College of Business and Economics

School of Accounting
Department of Accountancy

2020

ADFM/BPFM
PERFORMANCE MANAGEMENT
UNIT 3 PRACTICAL

SOLUTION
Question 1.1:
Rationale
The question examines candidates’ knowledge and understanding of relevant costs in the context of a
contract for a new customer.

The learning outcomes tested are (part a) A1 (c) discuss the particular issues that arise in pricing
decisions and the conflict between ‘marginal cost’ principles and the need for full recovery of all costs;
(part b) A1(a), discuss the principles of decision-making including the identification of relevant cash flows
and their use alongside non-quantifiable factors in making rounded judgments.
Suggested Approach
Carefully read the question to identify the resources needed, and their relevant costs, to satisfy the
contract.

Prepare a statement that adopts relevant costing principles to show the relevant costs of the contract.
Explain each relevant cost that has been included in the statement and explain why any values you have
excluded are not relevant.

Part (b) discuss problems that could possibly arise as a result of setting the price for the contract using
a relevant costing approach.

Notes
Material D 1 1,520
Components 2 49,920
Direct labour 3 11,050
Specialist machine 4 10,000
Machine operating costs 5 12,000
Supervision 6 500
Development time 7 NIL
General fixed overhead 8 NIL
Total relevant cost 84,990

Notes:
1. Material D is in regular use by CDF and must be replaced. Consequently, its relevant value
is its replacement cost. The historical cost is not relevant because it is a past cost and the
resale value is not relevant because CDF is not going to sell it because the material is in
regular use.

2. CDF could obtain the components externally at a cost of $15 each which total $60,000 or
they could be obtained from RDF. The transfer price from RDF is ($8 + 30%) + 20% =
$12.48 per component. Thus, the internal cost to CDF is $12.48 x 4000 = $49,920. The
opportunity cost to RDF is not relevant to CDF because from CDF’s viewpoint the relevant
cost is the price they have to pay to their supplier. Since this is lower than the external
buying price the relevant cost for the contract is $49,920.
3. The employees in department W will continue to be paid for their full hours regardless of
how the work is completed because they are working at 100% capacity. Therefore, their
cost is irrelevant. The choice is between using employees from department Z at a cost of
$15 per hour (total $12,750) or engaging sub-contract workers at a cost of $13 per hour
 (total $11,050). Since the use of sub-contract employees is the cheaper option this is the
relevant cost.

4. CDF has a number of options: (a)If the machine were to be hired it would have a cost of
$15,000; (b) if the machine were bought and then sold at the end of the work it would
have a net cost of $20,000; or (c) if the machine were bought and then modified to avoid
the need to buy the other machine it would have a net cost of $10,000 ( $50,000 plus
$5,000 modifications less $45,000 cost of another machine). Thus, the most economic
approach is buy the machine and then modify it so the relevant cost is $10,000.

5. The machine operating costs are future costs of doing the work and therefore are relevant.

6. The supervisor’s salary is irrelevant, but the bonus needs to be included because it is
dependent on this work and therefore is relevant.

7. The development time has already been incurred. Therefore, it is a past cost and not
relevant.

8. General fixed overhead costs and their absorption are not relevant because they will be
incurred whether the work goes ahead or not. Depreciation is also not relevant because
it is an accounting entry based on the historical purchase of assets. It is not affected by
the work being considered.

Question 1.2:

Two main issues arise when pricing work based on relevant costs:

• Profit reporting; and

• Pricing of future work.

With regard to profit reporting, the decision as to whether to proceed with the work will have
been based on the use of relevant costs, but the routine reporting of the profit from the work will
be based on the company’s normal accounting system. Since this system will be based on total
cost, it is probable that the costs of the work reported will be greater than its relevant cost.
Consequently the amount of profit reported to have been made on this order will be lower than
expected and may even be a loss. This may cause difficulties for the manager who accepted the
work as as an explanation will be required of the reasons why there is such a difference in profit.

With regard to the pricing of future work the difficulty lies in increasing the price for similar items
for the same customer in future. Once a price is set, customers tend to expect that any future
items will be priced similarly. However, where a special price has been offered based on relevant
cost because of the existence of spare capacity the supplier would not be able to continue to
price on that basis as it does not recover its long term total costs. There may also be difficulties
created by this method of pricing as other customers are being charged on a full cost basis and
if they were to discover that a lower price was offered to a new customer they would feel that
their loyalty was being penalised.
Question 2.1:

New sales = £4·0m x 1·20 = £4·8m

Variable costs are 60% of sales now but will reduce by 20% to 48% of sales (60% x 80%).
Thus, contribution will be 52% of sales:

New contribution = £2·496m / year

Old contribution = £1·600m / year
Increase in contribution = £0·896m / year

Cashflow s
0 1 2 3 4 5 6

Investment (3.000) 0.300

Old m/c 0·400
Contribution 0.896 0.896 0.896 0.896 0.896
(2.600) 0.896 0.896 0.896 0.896 1.196 -

DF @ 14% 1.000 0.877 0.769 0.675 0.592 0.519

PV (2.600) 0.786 0.689 0.605 0.530 0.621

Pre-Tax NPV = 0.631
Tax NPV = (0.368)
Post Tax NPV = 0.263 Worthwhile

Tax Depreciation
Old New
Year 1 £ £ £
WDV b/f 250,000
Disposal 400,000
(150,000)
Bal chg 150,000 (150,000)
NIL
Addition 3,000,000
WDA @ 25% (750,000) 750,000
600,000
2,250,000
Year 2
WDA @ 25% (562,500) 562,500

1,687,500
Year 3
WDA @ 25% (421,875) 421,875
 1,265,625
Year 4
WDA @ 25% (316,406) 316,406

949,219
Year 5
Disposal (300,000)
649,219
Ball All’ce (649,219) 649,219
NIL

Tax

Year Contribution (£m) CA’s (£m) Taxable (£m)

1 0.896 0.600 0.296
2 0.896 0.563 0.333
3 0.896 0.422 0.474
4 0.896 0.316 0.580
5 0.896 0.649 0.247

Tax payable

Payable
Year 1 2 3 4 5 6
£m £m £m £m £m £m
1 0.296 x 30% = 0.088 0.044 0.044
2 0.333 x 30% = 0.100 0.050 0.050
3 0.474 x 30% = 0.142 0.071 0.071
4 0.580 x 30% = 0.174 0.087 0.087
5 0.247 x 30% = 0.074 0.037 0.037
0.044 0.094 0.121 0.158 0.124 0.037
DF @ 14% 0.877 0.769 0.675 0.592 0.519 0.456
PV 0.039 0.072 0.082 0.094 0.064 0.017

NPV of tax = £0.368 million

Question 2.2:

Sensitivity Analysis is carried out before a decision is finally made. It is used to test how
sensitive a potential decision is to a change or inaccuracy in the variables that have been used to
reach the initial decision. Each variable is tested independently. The smaller the change required
to change the initial decision then the more sensitive is that variable and the more justified is a
manager in taking more care over the value of that variable. A key issue is the extent to which
each variable is controllable by management. These factors enable management to decide
whether or not to proceed with the initial decision.

In the context of this question sensitivity analysis

 measures the effect on NPV of changes in input variables.
 identifies the most critical input variable to the decision.

Contribution
The PV of contribution can reduce by £0.263 million before the proposal has a zero NPV.

Presently
£m
Pre-tax contribution has a PV of
2·496 x 3·433 8.569

Tax on contribution has a PV of

2·496 x 30% x 50% (yrs 1 - 5) = 0·3744

0·3744 x 3·433 = (1.285)

plus

2·496 x 30% x 50% (yrs 2 - 6) = 0·3744

0·3744 x 3·012 = (1.128)

6.156

Cumulative Discount Factors – DF Tables (Refer Below)

First half: Year 1 – 5: Sum of DF = 3.433 (Circled in red)
Second half: Year 2 – 6: Sum of DF = 3.012 (Circled in blue)

Thus, a reduction of 6.156/0.263 = 4.3% is needed before NPV = zero.

Tax rate

The PV of the tax payable = £0.368 million. This would have to increase by £0.263 million
before the proposal has an NPV of zero.

That is to say, tax rates would have to increase by 0.368/0.263 = 71.5%

Thus, the solution is more sensitive to changes in contribution than it is to changes in the rate
of tax.
Question 3.1:

Rationale
The question examines candidates’ knowledge and understanding of pricing based on profit maximisation
in imperfect markets.

The learning outcome tested is A3(a) apply an approach to pricing based on profit maximisation in
imperfect markets.
Suggested Approach
Part (a) required candidates to use the relevant formulae to calculate the price at which profit would be
maximised. Candidates then needed to use this price along with the associated demand and variable
costs per unit to calculate the contribution. Candidates needed to note the length of the introductory
phase. To calculate the maximum cost of the advertising campaign, three months’ contribution needed
to be calculated and the required profit subtracted from this.

Part (b) required an explanation of two reasons why it may not be appropriate to set the introductory
price of Product Z using the assumptions contained in the profit-maximisation model. Candidates needed
to give specific reasons appropriate to the circumstances detailed in the scenario that may result in the
assumptions used not being relevant.

To calculate the marginal revenue function, the demand function must first be established.

P = a – bx
b = 32.5 / 2,500 = 0.013
200 = a - 0.013*20,000, therefore, a = 460
P = 460 – 0.013x
MR = a – 2bx, MR = 460 – 2*0.013x
Profit is maximised when MR = MC
MC = $85 + $56 + $20 = 161
161 = 460 – 2*0.013x, therefore x = 11,500.
Substitute the value of x into the demand function to get price
460 – 0.013*11,500 = $310.50

Introductory phase three months 3*11,500 = 34,500 units

Per unit $ 3 months units Introductory phase $
Revenue 310.50 34,500 10,712,250

Material 85 34,500 2,932,500

Labour 56 34,500 1,932,000
Variable overhead 20 34,500 690,000
5,554,500
Contribution 5,157,750
Maximum advertising costs (balancing fig.) 2,657,750
Three-month profit target 2,500,000
Question 3.2:

The relationship between price and demand for product Z is an estimate. It is improbable that
relationships between price and demand for previous products at SAF are going to be relevant
for product Z. The new and innovative design of the Z is likely to mean that demand for the
product will be highly inelastic and potentially differ from the relationship observed with previous
products.

Price will not be the only factor affecting the demand for product Z. The significant advertising
and marketing campaign together with the unique nature of the product are likely to attract
consumers and impact demand. SAF must look to the external market to set a price for the launch
and establish a pricing strategy for the life of product Z as competitors launch rival products