Capital budgeting - 1
CORPORATE FINANCE - 1 UNIVERSITY OF EXETER MARK FREEMAN, 2004
Week 5
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Project valuation
Today, you are going to value the following project. Initial cost of the project: £2.5m to be invested immediately. The best projection for the number of items sold for the next seven years is (with nothing after this): Year Sales
1 2 3 4 5 6 7 10000 20000 22000 24200 24200 12100 0
Next year you expect to be able to sell these items at £100 each. There is a fixed cost of production each year of £500,000 and a variable cost of production of £25 an item. You pay no corporate tax The risk-free rate currently stands at 5% and inflation is at 3%. You believe that these cashflows should be discounted at a risk premium of 8%.
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Cashflows
The first thing you must do is to calculate the net cashflow. Now, it is very important that you remember to include the inflation component when calculating the cashflows. If you don’t do this, you will be in trouble. Year 0 Invested (2.50) (£m) Sales T/o (£m) Fixed cost (£m) Variable cost (£m) Net (2.50) Cashflow (£m)
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2
3
4
5
6
10000 20000 22000 24200 24200 12100 1.00 2.06 2.33 2.64 2.72 1.40 (0.50) (0.52) (0.53) (0.55) (0.56) (0.58) (0.25) (0.52) (0.58) (0.66) (0.68) (0.35) 0.25
1.02
1.22
1.43
1.48
0.47
3
Payback periods
The first way of evaluating this project is to calculate the payback period. How long does it take you to get back the initial £2.5m? By the end of year 1 you will have £0.25m By the end of year 2 you will have £1.27m By the end of year 3 you will have £2.49m You need £2.5m to payback the initial investment. So, a further £2.5 - £2.49m = £0.01m is needed. The payback period is therefore almost exactly 3 years. The advantage of using the payback period for evaluating projects is that it is simple and may be useful for companies that have serious problems with cash flow management. There are many disadvantages. It takes no account of the time value of money. It penalizes long-term projects in favour of short-term projects.
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Discounting the cashflows
When evaluating this project, the time value of money should be taken into account. First, we will discount the cashflows at the “required rate of return”. The risk-free rate is 5% and you require an 8% risk premium for this project. In other words, the “required rate of return” (or “discount factor”) for this project is 5% + 8% = 13%. Using this to get the “discounted cashflows (DCF)” Year Net Cashflow (£m) Discount factor DCF (£m)
0 1 (2.50) 0.25
1
2 1.02
3 1.22
4 1.43
5 1.48
6 0.47
0.885 0.783 0.693 0.613 0.524 0.480
(2.50) 0.22
0.80
0.85
0.88
0.78
0.23
The first thing we can do now is calculate the discounted payback period. Using the DCF numbers it is apparent that the discounted cashflows pay off the initial investment in 3 years and 8.6 months. Week 5
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Net Present Value (NPV)
The next way of doing the analysis is just to add up all the DCFs to get the net present value (NPV). NPV
= (2.50) + 0.22 + 0.80 + 0.85 + 0.88 + 0.78 + 0.23 = £1.26m.
The decision rule based on NPV analysis is: Positive NPV Negative NPV
Good project Bad project
Given that this is positive, this appears to be a good project. As we will see below, NPV analysis will be our chosen method of project appraisal. Before we reach this conclusion, though, we must consider some alternatives…
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Internal Rates of Return (IRR)
Rather than discounting at 13% and then calculating the NPV, the alternative is to see what discount rate would give an NPV of zero. This is called the internal rate of return (IRR). Using the Tools/Goals Seek method in Excel that we saw in week 1 we can work out the IRR. It is 27.67%. As this is above the “hurdle rate” of 13%, we should undertake this project. 4.00
3.50
3.00
2.50
NPV
2.00
1.50
1.00
0.50
0.00 0%
5%
10%
15%
20%
25%
30%
-0.50 Discount rate
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Changing the project
Suppose that, we can secure a further order from a customer that will be worth £4m in revenue at the end of the third year. This will lead to additional incremental costs of £7.4m. However, we can defer these costs to £2.9m at the end of the fifth year and a further £4.5m at the end of the sixth year. Does this new order make the project more or less attractive to us? It is “obvious” that this is a bad deal. The effective rate of return that we are paying on this new order is: 4=
2.9
+
4.5
(1 + r ) 2 (1 + r )3
Solving, r = 26.94%. For a project with a discount rate of 13%, this effective interest rate of 26.94% that we are paying to secure the new order is clearly too high. How does this look if we put it into our project analysis? Payback is now clearly within three years, as the cash inflow from the new order will pay off the initial investment.
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Changing the project - 2
Consider the cashflows now: Year Project Cashflow New order New net Cashflow Discount factor DCF (£m)
0 1 (2.50) 0.25
2 1.02
3 1.22
4 1.43
4.00 (2.50) 0.25 1
1.02
5.22
5 1.48
6 0.47
(2.90) (4.50) 1.43
(1.42) (4.03)
0.885 0.783 0.693 0.613 0.524 0.480
(2.50) 0.22
0.80
3.62
0.88
(0.74) (1.93)
The NPV is now –2.50 + 0.22 + 0.80 + 3.62 + 0.88 – 0.74 – 1.93 = £0.35m This NPV is lower than it was without the new order (when the NPV was £1.26m). Therefore, the decision rule that the higher the NPV the better the project works in this case.
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Changing the project - 3
If we work out the IRR of the project, though, there are two problems. 1)
2)
There is an internal rate of return = 28.70%. This is higher than the IRR without the new order (which was 26.94%). So, higher IRR does not mean better project. There is a second IRR of 0.142%. That is, the IRR is not unique. What does this mean? 0.35
0.30
0.25
0.20
NPV
0.15
0.10
0.05
0.00 0%
5%
10%
15%
20%
25%
30%
-0.05
-0.10 Discount rate
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Multiple IRRs
When, and why, do we have this problem of multiple IRRs? This arises when, after the initial investment, the net cashflows are sometimes positive and sometimes negative. In this example, the net cashflows start positive and end negative. As the discount rate increases this has two offsetting effects: 1) 2)
It makes the cashflows from the project less valuable in present value terms Our obligations in years 5 and 6 also have a lower present value.
Therefore, there are offsetting effects from increasing the discount rate. That is why the last graph is strangely “nonlinear” and why multiple IRRs exist. The more often the net cashflow changes between positive and negative, the more IRRs can potentially exist.
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Accounting ratios
Some managers like to evaluate projects on the basis of accounting ratios. For example, you could calculate a return on capital employed (ROCE) each year: ROCE =
Accounting profit after depreciation and tax Book value of capital employed at beginning of
year There are several reasons why this method is not favoured in finance. First, and most importantly, this number depends on somewhat subjective accounting conventions. Second, as this ratio varies year by year, it is not clear how to interpret it. The finance community prefers to use cashflows rather than accounting profits since cashflow numbers are uncontroversial. This technique is still quite commonly used in practice, however, as many senior finance directors come from an accounting background and are more confident dealing with accounting numbers than projecting cashflows.
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In summary
We have looked at four possible methods of evaluating projects. 1) 2) 3) 4)
NPV IRR Payback period ROCE
Problem with multiple IRRs Undervalues long-term projects Subject to accounting conventions
The preferred method is NPV because: a)
b)
c) d)
The decision rules are easy. You should (should not) undertake the project if the NPV is positive (negative). The higher the NPV, the better the project. It is unique. The technique is identical to the methods that we used to price Treasury securities and the discounted dividend model for valuing stock. The discounted cashflow method is a general method of valuing investment opportunities There is no subjectivity over accounting conventions. For those of you who like a very solid theoretical grounding for your methods, there is a “fundamental theorem of asset pricing” which demonstrates unambiguously that the NPV method is “correct” when excluding project flexibility.
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What do practitioners actually use?
Graham and Harvey (2001, Journal of Financial Economics) undertake a major survey of US corporations to see what corporate finance practices they actually use. They find that the following proportion of CFOs “almost always” use the following techniques1: Technique IRR NPV Payback period Sensitivity analysis Discounted payback Real Options ROCE
% managers using 76% 75% 57% 52% 29% 27% 20%
We will return to real options later in the course.
1
Other methods are also used by corporations, but these are much less important than NPV / IRR.
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The fundamentals of NPV analysis
There are three steps that must be completed before we can undertake an NPV analysis: 1)
2) 3)
We must estimate the expected pre-tax cashflows from the project for each period between the date that the project is started and the date it terminates. We must calculate the tax implications of these cashflows. We must calculate the appropriate discount rate to use.
For the rest of this class we shall concentrate on the fundamentals of estimating pre-tax cashflows.
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Inflating the cashflows
In the example given above, it was emphasized that we had to inflate the cashflows. Why? The required rate of return was calculated by adding a risk premium of 8% onto the risk-free rate of 5%. But this risk-free rate of 5% includes an inflation term of 3% and a real risk-free rate term of 1.94% (From Fisher’s theorem, 1.05 = 1.03 x 1.0194). That is, the discount rate includes the inflation component already. To be consistent, therefore, we need also to include the inflation element into our cashflows. This is called “nominal” discounting – we include inflation in both the discount rate and the cashflows.
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Real vs. nominal analysis
Some people do “real” discounting – that is, they remove the inflation component from the discount rate and then do not inflate the cashflows. If done correctly this should always give the same answer. My advice, though, is to do nominal analysis. The main reason for this is that certain cashflows do not inflate whatever happens to the inflation rate. In the example given above, the cashflows to and from the venture capitalist are not inflated. Of particular importance will be tax-related cashflows. These never inflate. So, if you do real analysis, not only do you have to deflate the discount rate, you also need to deflate certain cashflows. So, while doing “real” analysis is completely correct if done properly, my view is that you are more likely to make mistakes this way. For this reason, all the examples in this class will be done nominally.
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What cashflows do we discount?
We define the relevant net pre-tax cashflows as follows: Pre-tax Cashflow
= -
Cash received from sales Cash paid out on operating expenses Capital outlays as they occur Increases in net working capital
Or, comparing with profit: Pre-tax Cashflow
= + -
Earnings before interest and tax Non-cashflow expenses (mainly depreciation) Capital outlays Increase in net working capital
Key differences: 1) 2)
3) 4)
Cashflow takes the full amount of investment on the date the cost is incurred and does not depreciate them. Costs and revenues are included on the date when the cash is paid/received and not on the date when they accrue. Spending cash to increase inventory is considered a cashflow even though this has no effect on profit. Interest payments are not taken into account.
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Key issues in cashflow estimation
1)
2)
3)
4)
5)
Because cashflows are considered on the date that they are paid/received, sunk costs are never included in NPV analysis. These cashflows are in the past already. When evaluating a project, it is the incremental cashflows that are important. The cashflow that should be discounted is the difference between what we expect to receive if we undertake the project compared with what we would expect in the absence of the project. Incremental cashflows should include the opportunity cost of cashflows lost as a consequence of starting a project. NPV analysis should be undertaken from a corporate, not a divisional perspective. Whether these cashflows occur in your division or not is irrelevant. For this reason, the allocation of costs is completely irrelevant to NPV analysis.
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“Practical” cashflow estimation
While the appropriate technique for estimating cashflows varies widely from industry to industry, there are certain general rules that can be used. In particular, it is often possible to estimate cashflows with some precision in the short term. It is then difficult to make predictions as to what will happen in the longer term. For this reason, we need to worry about “terminal value calculations” – how we estimate the value of the project in the distant future. So suppose that we are able to make accurate profit forecasts for the next seven years, and that, in year 7 we will be making net operating cashflows of £1m per year. Assume that we are discounting the cashflows at 13% per year – reflecting a 5% risk-free rate and an 8% risk premium.
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Terminal values
There are several assumptions that we could make: 1) 2)
Assume that there are no more profits to be made. In this case the NPV just comes from the first seven years. Assume that the operating cashflows are going to decline – say straight line – to zero in say year 12. In this case, the NPV is the present value for the first seven years plus Year 8 800,000
Cashflo w Discount 0.376 PV 301,000
3)
Year 9 600,000
Year 10 400,000
Year 11 200,000
Year 12 0
0.332 200,000
0.295 118,000
0.261 52,000
0.231 0
Therefore, this gives an NPV of 671,000 more than method (1) Assume that profits will decline slowly indefinitely. That is, assume that the decline in net cashflows will be, say, 5% per year on a declining balance basis. In this case, we can use the Gordon Growth Formula to get the terminal value. In terms of year 7 pounds, the terminal value will then be: 1 − 0.05 1,000,000 * = 5,280,000 0.13 − (−0.05)
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Terminal values - 2
3...) This, though is in terms of year seven pounds. So, in year 0 pounds, this is equivalent to 5,280,000 /(1.13)7 = 2,240,000 . This gives a much higher PV than methods (1) and (2) 4) We could use the annuity formula to assume that cashflows will remain unchanged for, say, a further 5 years and then decline. 5) Any combination of these things. What I am trying to demonstrate here is that whether we get a positive NPV or not is often a factor of what terminal value assumptions we make. But, almost by definition, the terminal value is the hardest thing to estimate. This is a major problem with NPV analysis.
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Manipulated NPVs
Sometime managers have an incentive to “fix” their NPV. You should be aware of some of the tricks that they play. The easiest number to manipulate on an NPV is the terminal value. Therefore, when I am evaluating someone else’s NPV this is the first number that I look at. Essentially, I am very wary when “too much” of the present value comes from terminal cashflows. In some cases it can be as much as 50% of the total present value. This is clearly worrying and I would be very reluctant to accept such a project without seeing a detailed analysis of why the cashflows were taking so long to come through. So, beware. Do not spend 99% of your analysis time estimating cashflows for the first few years and then 1% of your time “throwing in” a terminal value – particularly if the terminal value accounts for a large proportion of the total present value. This is a very common mistake in practice.
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Sensitivity analysis
Hopefully, by now, you are realizing that there is a great deal of subjectivity when doing NPV analysis. How are you going to estimate your cashflows? What terminal value assumption do you make? … For this reason, it is strongly recommended that you do sensitivity analysis when undertaking NPV analysis. Try different scenarios. Under what conditions is the NPV positive and when is it negative? What is the worst (realistic) case? What would be the consequences in the worse case? That is, rather than accepting all projects with positive NPV and rejecting projects with negative NPV (the most naïve textbook approach), this technique should be used as a tool to help you make a management decision. Certainly, the more positive the NPV the more optimistic you should be about the project. But you should carefully consider the assumptions made in doing the analysis, consider how robust these assumptions are and what will happen if things do not go according to plan.
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Questions – Week 5
CORPORATE FINANCE - 1 UNIVERSITY OF EXETER MARK FREEMAN, 2004
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Question set 4 1)
Work out the payback period, the NPV and IRR of the following project. Assume that there is no taxation. The nominal discount rate is 15% and the inflation rate is 3% per year into the foreseeable future. Should you undertake the project or not? The project requires immediate capital investment of £250,000. Sales in year 1 are expected to be 5,000 items. In year 2 sales will increase to 10,000 items. From years 3 to 6, sales will be at 20,000 items a year. There will be no more sales after year 6. It is expected that, in year 1, each item will sell for £75. The expected fixed cost of production in year 1 is £500,000 with a marginal cost of production of £35 per item. All costs and revenues are expected to increase in line with inflation.
2)
How does the NPV that you calculated in question 1 change if the firm needs to hold 15% of annual sales (in value terms) in inventories?
3)
How does the NPV that you calculated in question 2 change if you have already invested £100,000 in management consulting fees in preparation for this project?
4)
How does the NPV that you calculate in question 3 change if, for each item you sell, another division within your organization loses £1 in profit (in terms of year 1 pounds) because you are “cannibalizing” some of their sales.
5)
How does the NPV that you calculated in question 4 change if you are allocated with £100,000 of central overheads per year?
6)
How does the NPV that you calculated in question 5 change if you assume that, instead of sales going to zero after year six, the net cashflows from question 1 decreases at 10% per year (after adjusting for inflation) indefinitely but that there are no cashflow implications from (2) – (5) after year 6?
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