Paper P1 Performance Operations: 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.

Question 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 question directed candidates to take this approach.

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

Just In Time Every Time (JITET) is a large organisation 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 replacement better than the figures calculated for the other options? A simple solution would be to calculate an average for each option as follows:

* Three years: [pounds sterling] 35,345 / 3 = [pounds sterling] 11,782.

* Four years: [pounds sterling] 44,224 / 4 = [pounds sterling] 11,056.

* Five years: [pounds sterling] 53,289 / 5 = [pounds sterling] 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 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:

* Three years: [pounds sterling] 35,345 / 2.487 = [pounds sterling] 14,212.

* Four years: [pounds sterling] 44,224 / 3.170 = [pounds sterling] 13,951.

* Five years: [pounds sterling] 53,289 / 3.791 = [pounds sterling] 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 evaluates 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 evaluate 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 introduction 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 companies to compare apples and pears.

[ILLUSTRATION OMITTED]

By the examiner for paper P1
```1. Replace the vans after three years

Year Investment Running Residual Net cash
costs value flow

0 -[pounds -[pounds
sterling] sterling]
15,000 15,000

1 -[pounds [pounds
sterling] sterling]
9,900 9,900

2 -[pounds -[pounds
sterling] sterling]
10,000 10,000

3 -[pounds [pounds -[pounds
sterling] sterling] sterling]
10,100 6,000 4,100

4 0

5 0

Cost of 10% NPV -[pounds
capital sterling]
35,345

2. Replace the vans after four years

Year Investment Running Residual Net cash
costs value flow

0 -[pounds -[pounds
sterling] sterling]
15,000 15,000

1 -[pounds [pounds
sterling] sterling]
9,900 9,900

2 -[pounds -[pounds
sterling] sterling]
10,000 10,000

3 -[pounds -[pounds
sterling] sterling]
10,100 10,100

4 -[pounds [pounds -[pounds
sterling] sterling] sterling]
10,400 4,000 6,400

5 0

Cost of 10% NPV -[pounds
capital sterling]
44,224

3. Replace the vans after five years

Year Investment Running Residual Net cash
costs value flow

0 -[pounds -[pounds -[pounds
sterling] sterling] sterling]
15,000 9,900 15,000

1 -[pounds [pounds
sterling] sterling]
10,000 9,900

2 -[pounds -[pounds
sterling] sterling]
10,100 10,000

3 -[pounds -[pounds
sterling] sterling]
10,400 10,100

4 -[pounds [pounds -[pounds
sterling] sterling] sterling]
11,200 1,000 10,400

5 -[pounds
sterling]
10,200

Cost of 10% NPV -[pounds
capital sterling]
53,289
```
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