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Performance operations: since the very first sitting under the 2010 syllabus, all P1 papers have contained questions on investment projects, vet candidates still make the most basic blunders when applying standard appraisal techniques.

By the examiner for P1

The section on common errors in each P1 post-exam guide is a great resource. It helps students to see where past candidates have gone wrong when appraising investment projects--and to ensure that they don't follow suit. But it's clear, from seeing the same lapses listed repeatedly in these guides, that many students are failing to learn from their predecessors' mistakes.

There are three areas that you need to understand fully before you even come to calculate the net present value (NPV) of a project: the relevant costs and revenues; the timing of cash flows; and the application of taxation.

The relevant costs and revenues

CIMA defines relevant costs and revenues as those that are "appropriate to a specific management decision. These are represented by future cash flows, whose magnitude will vary depending on the outcome of the management decision. If stock is used, the relevant cost, used in the determination of the profitability of the transaction, would be the cost of replacing the stock--not its original purchase price, which is a sunk cost."

The only costs and revenues that should interest us, then, are future cash flows that will be affected by the decision. Any cash flows that arise, no matter what decision is taken, are irrelevant and can be ignored--as can any past costs. Questions often feature a sunk cost--for example, a feasibility study that has already been conducted. You should ignore such costs, since they have been incurred and the investment decision cannot affect them. Unfortunately, many candidates fail to realise this, adding these on to the initial investment.

The question will normally detail the initial investment and how it is depreciated. This is important information, as depreciation is not a cash flow and so must not be included in your calculations. You need to check whether the figures provided for future costs include or exclude depreciation. If it is included, you need to remove it and use the figures excluding depreciation as the cash outflow. Too many candidates either don't adjust for depreciation or do it wrongly.

Perhaps the area that causes most difficulty is the concept of opportunity cost. This is the value of the benefit foregone when choosing one course of action over the next best option. It has arisen many times in P1, where the decision to start a particular project will have an effect on current operations. In March 2013's paper, for instance, the question centred on a potential investment in a mobile tyre-fitting service. The effect of making the investment was that some of the customers who would previously have used the firm's depots for replacing tyres would use the mobile service instead. The lost contribution from the depot sales needs to be treated as a cash outflow arising from the investment decision. Some candidates treated this as an inflow, which is obviously wrong.

You should also note that in some scenarios the cash inflows from a project may not take the form of sales revenue. Firms may decide to invest in equipment that will result in cost savings. These future savings represent the cash inflows from the project because, as costs are reduced, cash inflows will be increased.

The timing of cash flows

The timing of cash flows is crucial, since the value of money today is not the same as it will be in a year's time. In project appraisals the convention is to refer to year zero, year one, year two and so on. You need to be clear what this means.

To make discounting easier, we make the simplifying assumption that cash flows arise at year ends, so cash flows in year one arise at the end of year one. But year-zero cash flows arise at the start of year one or right at the start of the project. These are not discounted, since they are assumed to arise now. The initial investment should therefore always be treated as arising in year zero and not be discounted. Students still make the error of including the initial investment in year one and discounting it at the cost of capital. This is clearly wrong, because the initial investment is incurred at the outset and at today's time value of money. Also remember that any residual value in the project should be treated as a cash inflow at the end of the project.

It's normally assumed that working capital will remain the same throughout the project. Unless you are told otherwise, you should treat the investment in working capital as a year-zero cash outflow. Most candidates do this, but what some then fail to do is to bring back the working capital as an inflow when the project finishes. The idea is that the firm sells any inventory, recovers its accounts receivable and pays its accounts payable, resulting in a cash inflow at the end.

The application of taxation

The tax calculations in project appraisals can be a minefield. If tax is included in the scenario, you'll normally need to calculate tax depreciation and the corporation tax due on the net cash flows.

Accounting depreciation is not an allowable expense for tax purposes, but the authorities have a system of tax depreciation that enables the net cost of assets to be deducted as an allowable expense. Note that the tax depreciation claimed in the final year is the tax-written-down value minus any residual value. It is worth checking that the total tax depreciation you calculate over the lifetime of the project equals the initial investment less the residual value. Tax depreciation is calculated each year at 25 per cent of the tax-written-down value of the assets.

Let's look at the simple example of a firm called X with a project that involves an initial investment of $1,000,000 in machinery that will have a residual value of $200,000 at the end of five years. The project has net cash inflows of $500,000 each year. The investment is eligible for tax depreciation. The company has a cost of capital of 10 per cent.

Table 1 shows how the tax depreciation is calculated. The total tax depreciation over the life of the project is $800,000--that is, $1,000,000 less the residual value of $200,000. Table 2 shows how the tax payable on the cash flows is calculated (the tax rate is usually 30 per cent, but the question will specify the rate). A common error is to include the initial investment and/or the residual value in the calculations. This is wrong, because both of these have already been included in the calculation of tax depreciation.
1 Calculating the tax depreciation on X's investment project

Year Tax depreciation Tax-written-down value

0 0 $1,000,000
1 25% x $1,000,000 = $250,000 $1,000,000 - $250,000 = $750,000
2 25% x $750,000 = $187,500 $750,000 - $187,500 = $562,500
3 25% x $562,500 = $140,630 $562,500 - $140,630 = $421,870
4 25%x $421,870 = $105,470 $421,870 - $105,470= $316,400
5 $316,400 - $200,000 = $1 16400 Residual value
 of machinery = $200,000
 $800,000

2. Calculating the tax payable on the cash flows of X's investment
project

 Year 1 Year 2 Year 3 Year 4

Cash flow $500000 $500,000 $500,000 $500,000

Less tax $250,000 $187,500 $140,630 $105,470
depreciation

Taxable cash $250,000 $312,500 $359,370 $394,530
flow

Taxation @ ($75,000) ($93,750) ($107,811) ($118,359)
30%

 Year 5

Cash flow $500,000

Less tax $116,400
depreciation

Taxable cash $383,600
flow

Taxation @ ($115,080)
30%


We can now perform our NPV calculation, which is shown in table 3. Adding up all the present values on the bottom line of the table gives an NPV of [pounds sterling]657,560. Some students treat the tax depreciation incorrectly as a cash outflow--it results in a reduction in tax payable but is not an outflow itself. To work out the NPV we need to use the cash flows before deducting tax depreciation and then deduct the tax payments. In the exam you will be given information about the timing of the cash flows, but usually half is payable in the year it arises and the remainder is payable in the subsequent year.
3. Calculating the net present value of X's investment project

 Year 0 Year 1 Year 2 Year 3 Year 4

 $ $ $ $ $

Cash (1,000,000) 500,000 500,000 500,000 500,000
flow

Residual
value

Less tax (37,500) (37,500) (53.926) (53,905)

payments (46,875) (46,875) (59,180)

Netcash (1,000,000) 462,500 415,625 399,219 386,915
flow

Discount 1,000 0.909 0.826 0.751 0.683
factor

Present (1,000,000) 420,413 343,306 299,813 264,263
value

 Year 5 Year 6

 $ $

Cash 500,000 0
flow

Residual 200,000
value

Less tax (57,540) (57,540)

payments (59,179)

Netcash 583,281 (57,540)
flow

Discount 0.621 0.564
factor

Present 362,218 (32,453)
value


The NPV calculation is relatively easy. The harder aspect is getting the cash flows and tax figures right. Once you have gained a good understanding of these areas you'll be able to tackle project appraisal questions with confidence.
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Title Annotation:Paper P1
Publication:Financial Management (UK)
Date:Sep 1, 2013
Words:1556
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