prepared to pay extra up to $3.40 extra per kg. (If we paid more extra than that, then we would lose money) Although that is all that is asked, it means we would be prepared to pay up to $5.40 per kg ($2 + $3.40). The shadow price is the most extra that we are prepared to pay.

Ssheha11y ago#2

Oops. I missed our that important detail. Thats right. It is $2 per kg. If in the question, fixed cost was also given, would it be right if I had used the profit instead to find shadow pricing? I can understand that we are finding how much more we are willing to pay for an extra kilo of material. But, I dont understand why use the contribution when part of contribution is to cover fixed cost.

John MoffatTutor11y ago#3

No - the fixed cost would not be relevant because (by definition) it would stay the same. All that would change if we were able to make more units would be the contribution.

ZZa9y ago#4

Hi, just wanted to ask how we got the 2.5kg for product B for this question?

John MoffatTutor9y ago#5

The materials per unit cost $5 Materials cost $2 per kg. Therefore each unit must use 5/2 = 2.5 kg (2.5 kg x $2 per kg = $5 per unit)

ZZa9y ago#6

Hello John, I understand the 3.40 because this is the contribution per kilo that we could use to buy more kilos. If the selling price is 18 and the direct labour + v/oh equates to 4.50, surely we have more than 5.40 to play with before we start making a loss?

John MoffatTutor9y ago#7

Not at all!! The selling price less the direct labour and overheads is $13.50 per unit. Since is uses 2.5 kg of material per unit, this means a maximum of $13.50/2.5 = $5.40 per kg, and the question wants the shadow cost of material. Have you watched my free lectures on this? The lectures are a complete free course and cover everything needed to be able to pass the exam well. (By the way, have you got a current edition of a Revision Kit from one of the ACCA approved publishers? If not then it is vital that you get one because they contain lots of exam standard questions to practice on, and question practice is essential to passing the exam.)