17 Oct In this workshop we will look at techniques that enable managers to appraise, or weigh up, investment in long-lasting assets by relating the init
Complete the five questions at the end of the file. Be show to show your work. You may do the work in excel but be sure your answers are clearly highlighted and that the formulas work within the excel document.
Investment Analysis
Almost every organization at one time or another has to take decisions about making investments. These decisions may involve something as big as the construction of a new plant or something more mundane like the purchase of a new piece of machinery. One of the main difficulties that managers face when taking these sorts of decisions is that the cost of making the investment is incurred when the plant is built or the machine is purchased, yet the income which it is intended to help generate arises in the future, perhaps over many years.
In this workshop we will look at techniques that enable managers to appraise, or weigh up, investment in long-lasting assets by relating the initial outlay to the future revenue. These techniques are used by businesses both to assess specific investments and to decide between alternative investments. Companies take these decisions very seriously because they involve large amounts of resources and once made they cannot be reversed.
We will begin with the accounting rate of return method then we will consider the payback period approach, and finally the more sophisticated discounting techniques. Despite the differences between them they all involve the determination of single figures that summarize the financial appeal of an investment project.
The Accounting Rate of Return
Generally, a rate of return expresses the return or profit resulting from the use of assets such as machinery or equipment in terms of the expenditure involved in purchasing them, usually in percentage terms. You will find that accountants make extensive use of these types of summary measure; look at a business newspaper or a company report and you will probably find reference to measures like the ROCE (Return on Capital Employed). These measures are used by companies to indicate how effectively they have managed the assets under their control.
The accounting rate of return, often abbreviated to ARR, is the use of this approach to weigh up the attraction of an investment proposal. To apply it we need to establish the average (mean) profit per year and divide that by the average level of investment per year.
To calculate the average profit per year we add up the annual profits and divide by the number of years over which the investment will help generate these revenues. Having said that, the profit figures we use must be profits after allowing for depreciation. Depreciation is the spreading of the cost of an asset over its useful life. The simplest way of doing this is to subtract the residual value of the asset, which is the amount that the company expects to get from the sale of the asset when it is no longer of use, from the purchase cost of the asset and divide by the number of years of useful life the asset is expected to have. This approach is known as straight-line depreciation and it assumes that the usefulness of the asset, in terms of helping to generate profits, is reasonably consistent over its useful life.
To work out the average level of investment, we need to know the cost of the asset and the residual value of the asset. The average investment value is the difference between the initial cost and the residual value divided by two, in other words we split the difference between the highest and lowest values of the asset while it is in use. After dividing the average return by the average investment we multiply by 100 so that we have a percentage result. The procedure can be represented as:
Accounting rate of return = average annual return * 100
Average annual investment
where
average annual investment = (purchase cost – residual value)
2
Example 1
The Budisha Bus Company is thinking of purchasing a new luxury coach to sustain its prestige client business. The purchase cost of the vehicle, including licence plates and delivery, is £120,000. The company anticipates that it will use the vehicle for five years and be able to sell it at the end of that period for £40,000. The revenue the company expects to generate using the coach is as follows:
|
By the end of year |
Net profit before depreciation (£) |
|
1 |
30,000 |
|
2 |
30,000 |
|
3 |
30,000 |
|
4 |
25,000 |
|
5 |
20,000 |
What is the accounting rate of return for this investment?
The average annual profit before depreciation is:
(30,000+30,000+30,000 + 25,000+20,000) = 135,000 = 27,000
5 5
From this amount we must subtract the annual cost of depreciation, which is:
(120,000 – 40,000) = 80,000 = 16,000
5 5
The annual average profit after depreciation is: 27000 — 16000 = £11000
The average annual investment is:
(120,000 – 40,000) = 80,000 = 40,000
2 2
The accounting rate of return is:
11,000 * 100= 27.5%
40,000
Should the company in Example 1 regard the accounting rate of return for this project as high enough to make the investment worth its while? In practice they would compare this figure to accounting rates of return for alternative investments that it could make with the same money, or perhaps they have a company minimum rate that any project has to exceed to be approved.
The accounting rate of return is widely used to evaluate investment projects. It produces a percentage figure which managers can easily compare to interest rates and it is essentially the same approach to future investment as accountants take when working out the ROCE (Return on Capital Employed) to evaluate a company’s past performance.
The critical weakness in using the accounting rate of return to appraise investments is that it is completely blind to the timing of the initial expenditure and future income. It ignores what is called the time value of money. The value that an individual or business puts on a sum of money is related to when the money is received; for example if you were offered the choice of a gift of £1000 now or £1000 in two year’s time you would most likely prefer the cash now. This may be because you need cash now rather than then, but even if you have sufficient funds now you would still be better off having the money now because you could invest the money in a savings account and receive interest on it.
The other investment appraisal techniques we shall examine have the advantage of bringing the time element into consideration. The other difference between them and the accounting rate of return approach is that they are based on net cash flows into the company, which are essentially net profits before depreciation.
Payback Period
The payback period approach to investment appraisal does take the timing of cash flows into account and is based on a straightforward concept – the time it will take for the net profits earned using the asset to cover the purchase of the asset. We need only accumulate the negative (expenditure) and positive (net profits before depreciation) cash flows relating to the investment over time and ascertain when the cumulative cash flow reaches zero. At this point the initial outlay on the asset will have been paid back.
Example 2
Work out the payback period for the investment proposal being considered by the Budisha Bus Company in Example 1.
The net cash flows associated with the acquisition of the luxury coach can be summarized as follows:
|
End of Year |
Cost/Receipt |
Net Cash Flow (£) |
Cummulative Cash Flow (£) |
|
0 |
Cost of Coach |
-120000 |
-120000 |
|
1 |
Net profit before depreciation |
30000 |
-90000 |
|
2 |
Net profit before depreciation |
30000 |
-60000 |
|
3 |
Net profit before depreciation |
30000 |
-30000 |
|
4 |
Net profit before depreciation |
25000 |
-5000 |
|
5 |
Net profit before depreciation |
20000 |
15000 |
|
5 |
Sale of coach |
40000 |
55000 |
Payback is achieved in year 5. We can be more precise by adding the extra cash flow required after the end of year four to reach zero cumulative cash flow (£5000) divided by the net cash flow received by the end of the fifth year (£20,000):
Payback period = 4 + 5000 = 4.25 years
20000
Note that in the net cash flow column of the table in Example 2 the initial outlay for the coach has a negative sign to indicate that it is a flow of cash out of the business. You will find that accountants use round brackets to indicate an outflow of cash, so where we have written − 120000 for the outgoing cash to buy the coach an accountant would represent it as (120000).
The payback period we found in Example 2 might be compared with a minimum payback period the company required for any investment or with alternative investments that could be made with the same resources.
The payback period is a simple concept for managers to apply and it is particularly appropriate when firms are very sensitive to risk because it indicates the time during which they are exposed to the risk of not recouping their initial outlay. A cautious manager would probably be comfortable with the idea of preferring investment opportunities that have shorter payback periods.
The weakness of the payback approach is that it ignores cash flows that arise in periods beyond the payback period. Where there are two alternative projects it may not suggest the one that performs better overall.
Example 3
Gravura Print specialize in precision graphics for the art poster market. To expand their business they want to purchase a flying-arm stamper. There are two manufacturers that produce such machines: Smeshnoy and Pazorna. The cash flows arising from the two ventures are expected to be as follows:
Smeshnoy machine
|
End of Year |
Cost/Receipt |
Net Cash Flow (£) |
Cummulative Cash Flow (£) |
|
0 |
Cost of Coach |
-30000 |
-30000 |
|
1 |
Net profit before depreciation |
7000 |
-23000 |
|
2 |
Net profit before depreciation |
8000 |
-15000 |
|
3 |
Net profit before depreciation |
8000 |
-7000 |
|
4 |
Net profit before depreciation |
7000 |
0 |
|
5 |
Net profit before depreciation |
7000 |
7000 |
|
5 |
Sale of coach |
5000 |
12000 |
Pazorna machine
|
End of Year |
Cost/Receipt |
Net Cash Flow (£) |
Cummulative Cash Flow (£) |
|
0 |
Cost of Coach |
-30000 |
-30000 |
|
1 |
Net profit before depreciation |
12000 |
-18000 |
|
2 |
Net profit before depreciation |
12000 |
-6000 |
|
3 |
Net profit before depreciation |
6000 |
0 |
|
4 |
Net profit before depreciation |
2000 |
2000 |
|
5 |
Net profit before depreciation |
1000 |
3000 |
|
5 |
Sale of coach |
2000 |
5000 |
In Example 3 the payback period for the Smeshnoy machine is four years and for the Pazorna machine three years. Applying the payback period criterion we should choose the Pazorna machine, but in doing so we would be passing up the opportunity of achieving the rather higher returns from investing in the Smeshnoy machine.
A better approach would be to base our assessment of investments on all of the cash flows involved rather than just the earlier ones, and to bring into our calculations the time value of money. Techniques that allow us to do this adjust or discount cash flows to compensate for the time that passes before they arrive. The first of these techniques that we shall consider is the net present value.
Net Present Value
The net present value (NPV) of an investment is a single figure that summarizes all the cash flows arising from an investment, both expenditure and receipts, each of which have been adjusted so that whenever they arise in the future it is their current or present value that is used in the calculation. Adjusting, or discounting them to get their present value means working out how much money would have to be invested now in order to generate that specific amount at that time in the future.
To do this we use the same approach as we would to calculate the amount of money accumulating in a savings account. We need to know the rate of interest and the amount of money initially deposited. The amount in the account at the end of one year is the original amount deposited plus the rate of interest, r, applied to the original amount:
Amount at the end of the year = Deposit + (Deposit * r)
We can express this as:
Amount at the end of the year = Deposit * (1 + r)
If the money stays in the account for a second year:
Amount at the end of the second year = Deposit * (1 + r) * (1 + r) = Deposit * (1 + r)2
Example 4
If you invested £1000 in a savings account paying 5% interest per annum, how much money would you have in the account after two years?
Amount at the end of the first year = 1000 * (1 + 0.05) = £1050
If we invested £1050 for a year at 5%, at the end of one year it would be worth:
1050* (1 + 0.05) = £1102.5
We can combine these calculations:
Amount at the end of the second year = 1000 * (1 + 0.05)2
=1000 * (1.05)2
= 1000 * 1.1025
= £1102.5
In general if we deposit an amount in an account paying an annual interest rate r for n years, the amount accumulated in the account at the end of the period will be:
Deposit * (1 + r)n
The deposit is, of course, the sum of money we start with, it is the present value (PV) of our investment, so we can express this procedure as:
Amount at the end of year n = PV * (1 + r)n
This expression enables us to work out the future value of a known present value, like the amount we deposit in an account. When we assess investment projects we want to know how much a known (or at least expected) amount to be received in the future is worth now. Instead of knowing the present value and wanting to work out the future, we need to reverse the process and determine the present value of a known future amount. To obtain this we can rearrange the expression we used to work out the amount accumulated at the end of a period:
Present Value (PV) = Amount at the end of year n
(1 + r)n
Example 5
You are offered £1000 to be paid to you in two years’ time. What is the present value of this sum if you can invest cash in a savings account paying 5% interest per annum?
Present value = 1000 = 1000 = 1000 = 907.029
(1+0.05)2 1.052 1.1025
The present value of £1000 received in two years’ time is £907.03, to the nearest penny. In other words, if you invested £907.03 at 5% now in two years’ time the amount would be worth
Amount at the end of year two = 907.03 *(1 – 0.05)2 = 907.03 * 1.1025
= £1000.00 to the nearest penny
When companies use net present value (NPV) to assess investments they discount future cash flows in the same way as we did in Example 5, but before they can do so they need to identify the appropriate rate of interest to use. In Example 5 we used 5% as it was a viable alternative that in effect reflected the opportunity cost of not receiving the money for two years, that is, the amount you have had to forego by having to wait.
The interest, or discount, rate a company uses is likely to reflect the opportunity cost, which may be the interest it could earn by investing the money in a bank. It may also reflect the prevailing rate of inflation and the risk of the investment project not working out as planned.
Example 6
What is the net present value of the proposed investment in a luxury coach by the Budisha Bus Company in Example 2. Use a 10% interest rate.
The cash flows involved in the project were:
|
End of Year |
Net Cash Flow (£) |
Discount Factor |
PV ( to the nearest £) |
|
0 |
-120000 |
1.00 |
-120,000 |
|
1 |
30000 |
0.91 |
27,273 |
|
2 |
30000 |
0.83 |
24,793 |
|
3 |
30000 |
0.75 |
22,539 |
|
4 |
25000 |
0.68 |
17,075 |
|
5 |
20000 |
0.62 |
12,418 |
|
5 |
40000 |
0.62 |
24,837 |
|
Discount Rate |
10% |
Net Present Value |
8,936 |
The net present value of the project in Example 8.11 is £8936. The initial outlay of £120,000 in effect purchases future returns that are worth £128,936. Because the discount rate used is in effect a threshold of acceptable returns from a project, any opportunity that results in a positive NPV such as in Example 6 should be approved and any opportunity producing a negative NPV should be declined.
The Internal Rate of Return
A fourth investment appraisal method widely used by businesses is the internal rate of return (IRR). It is closely related to the net pr
