# December 2004 , Woods Ltd.

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• princeacid
Participant

My question is from December 2004 , Question 4 , part (a) (ii).

I want to know how did the examiner performed the calculations which are highlighted in bold below.

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(i) Calculations showing an estimate of the minimum reduction in sales units required that would, on purely financial
grounds, justify the withdrawal of the ‘Super kooler’ from the market on 1 January 2005:
If we assume that the marketing director’s statement that the minimum reduction in sales volume that will occur is
10,000 units per annum for each year that the ‘Super kooler’ is manufactured is correct, then the maximum sales
volumes and contribution would be:

Year ended Sales units CPU Contribution
31 December (£60) (£’000)
2005 170,000 £60 10,200
2006 160,000 £60 9,600
2007 150,000 £60 9,000
2008 140,000 £60 8,400

The contribution that we could expect to earn from sales of the ‘Ultimate’ model amounts to £9,000,000 for each year
that it is sold (100,000 units at £200 – £110) per unit. Using a NPV approach the evaluation of the proposed
replacement of the ‘Super Kooler’ model by the ‘Ultimate’ model is as follows;
Year Initial Lost Contribution Contribution Fixed Net D.Factor Present
investment from from overheads cash at 9% p.a value

‘Super kooler’ ‘Ultimate’ flow
£’000 £’000 £’000 £’000 £’000 £
0 (1,200) (1,200) 1·000 (1,200,000)
2005 (10,200) 9,000 (150) (1,350) 0·917 (1,237,950)
2006 (9,600) 9,000 (150) (750) 0·842 (631,500)
2007 (9,000) 9,000 (150) (150) 0·772 (115,800)
2008 (8,400) 9,000 (150) 450 0·708 318,600
Net present value = £–2,866,650
A negative net present value indicates that if sales volume is expected to fall by 10,000 units per annum with effect
from 1 January 2005 it would be preferable to continue manufacturing the ‘Super kooler’.

(ii) The evaluation prepared (a)(i) clearly shows that a decrease of more than 10,000 in unit sales of the ‘Super Kooler’ will
be required in order to justify the withdrawal of the ‘Super Kooler’ from the market with effect from 1 January 2005. If
we assume that sales volume will decline by 20,000 units per annum then the resultant NPV can be calculated as
follows:
Year Initial Lost Contribution Contribution Fixed Net cash Discount Present
investment from from overheads flow factor value

‘Super kooler’ ‘Ultimate’ at 9% p.a
£’000 £’000 £’000 £’000 £’000 £
0 (1,200) (1,200) 1·000 (1,200,000)
2005 (9,600) 9,000 (150) (750) 0·917 (687,750)
2006 (8,400) 9,000 (150) 450 0·842 378,900
2007 (7,200) 9,000 (150) 1,650 0·772 1,273,800
2008 (6,000) 9,000 (150) 2,850 0·708 2,017,800
Net present value = £1,782,850
20
This NPV clearly shows that it would be beneficial to withdraw the ‘Super Kooler’ from the market with efffect from
1 January 2005.
The minimum reduction in sales volume to justify the withdrawal of the ‘Super Kooler’ from the market with effect from
1 January 2005 is the decrease that causes the NPV to equal £0. This can be calculated as follows:
(1 + 2,866,650/(2,866,650 + 1,782,850)) x 10,000 units = 16,165 units.

Thank you John.

John Moffat
Keymaster

I have already written an explanation in answer to another post, but here it is again below.

What he has done is the same idea as calculating an IRR – two guesses and approximate.

I assume that you are happy with part (1) where he has calculated the NPV as (2866650) if sale drop by 10,000 units per year.

Since sales would have to therefore drop by more that 10,000 units to get zero NPV (at which stage you would be prepared to start dropping SuperKooler) he has made a guess at a drop of 20,000 units and recalculated the NPV as +1782850. (You could have guessed differently – a drop of 30000 for example – and continued as below).

Having got two NPVs (for 10000 units and for 20000 units drop) he then say that because one gave a – NPV and one gave a + NPV then for zero NPV is must be somewhere between 10000 and 20000. He then approximates between the two to get the drop giving an NPV of zero.

So…..between 10000 units and 20000 units is a difference of (20000 – 10000) 10000 units. At the same time the NPV changes from -2866650 to +1782850 = a change in NPV of 4649500.

If we start from 10000 units, (when the NPV is -2866650) then to get zero NPV we need the NPV to increase by 2866650.

We know that a change of 4649500 needs a change of 10000 units, and so a change of 2866650 needs a change of 2866650/4649500 x 10000 units, which equals 6165 units. Add this to the original 10000 and you get 16165 units.

(This assumes that the NPV changes linearly, which it will not do, so the answer is only approximate. If you had tried different that 20000 units for the second guess, then you would get a slightly different answer)

(He has done exactly what I have done above – the reason he has written (1+….) at the beginning is simply for adding the 10,000 to the 6.165)

Hope that helps!!

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