W4 - Joint & Byproduct Costing, Linear Programming Flashcards
Joint & Byproducts def.
Joint products: More than one product resulting from a single process e.g. crude oil refining. If these products have similar sales values, they are known as joint products
By products: If one has a very low relative value, its known as a byproduct
Apportioning costs by Volume to Joint products and byproducts
At split-off point, subtract the sales revenue from the By-Product from the total Cost of Joint Process to get the Costs to be attributed to the Joint Products.
HOWEVER, remember that if the byproduct comes from another process, not the initial joint process, it isn’t subtracted from the joint costs, instead its subtracted from the OWN COSTS of the product hose process created it
Create table with columns of Product A, Product B & Total
Rows:
Revenue:
Own costs:
NRV at split off: ( rev - own costs)
Joint costs apportioned by sales volume: (e.g. total sales volume is 60,000kg and Product A is 10k, B is 50k. Find percentage for both i.e. 10K/60K and then multiply this by the total costs for Joint Products THAT WAS CALCULATED EARLIER
Profit/Loss by sales volume:
Apportioning costs by Sales Value to Joint products and byproducts
Table is similar to the Sales Volume apportioing table.
First 3 rows (Revenue, Own Costs, NRV at split-off) will have identical numbers from the Sales Volume table (if you’ve been asked to apportion using that previously in the question)
Differs after this. Apportion Joint Costs as a % of the sales value total.
Profit/Loss by sales value
Should give same total profits as Sales Volume, but the ratio per product will differ
Apportioning costs by NRV to Joint products and byproducts
Table identical as the previous methods up to NRV at split-off
Joint costs apportioned by NRV which is listed in the above row:
Profit/Loss by NRV
NRV is a better tool for decision-making. One product may now make profit where it didn’t in the other two methods, showing we shouldn’t abandon that product, where the others would suggest we should. If NRV apportionment shows a product is STILL making a loss, it should be abandoned.
Selling the products at split-off point questions. Is it better?
Essentially a relevant costing question.
Create a table, Product A & B
Lose: Current NRV at split-off:
Gain: New Revenues (sales price at split-ff will be listed in the question):
Net gain/net loss:
If there is a net gain, then we should sell that product at split-off instead of undergoing further processing and vice versa. Net loss means we should keep it and sell after further processing
Key Factor Analysis - When to use and run through.
4 STEPS
Use when there is 1 limiting factor
Step 1) Determine limiting factor. Find the number of the factor required to make maximum demand and see if it exceeds the amount available. If it is less then its a limiting factor
Step 2) Find contribution per unit per hour of limiting factor. Find contribution per unit for the entire company, then divide the contribution per unit by the amount of limiting factor required per unit. e.g. CpU is £10 and one unit requires two labour hours. CpU of limiting factor is 10/2 = £5
Step 3) Rank the products in order of CpU of limiting factor.
Step 4) Find optimal production plan. Produce maximum of each product based on their ranking until there is not enough, then we complete as much as possible of next highest ranking products
Linear Programming - When to use and method.
7 STEPS
Use when there are 2 limiting factors
1) Define the unknowns. X = First limiting factor, Y = 2nd limiting factor
2) Formulate the objective function.
Maximum contribution = ‘…‘x + ‘…‘y
Blanks are the contribution per unit of each item, e.g. £100 and £200
3) Express constraints in terms of inequalities. e.g.
First constraint may be: labour constraint (polishing): 3x + 4y <_ 4,800
Labour constraint (polishing): 2x + 6y <_ 4,800
Production constraint (desk): X <_ 1,200
Non negativity, so X & Y must be >_ 0
4) Plot constraints on a graph of two unknowns - identify all feasible solutions.
We’ll draw a graph increasing by 200 each time on both axes for example.
Using our inequalities formulas. Assume that Y is 0 and vice versa which will give you a point.
e.g. 3x + 4y = 4,800
If X is 0, y = 1,200
If y is 0, x = 1,600.
So plot these on the graph to get our line.
Repeat for each inequality formula we have
5) Plot the objective function and identify the optimal point.
Now take our objective function (from Step 2), in this case is: Max Contribution = 100x + 200y
Maxe the max contribution equal any random number, e.g. 80,000
Plot this line on the graph.
Move this line, keeping gradient the same, to the highest point where it touches our feasible region (the region between each plotted line)
6) Solve algebraically for the unknowns.
We know that 3x + 4y = 4,800, and 2x + 6y + 4,800
Solve simultaneously, so multiply one side to get either the same X or Y, which you can subtract off.
Giving us a value for Y or X, then plug in to get the other value
7) Calculate the max profit given the constraints.
So, 100 x 960 + 200 x 480 = £192,000
Shadow Price def. and method
Take our original formula for the limiting factor in the question.
e.g. if the Q asked calculate shadow value of Assembly labour hours, we’d use 3x + 4y = 4,800
iNCREASE THIS BY ONE LABOUR HOUR, so we get 3x + 4y = 4,801
If we now simultaneously solve for this, we’ll get x = 960.6 and Y - 479.8
Inputting these new values into our objective function, we get £192,020
So our shadow price is new contr. - old contr. = £20
Finding validity range of shadow price
After finding the shadow price, may be asked to find validity range
Using the vertical line we plotted earlier, x >_ 1,200, solve for this and the other limiting factors formula: in this case 2x + 6y = 4,800
Giving x = 1,200 and y = 400
Plug this into the labour assembly hour (or whatever factor we’re finding the shadow value range for), giving us 3 x 1,200 + 4 x 400 = 5,200
5,200 - 4,800 = 400
So validity range of shadow price = 400
Sensitivity analysis
Check lecture online
Linear programming, assumptions and limitations
6
Linearity is assumed over the whole range being considered
Infinite divisibility of products and resources - solution may not have integer values. Solution must be an integer so we round down
Quality/reliability of input data - complete/accurate/valid
Only one objective to be satisfied and it must be quantifiable (non-financial objectives not considered e.g. maximising customer satisfaction or product quality)
Dual values/shadow prices are only valid over a certain range
Non-financial factors to consider in making the decision
Joint Costing, evaluating additional offers
See Exercise lecture week 4
Company may: offer $ per kg for 10,000 additional units of …
Develop a financial evaluation of the offer
Revenue
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