44 Study notes

‘CIMA provides cumulative discount factor tables at the back of the exam paper’

Paper P1

OperationsPerformance

By the examiner for paper P1

When you’re conducting investment appraisals or making capital budgeting decisions, the annualised equivalent method will allow you to make a proper comparison of assets with unequal lifespans

Q uestion 4 of the November 2011 Performance Operations paper presented a scenario in which a company needed to decide between two replacement computer systems that had different lifespans. Many

candidates calculated the net present values (NPVs) of both systems, but didn’t seem to appreciate that these weren’t directly comparable, because the first system had a lifespan of three years while the second would last for five years.

The second system’s NPV ($671,000) worked out as significantly higher than that of the first one ($350,000). But if the company were to choose system one, it would be able to invest in another after three years. The systems’ NPVs needed to be adjusted so that they could be compared on a like-for-like basis. One way of doing this is known as the annualised equivalent method – indeed, the ques-tion directed candidates to take this approach.

A similar situation occurs when a company needs to determine how long to keep an asset before rep-lacing it. A good example of this type of decision concerns the replacement of vehicles – a problem faced by both companies and individuals. The fol-lowing example demonstrates how the annualised equivalent method applies in such situations.

Just In Time Every Time (JITET) is a large org-anisation that specialises in delivering goods from retailers to consumers. The company, which has more than 100 vans, is considering whether it should replace these vehicles after three, four or five years. Tables 1, 2 and 3 contain the investment appraisal for each option based on a cost of capital of ten per cent. But the NPVs calculated for each option cannot be compared with each other, since they cover different periods.

Is the NPV of £35,345 for the three-year replace-ment better than the figures calculated for the other options? A simple solution would be to calculate an average for each option as follows:

l Three years: £35,345 ÷ 3 = £11,782.l Four years: £44,224 ÷ 4 = £11,056.l Five years: £53,289 ÷ 5 = £10,658.

These calculations indicate that JITET should actually use a five-year replacement cycle, because this produces the lowest annual cost, but they don’t provide a valid comparison, either. The three options can be compared only by calculating an annualised equivalent cost for each one.

In order to do this, a cumulative discount factor or annuity factor must be obtained for three, four and five years. Fortunately, this is not difficult to do. CIMA provides cumulative discount factor

1. Replace the vans after three yearsYear Investment Running costs Residual value Net cash flow0 -£15,000 -£15,0001 -£9,900 -£9,9002 -£10,000 -£10,0003 -£10,100 £6,000 -£4,1004 05 0

Cost of capital 10% NPV -£35,345

2. Replace the vans after four yearsYear Investment Running costs Residual value Net cash flow0 -£15,000 -£15,0001 -£9,900 -£9,9002 -£10,000 -£10,0003 -£10,100 -£10,1004 -£10,400 £4,000 -£6,4005 0

Cost of capital 10% NPV -£44,224

3. Replace the vans after five yearsYear Investment Running costs Residual value Net cash flow0 -£15,000 -£15,0001 -£9,900 -£9,9002 -£10,000 -£10,0003 -£10,100 -£10,1004 -£10,400 -£10,4005 -£11,200 £1,000 -£10,200

Cost of capital 10% NPV -£53,289

46

Paper P1Performance Operations

Study notes

tables at the back of the exam paper, so you won’t need to apply a formula. The cumulative discount factor for three years is found here by identifying the factor in the interest rate column of ten per cent for period three – ie, 2.487. The cumulative discount factors for four and five years can found underneath this figure and are 3.170 and 3.791 respectively. So the annualised equivalent costs of each option are as follows:l Three years: £35,345 ÷ 2.487 = £14,212. l Four years: £44,224 ÷ 3.170 = £13,951. l Five years: £53,289 ÷ 3.791 = £14,057.

From these calculations, JITET should use a four-year replacement policy, since this entails the lowest annual cost.

It is possible to perform this type of analysis using the lowest-common-multiple method. This evalu-ates the options over a common time horizon that covers complete cycles of all the alternatives. The problem with this approach is that it can involve a significant number of calculations. For example, JITET would have to use a 60-year period to evalu-ate the alternative replacement cycles, since this is the smallest number divisible by three, four and five.

Most investment appraisal projects also have qualitative factors associated with them. These are

hard to express in financial terms. In this case JITET might be concerned that using older vehicles could tarnish the company’s image and delay its introduc-tion of more efficient new vans that should come on to the market in the next few years. It isn’t easy to get it right, but calculating annualised equivalent costs for these types of decisions will help compa-nies to compare apples and pears.

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