Solution to question 1:
The transfer price will be $40 as we assume marginal cost is equal to variable cost and that there is excess capacity unless stated otherwise.
Solution to question 2:
i) Minimum Transfer Price
The minimum transfer price will usually be marginal cost unless there is an opportunity cost to the division providing the goods/services.
If we read the question carefully there is an opportunity cost for S because they can avoid paying a third of their overhead costs if they stop selling to B.
|S Division Costs|
|Total Marginal Cost||$8.60|
|Opportunity Cost (1/3 of fixed overheads)|
|Minimum Transfer Price||$9.00|
ii) Maximum Transfer Price
The maximum transfer price B will be willing to pay is $14 as otherwise they could buy the goods externally at a cheaper rate.
Solution to question 3:
i) Number of units to be sold to maximise profit
Answer 300 units
To find the optimum number of units we use the formula:
MR = a – 2bx
a = 75
b = 0.08 -> ($4/50 units) Demand increases by 1 unit for every £0.08 reduced from the price.
MR = 75 – (2 * 0.08) x
MR = 75 – 0.16x
Profit is maximised at MR = MC. MC is given as $27 in the question so:
75 – 0.16x = 27
48 = 0.16x
300 = x
Therefore, at 300 units, profit is maximised
ii) Price to be charged to maximise profit
To find the optimum selling price to be charged we use the formula:
P = a – bx
P = 75 – (0.08 * 300)
P = 75 – 24
Therefore, at a price of $51, profit is maximised
iii) Revenue generated
Revenue is calculated as 300 units sold at $51 each = $15,300