transfer pricing

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CHAPTER 8

Transfer Pricing1 Principles of transfer pricingWhat is a transfer price?A transfer price is the price at which goods or services are transferred from oneprofit centre to another within the same organisation..

Objectives of a transfer pricing system♦ Goal congruence The decisions made by each profit centre manager

should be consistent with the objectives of the organisation as a whole.

♦ Performance appraisal The performance of each responsibility centreshould be capable of being assessed.

♦ Divisional autonomy The system used to set transfer prices should seekto maintain the autonomy of profit centre managers

2 Transfer pricing with no external marketThe receiving division may be selling on a perfect market or an imperfectmarket.

♦ A perfect market is one where the receiving division must accept thismarket price (because there are many companies in the field and no onecompany can dictate to the market).

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♦ An imperfect market is one where the receiving division sets the marketprice for the final product (perhaps because there is a monopoly).

ExampleA firm manufactures and sells shepherds’ crooks. The company is organisedinto two divisions, one of which concentrates on manufacturing the basic crook,while the other finishes the crook and is responsible for selling and distribution.The total annual cost and demand functions are as shown below.

Total annual cost in manufacturing division,

CM = 5,000 + 4Q + 0.0001Q2

Total annual cost in selling division,

CS = 10,000 + 8Q + 0.00005Q2

Selling price, PS = 24 – 0.00048Q

All cost and price figures are in pounds and Q denotes annual production andsales. CS excludes any costs transferred from the manufacturing division.

Required

Calculate the optimal transfer price to maximise overall profitability.

SolutionProfit is maximised when marginal cost and marginal revenue are equal.Looking at the company overall, the optimal activity level can be found byequating expressions for marginal revenue and the combined marginal cost ofeach division. Notice that the marginal revenue and marginal cost are obtainedby differentiating the revenue and cost functions.

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Selling price PS = 24 – 0.00048Q

Revenue RS = PS x Q = 24Q – 0.00048Q2

Marginal revenue MRS =dQdR = 24 – 0.00096Q

Company’s total cost CC = CM + CS = 15,000 + 12Q + 0.00015Q2

Company’s marginal cost MCC =dQ

)(Cd c = 12 + 0.0003Q

Profit is maximised when marginal cost equals marginal revenue, ie when:

24 – 0.00096Q = 12 + 0.0003Q

0.00126Q = 12

Q = 9,524

PS = 24 – 0.00048Q

= £19.43

The company should manufacture 9,524 crooks a year and sell them at £19.43each.

We now use this to establish a transfer price.

Any transfer price that is fixed represents marginal revenue to themanufacturing division and additional marginal costs to the selling division. Theprice must be set to ensure that each division’s profit is maximised at an activitylevel of 9,524 crooks a year.


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The marginal cost in the manufacturing division at a level of 9,524 is found asfollows.

MCM =Q

)C( Md

d = 4 + 0.0002Q

When Q is 9,524, MCM = 4 + 0.0002 x 9,524 = 5.9048

This, therefore, should be the transfer price: £5.90½

The marginal cost in the selling division, excluding the transfer price, is givenby:

MCS = 8 + 0.0001Q

Including the transfer price, this becomes:

Marginal costs = 13.905 + 0.0001Q

It will be seen that by comparing this with the selling division’s marginalrevenue,

MR = 24 – 0.00096Q

the selling division’s profit is maximised when:

13.905 + 0.0001Q = 24 – 0.00096Q

Q =00106.0

095.10 = 9,524

Thus, using a transfer price of £5.90½ per crook, each division’s profit ismaximised at an activity level of 9,524, which is also the optimal activity level forthe company overall.


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3 Transfer pricing with an external marketA perfect market for the intermediate productThe situation we are now considering is illustrated below.

Externalmarket

Imperfect marketfor final product

SupplyingDivision

ReceivingDivision

Perfect marketfor intermediate

product

Intermediateproduct

To show the effects of this new situation we extend our previous example bysupposing that a perfect market exists for unfinished crooks.

The transfer price will be the same as the market price.

♦ If a transfer price were set above this figure, the second (finishing andselling) division would not wish to buy from the manufacturing divisionbut would prefer to buy from outside.

♦ If a transfer price was set below market price, the first (manufacturing)division would not wish to transfer to the selling division but would preferto sell outside.


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An imperfect market for the intermediate productThis situation is illustrated below.

An imperfect market for the intermediate product

Externalmarket

Imperfect marketfor final product

SupplyingDivision

ReceivingDivision

Imperfect marketfor intermediate

product

Intermediateproduct

The manufacturing division is now faced with a decision as to which of twomarkets the unfinished crooks should be sold in.

Suppose unfinished crooks could be sold in a market where the followingdemand curve applied:

Selling price, unfinished crooks, PM = 12 – 0.0002Q

It is in the company’s best interests for the manufacturing division either to sellcrooks in the intermediate market or to pass them on to the selling divisionaccording to where marginal revenue (in the case of the selling division, netmarginal revenue) is the greater.

MCM = 4 + 0.0002QMRM = 12 – 0.0004QNMRS = 16 – 0.00106Q


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Initially the manufacturing division should pass crooks on to the selling division,but eventually the net marginal revenue from the selling division will fall to £12(the same as marginal revenue initially in the intermediate market), at a saleslevel of 3,774. From then on the manufacturing division should also selloutside.

Suppose that the manufacturing division produces D units for sale on theintermediate market and E units to the selling division for conversion intofinished crooks. Profit will be maximised when:

MCM = MRM = NMRS

4 + 0.0002 (D + E) = 12 – 0.0004D = 16 – 0.00106E

Equating the first two and the second two:

4 + 0.0002D + 0.0002E = 12 –

0.0004D

12 – 0.0004D = 16 – 0.00106E

Rearranging:

2E + 6D = 80,000 (1)

10.6E – 4D = 40,000 (2)

Solving simultaneously:

D = 10,726

E = 7,821

C = D + E = 18,547

The optimal transfer price can be found by substituting C, D or E into theappropriate marginal cost or revenue expression. Using the expression formarginal cost:


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Optimal transfer price = 4 + (0.0002 x 18,547)

= £7.71

4 Transfer pricing in practiceTransfer prices based on market pricesThe market price used for an internal transfer price should be that charged bythe supplier who most accurately reflects the product quality, delivery and otherauxiliary terms and services offered by the internal producer.

It will often happen that a slightly lower price than market price may be used forinternal transfer purposes, to take account of the lower transaction costsinvolved.

Outside purchases

Divisional independence involves the freedom for a buying division to make useof outside sources of supply. This might occur, for example, when owing tomarket imperfections, an outside supplier’s price is below that of the internalsupplying division.

If the supplying division had unutilised capacity, it would normally be preferableto make use of that capacity rather than to purchase from outside. Divisionalautonomy might therefore be overridden by a central directive that purchaseswill be made internally whenever the capacity exists.

Transfer prices based on costs

It may happen that there is no open market price for the intermediate product.


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Actual or standard costs?

Unless the intermediate product is a ‘one-off’ customised order, it is best to usethe long-run standard cost as a basis for transfer pricing.

Full or variable costs?To provide incentive to the supplying division, the transfer price system wouldneed to give some contribution towards fixed costs and profit. However, if thisis done by setting the transfer price on a full cost plus basis, it may lead to sub-optimal decisions being taken.

IllustrationDivision B sells a final product to outside customers at £14 per unit. It buys anintermediate product from Division A at £4 per unit and incurs additionalvariable processing costs of £10.50 per unit.

The transfer price of £4 from Division A comprises:

Per unit£

Variable costs 1.50Fixed costs, absorbed on the basis of budgeted activity 1.20Profit 1.30

____Transfer price 4.00

====

Division B thus loses £0.50 on every unit of final product, and will be motivatedeither to discontinue the product or to seek an outside alternative supplier toreplace Division A.


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If we look more closely at the figures we find that it is in fact the best course forthe company as a whole for B to continue purchasing from A and selling thefinal product.

For the company as a whole, each outside sale yields contribution as follows.

£ £Final selling price 14.00Variable costsDivision A 1.50Division B 10.50

_____12.00_____

Contribution towards the company’s fixed costs andprofit

2.00=====

Here, a transfer price has been set which has sent the wrong signals to themanager of Division B, leading him to act in a way which, although it appearsoptimal for his own division, is not optimal for the company as a whole.

Transfer prices based on opportunity costAn often-quoted method of setting transfer prices is that they should be basedon marginal cost of producing the item transferred plus opportunity cost to thecompany of making the transfer.

transfer pricing

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