→One of the key areas of long-term decision-making that firms must tackle is that of investment→ that is →the need to commit funds by purchasing land, buildings, machinery and so on, in anticipation of being able to earn an income greater than the funds committed.
→Long term decisions are capital investment decisions.
→Capital investment could be a decision by:
· a flourist to purchase/lease a new delivery van;
· a law firm to upgrade its computer system;
· Toyota to invest in new automated production equipment;
· Tesco to build or open a new store.
→In order to handle these decisions, firms have to make an assessment of the size of the outflows and inflows of funds, the lifespan of the investment, the degree of risk attached and the cost of obtaining funds.
→So far we have considered ‘Payback Period’ and Accounting Rate of Return’ as techniques involved in making long term investment decisions. These techniques fail to consider the time value of money.
Therefore, we shall now have a look at other techniques that consider an important factor which is ‘time value of money’. In this paper we shall discuss the Net Present Value technique, a method that considers the discounting of cash flow. We shall look at some assumptions of net present value and also some related calculations.
Time value of Money:
It is important to recollect that a key factor to consider in long term purchasing decision is the return on investment (that is → whether the benefits of the investment exceeds its costs).
Because capital investments involve large sums of money and last for many years, a quantitative analysis of the costs and benefits of capital investment must consider the time value of money.
The focus of ‘time value of money’ is on cash flow.
The time value of money calculations are based on the concept of that:
· £1 received now is worth more than £1 received in the future; or
· £1 received in the future is worth less than £1 received now.
Cash outflows include: original investment (initial capital outlay) in the project, any additional working capital needed during the life of the investment, repairs and maintenance needed for machinery and equipment, and operating costs that may be incurred.
Cash inflows include: projected incremental revenues from the project, cost reduction in operating expenses, salvage values (if any) of the investment at the end of its useful life and the release of the working capital at the end of a project’s useful life.
With the exception of the initial cash outflows associated with the investment, other cash inflows and outflows are likely to be estimated.
As a basis for capital investment decisions, future cash flows are compared with present cash flows→ and that the time value of money is important when this done →because ‘like should be compared with like’. For this reason, future cash flows are converted into a value at the present time through the process known as ‘discounting’. (Discounting is the process of converting cash to be received in the future into a value at the present time)
Discounted Cash Flow (DCF)
If future receipt/future cash flows are to be compared with present outlay/present cash flows, they should be discounted to present day values.
The time value of money is reflected in capital investment decisions by discounted cash flow.
To discount cash flows means → to convert future cash flows to present day values.
There are two major discounted cash flow (DCF) analysis methods. These are:
i. the net present value (NPV) method;
ii. the internal rate of return (IRR) method.
The Net Present Value (NPV)
This is a method in which we calculate the present values of all the money coming in from a project in the future and these are set against the money being spent on the project today. The result is the net present value of the project. Net Present Value (NPV) is the present value of the sum of discounted cash flows minus initial investment.
Therefore, net present value (NPV) is the difference between amount invested now and the present value of future cash flows. This difference (NPV) can either be positive or negative.
The net present value of a project can be compared with those of other projects to find out the one that has the highest return in real terms and should therefore be chosen. Projects are only worth carrying out if the net present value is positive.
Assumptions
As it is generally common to the discounted cash flow methods, when discounting cash flows to their present values, using the net present value (NPV) method, it is assumed that:
· all cash flows associated with the project/investment are assumed to occur at the end of each period (typically, at the end of a year). Although, most cash inflows resulting from increased sales actually occurred uniformly throughout the year. This assumption greatly simplifies the calculations of present values.
· all cash flows associated with the project/investment are immediately reinvested in another project or investment. Using the NPV method, cash flows are assumed to be reinvested at the discount rate used in the analysis.
· all cash flows associated with investment/projects as treated as if they were known with certainty. However, risk adjustments can be made to account (in part) for cash flow uncertainties.
· there is a perfect capital market.
Calculation of Net Present Value (NPV)
As already highlighted, the computation of the net present value (NPV) requires comparing the present values of future cash inflow associated with the project, with the present values of cash outflows. In order to have present values, we require the use of discount rates.
Usually, many companies take the discounting rates to be the cost of capital which represents what the company will have to pay when borrowing or raising funds from the financial markets. (For instance, if money has to be borrowed at 8% interest rate per annum to finance investment in a project → the cost of capital is 8% and the future cash flows will be discounted at 8%). This discount rate is the minimum rate of return that the company feels must be earned for any potential investment to be profitable. Therefore, in calculating, net present value, the following steps are necessary:
i. Calculate initial cash flows
ii. Choose a discount rate (normally based on the company’s cost of capital)
iii. Discount the cash original cash flows using the discount rate
iv. Match the discounted cash flows against initial investment→ so as to arrive at the net present value.
We can express the above as:
NPV = Future CF1 + Future CF2 + Future CF3 +………………+ Future CFn – I0
(1 + r)1 (1 + r)2 (1 + r)3 (1 + r)n
In the alternative:
NPV = {Future CF1 X
Where:
Future CF represents the future values received in years 1 to n
R represents the rate of return
I0 represents the initial investment outlay
Illustration:
A project having an expected life of 3 years has an investment outlay of £1 and the cash flow for the life of the project are:
Year 1 300,000
Year 2 1,000,000
Year 3 400,000
If the cost of capital for the project is 10%, you are required to calculate the net present value for the project.
Solution:
NPV = £300,000 + £1,000,000 + £400,000 – £1,000,000
(1.10)1 (1.10)2 (1.10)3
= £399,700
Alternatively, the net present value can be calculated by referring to the published table of present values where we can simply find the discounting factors by referring to each year of cash flow and the appropriate interest rate (cost of capital).
Using the attached table, if the cost of capital is 10% and you refer to year 1, the 10% column at year 1will show a discounting factor of 0.9091. For years 2 and 3, the discounting factors are 0.8264 and 0.7513 respectively and so on. You then multiply the cash flows by the discounting factors to find the present values of the cash flows.
Therefore, the above illustration can be solved in an alternative way thus:
Year Amount (£000) Discounting Factor Present Value (£)
1 300 0.9091 272, 730
2 1,000 0.8264 826,400
3 400 0.7513 300, 520
1,399,650
Less initial outlay 1,000,000
Net present value 399,650
The difference between the two calculations is due to rounding differences.
It is important to note that the discounting factors in the present values table are based on £1 received in n year time. For example, £1 received in years 1, 2, and 3 when the interest rate is 10% is calculated as:
Year 1 = £1/1.10 = 0.9091
Year 2 = £1/(1.10)2 = 0.8264
Year 3 = £1/(1.10)3 = 0.7513
Decision Rules in NPV method:
Since the NPV allows a company to choose which projects are worth investing in and also to choose between competing projects, it necessary to be aware of the decision rules for NPV technique.
→Positive net present values indicate good investments while negative ones indicate poor investments.
→The golden rule is: Accept an investment with a positive NPV and reject an investments with a positive NPV.
→Make an investment if the NPV is positive. Projects are only worth carrying out if the net present value (NPV) is positive.
→Among alternatives and competing projects → choose the project with the highest value. This will increase the shareholder’s wealth.
→If an investment shows a negative NPV (that is present value of money being spent is greater than the present value of money being received), the company would be better off putting the money in the bank and earning the current interest rate.
Advantages of NPV
1. It takes opportunity of the opportunity cost of money into account.
2. It is a single measure which takes the amount and timing of cash flow into account, thereby considering the time value of money.
3. It can consider different scenarios.
Disadvantages of NPV
1. Its calculation and estimation of cost of capital may be difficult.
2. It is only comparable between projects if the initial investment is the same
Illustration
The Ever-Ready Building Society is contemplating launching a new on-line banking service, called Falcon. There are three alternative approaches, each involving £20,000 initial capital investment. Cash inflows for each year are as s stated below.
Year Project A Project B Project C
Cash flow £ £ £
0 (20,000) (20,000) (20,000)
1 4,000 8,000 8,000
2 4,000 6,000 8,000
3 8,000 6,000 6,000
4 6,000 3,000 6,000
5 6,000 2,000 3,000
The cost of capital is 10%.
Required:
Calculate the net present value for each of the projects under consideration and advise of which project to choose.
Solution:
Year Project A Project B Project C Discounting DCF A DCF B DCF C
£ £ £ Factor (10%) £ £ £
0 (now) (20,000) (20,000) (20,000) 1 (20,000) (20,000) (20,000)
1 4,000 8,000 8,000 0.9091 3,636 7,273 7,273
2 4,000 6,000 8,000 0.8264 3,306 4,958 6,611
3 8,000 6,000 6,000 0.7513 6,010 4,508 4,508
4 6,000 3,000 6,000 0.6830 4,098 2,049 4,098
5 6,000 2,000 3,000 0.6209 3,725 1,242 1,863
Net Present Value 775 30 4 353
Decision:
All the three projects have positive net present value and therefore are all worth carrying out. However, Project C has the highest NPV of £4,353 and thus, should be chosen.
Net Present Cost
If projects have differing lifetimes, we are not comparing equal benefits unless we equalise the lifetimes. Therefore, when investment/project alternatives have same life expectancy and cost is the only major consideration, net present cost is used.
Net present cost is the discounted value of a stream of future costs and benefits for projects or investments with the same life span. It is used to describe the difference between the present value of a stream of costs and a stream of benefits. The net present cost method is therefore very helpful for comparing projects that have identical lifetimes. If a number of options are being considered then the option with the lowest Net Present Cost will be the most favourable financial option.
A Paper Presented at Bournemouth and Poole College, Bournemouth, United Kingdom
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