Tuesday, April 11, 2006


Capital Budgeting

A capital investment problem is essentially one of determining whether the anticipated cash inflows from a proposed project are sufficiently attractive to warrant risking the investment of funds in the project.

In the net present value method the basic decision rule is that a proposal is acceptable if the present value of the cash inflows expected to be derived from it equals or exceeds the present value of the investment. To use this from it equals or exceeds the present value of the investment. To use this rule, one must estimate:
(1) the required rate of return
(2) the economic life
(3) the amount of cash inflow in each year
(4) the amount of investment, and
(5) the terminal value.

The internal rate of return method finds the rate of return that equates the present value of cash inflows to the present value of the investment- the rate that gives the project an NPV of zero. The simple payback method finds the number of years of cash inflows that are required to equal the amount of investment. The discounted payback method finds the number of years required for the discounted cash inflows to equal the initial investment. The unadjusted return on investment method computes a project’s net income according to the principles of accrual accounting and expresses this profit as a percentage of either the initial investment or the average investment. The simple payback and unadjusted return methods are conceptually weak because they ignore the time value of money.

In preference problems the task is to rank two or more investment proposals in order of their desirability. The profitability index – the ratio of the present value of cash inflows to the investment – is the most valid way of making such a ranking.

The foregoing are monetary considerations. Non-monetary considerations are often as important as the monetary considerations and in some cases are so important that no economic analysis is worthwhile. In some instances a manager’s aversion to risk may cause a project with an acceptable return to be rejected or not even proposed.


1. Select a required rate of return. This rate applies to projects deemed to be of average risk and may be adjusted for a specific proposal whose risk is felt to be above or below average.
2. Estimate the economic life of the proposed project.
3. Estimate the differential cash inflows for each year during the economic life, being careful that the base case is properly defined and quantified.
4. Find the net investment, which includes the additional outlays made at Time Zero, less the proceeds (adjusted for tax effects) from disposal of existing equipment and the investment tax credit, if any.
5. Estimate the terminal value at the end of the economic life, including the residual value of equipment and current assets that will be liquidated.
6. Find the present value of all the inflows identified in steps 3 and 5 by discounting them at the required rate of return, using Table A (for single annual amounts) or Table B (for a series of equal annual flows).
7. Find the net present value of the inflows. If the net present value is zero or positive, decide that the proposal is acceptable insofar as the monetary factors are concerned.
8. Taking into account the non-monetary factors, reach a final decision. (This part of the process is at least as important as all the other parts put together, but there is no way of generalizing about it.)


When the NPV method is used, the required rate of return must be selected in advance of making the calculations because this rate is used to discount the cash inflows in each year. As already pointed out, the choice of an appropriate rate of return is a difficult matter. The IRR method avoids this difficulty. It computes the rate of return that equates the present value of the cash inflows with the present value of the investment - the rate that makes the NPV equal zero. This rate is called IRR, or the discounted cash flow (DCF) rate of return. (The IRR method is sometimes called the DCF method.)

If the management is satisfied with the internal rate of return, then the project is acceptable. If the IRR is not high enough, then the project is unacceptable. In deciding what rate of return is high enough, the same considerations apply as those in selecting a required rate of return.


There are two classes of investment problems: screening problems and preference problems. In a screening problem the question is whether or not to accept a proposed investment. The discussion so far has been limited to this class of problem. Many individual proposals come to management’s attention; by the techniques described above, those that are worthwhile can be screened out from the others.

In preference problems (also called ranking, or capital rationing problems), a more difficult question is asked: Of a number of proposals, each of which has an adequate return, how do they rank in terms of preference? If not all the proposals can be accepted, which ones are preferable? The decision may merely involve a choice between two competing proposals, or it may require that a series of proposals be ranked in order of their attractiveness. Such a ranking of projects is necessary when there are more worthwhile proposals than funds available to finance them, which is often the case.

Criteria for Preference Problems

Both the IRR and NPV methods are used for preference problems. If the IRR method is used, the preference rule is as follows: the higher the IRR, the better the project. A project with a return of 20% is said to be preferable to a project with a return of 18%, provided that the projects are of equal risk. If the projects entail different degrees of risk, then judgment must be used to decide how much higher the IRR of the more risky project should be.

If the net present value method is used. The present value of the cash inflows of one project cannot be compared directly with the present value of the cash inflows of another unless the investments are of the same size. Most people would agree that a $1,000 investment that produced cash inflows with a present value of $2,000 is better than a $1,000,000 investment that produces cash inflows with a present value of $1,001,000, even though they each have an NPV of $1,000. In order to compare two proposals under the NPV method, therefore, we must relate the size of the discounted cash inflows to the amount of money risked. This is done simply by dividing the present value of the cash inflows by the amount of investment, to give a ratio that is called the probability index. Thus, a project with an NPV of zero has a probability index of 1.0. The preference rule is: the higher the probability index, the better the project.

Application Problem:

Suppose you are in the real estate business. You are considering construction of an office block. The land would cost P50,000 and construction would cost further P300,000. You foresee a shortage of office space and predict that a year from now you will be able to sell the building for P400,000. Thus you would be investing P350,000 now in the expectation of realizing P400,000 at the end of the year. You should go ahead if the present value of the P400,000 payoff is greater than the investment of P350,000.

Assume for the moment that the P400,000 payoff is a sure thing. The office building is not the only way to obtain P400,000 a year from now. You could invest in a 1-year US Treasury bill. Suppose the T-bill offers interest of 7%. How much would you have to invest in it in order to receive P400,000 at the end of the year? That’s easy: you would have to invest

P400,000 x 1/1.07 = P400,000 x .935 = P373,832

Therefore, at an interest rate of 7%, the present value of the P400,000 payoff from the office building is P373,832.

Net present value

Q. It's been a while since I bought anything except by seat-of-the-pants intuition. Can someone bring me up to speed on Net Present Value calculations for machinery?
Forum Responses It would seem to me that what you paid for it, less what you have depreciated it on your taxes, would equal what its net present value is. That's presuming you don't still owe on it. Am I close?
From contributor Q: Here is what I know about NPV. It is the value today of a future payment. (Present value of revenues - Present value of costs). The equation for present value is Revenue or Cost/(1+interest rate) to the power of years. Most industry uses 7-8% interest or hurdle rate, I am pretty sure. You will have to figure out annual costs and incomes from the machine. Sometimes this can get pretty detailed. The purchase of the machine is in year 0 so there is no calculation for that.
Contributor Q, with the highest respect, you lost me totally. Why would a woodworker need to make such a wild calculation?
From the original questioner: If you can show a positive NPV to your banker, she might just give you the loan for that overpriced profile grinder.
If I remember correctly, the calculation requires that you set a reasonable desired return on investment, market value of the equipment after x years, increase in productivity, increase or decrease in labour inputs, and so on. The idea of using the NPV evaluation is that it takes into consideration that money now is worth more than money later. (More sophisticated tool than other evaluation models.)
I work in the finance field (Chartered Accountant).
NPV is the value of a project, expressed in today's dollars. Value is defined as increased earnings (or decreased cost) net of expenses incurred to implement the project - including the interest to finance the project's acquisition and the tax break that writing off the project affords.
Unfortunately, sometimes there's no way to simplify an idea without losing important information.
Seems to me the present value of a machine is what you can sell it for. Too simple?
From contributor G: If you bought a machine today and tomorrow it did its job and the money you got for the job it did was greater than the cost of the machine, you would make the investment. That is, there would be a profit. The *net* profit would be the gross receipt minus the machine expense. But you probably also had labor costs, maybe some energy, etc., so often these operating costs are subtracted from the profit. You may also want to subtract taxes. You may wish to sell the machine immediately and add this back into the value. When you are done, you have the *net present value after taxes*. If the number is positive, then it is a good investment - it is profitable; if the NPV is negative, then it is not a good investment.
Now here is the hard part. When you buy a machine, it does not pay back everything tomorrow, but it will pay you (or generate profit) over a long period of time - say three years. So, if it will generate $3000 for me in three years, what is such money worth today? Well, it depends on the interest rate. (One suggested change from the previous postings: Use an interest rate for a small business that is the rate at which you can borrow money. Maybe 12% interest rate today. Sometimes this is called the discount rate.) So, $3000 three years from now needs to be reduced (discounted) by 12% for every year to get a true value of that money in today's dollars. So, for year three, we calculate that the value is $360 less, or $2640. For year two, we again reduce the new value of $2640 by 12%, or $317. So, for year two it is worth $2327. And finally for year one, we reduce the value by 12% again, giving us $2048.
Stated another way, if you had $2048 that you put in a CD bearing 12% annually in interest and left the interest to accumulate and earn additional interest, you would have $3000 in three years. So, the *present value* in my example is $2048. Now, if I had to invest $2000 in order to get a machine that would pay me the $3000 in three years, then I subtract the machine cost from the present value ($2048 - $2000), giving me the *net present value* of $48. Another way to look at this is that the investment of $2000 in a machine that will give me $3000 in three years will be returning a little more than 12% on my investment - $48 more.
Some people like to figure out what interest rate (discount rate) will give a 0 NPV. In my example, this is about 12.6%. (If you got a loan for the $2000 and the interest was over 12.6%, you would lose money!) The value of 12.6% is called the Internal Rate of Return (IRR). (As mentioned, you may wish to make several subtractions and additions to your numbers.)
From the original questioner: Thank you so much! Your description brought me back to the example used when I first heard of NPV. In that case, the contemplated acquisition was a chop optimizer vs. 4 or 5 guys chained to upcut saws.
I get the impression that NPV analysis is more relevant as you move towards commodity production and less relevant as you move toward specialized products where strategic purchases and company image are more important to price premiums. Or is it just that these things are harder to quantify for the arithmetic?
A former employer of mine (video equipment rentals) recently had to decide if he was going to buy 25 digital VTRs worth over $1,000,000 when he was assured of only one rental on them (World's Track & Field). He did, and had trouble sleeping until they were booked for the SLC games. If he didn't buy them, though, a competitor may have done so and he could have lost a regular customer.
I can also imagine that changing technology like CNC could not only change the throughput, but also demand for product and market price if others invested in it too. Some tools are so versatile that you know darn well that in a year's time you'll be making something you could never have forecast.
Still, I think I'm going to make use of NPV for my next programme. I think using it will force me to evaluate all the ins and outs of doing something.
From contributor C: Net present value, return on capital and rate of return are all methods used to justify projects or purchases. They are mostly used by large corporations to put a ranking on all capital projects so they can get the most from their available capital or to determine if some borrowing is necessary. The ranking is of course especially necessary when the decision-makers are far removed from the projects and don't know (or want to know) the details of every project.
For everyone else, it's usually obvious if there is enough potential profit to justify the purchase. The real danger is in underestimating the total cost of everything needed to get the job done and then your calculations are for naught. One of the deliberate abuses of the method (in the large companies) is to not include everything that will eventually be necessary and then after you start, you create justification for the rest of the project.
From contributor G: Contributor C, the problem I see most often is that the NPV or IRR is very good, but the cash flow is terrible. Small firms use their capital to purchase equipment rather than borrow and use the cash for slow weeks/months.
From contributor C: Contributor G, I wish I could say that I have never done that, but it would not be the truth.
The large corporations usually have a very formal system for capital expenditures and they have a set amount of retained earnings that is set aside for that purpose. All the projects compete for those funds through the rate of return method and yes, the returns are very high - typically 20% minimum and a good benchmark would be $1 back every year for every $2 you spend. If there is not enough money to fund the best projects, they are either not approved, delayed, or they release more stock, sell bonds, or borrow money for the best projects. These companies even have people to watch the cash balance on an hourly basis and borrow or loan money for days at a time to maximize return on cash balances.
The big hazard in this system, other than spending the money for daily operations, is underfunding projects. This is usually caused by: 1. Trying to beat the rate of return system for a favorite project. After you start the project, you create justification for the additional capital needed. 2. Underestimating all the equipment, tooling, space, etc. needed to fully complete the project. It's never ignorance, just being overly optimistic. 3. Unforseen problems. There is usually contingency money for the small problems, but it never is enough for big problems. There is sometimes a "risk factor" added to the rate of return system to account for this and new technology projects naturally carry the highest risk.


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