Tools and Forms contains a simple "present value of $1" table that you can use to figure the NPV of your project.
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At the simplest level of analysis, you'll want to make sure that the total costs of any major project you undertake are less than the total benefits resulting from the project. You could simply add up the costs, and then add up your expected revenue increases and cost savings over the next few years, and compare the two.
However, if you did that, you'd be ignoring the fact that many of the costs will be incurred at the beginning of the project, while many of the revenues or cost savings will occur later, over a period of months or, more likely, years.
We've reviewed a number of more formal ways to evaluate the costs or benefits that a major purchase or project will bring to your company. The most commonly used include:
Each of these methods has its advantages and drawbacks, so generally more than one is used for any given project. And no financial formula, or combination of formulas, should be used to the exclusion of common sense.
A project may "fail" your tests under some or all of these methods, but you might decide to go forward with it anyway because of its value as part of your long-range business plan.
The payback method is the simplest way of looking at one or more major project ideas. It tells you how long it will take to earn back the money you'll spend on the project. The formula is:
Thus, if a project cost $50,000 and was expected to return $12,000 annually, the payback period would be $50,000 ÷ $12,000, or 4.16 years.
If the return from the project is expected to vary from year to year, you can simply add up the expected returns for each succeeding year, until you arrive at the total cost of the project.
For example, in our previous cash flow example, the project costs $100,000 and the expected returns were as follows:
The project would be completely paid for about 10 1/2 months into the fourth year, because $100,000 (cost of project) is equal to all of the first three years' revenues, plus $28,477. $28,477 is equal to about 10.7/12 of the fourth year's revenues.
Under the payback method of analysis, projects or purchases with shorter payback periods rank higher than those with longer paybacks. The theory is that projects with shorter paybacks are more liquid, and thus less risky—they allow you to recoup your investment sooner, so you can reinvest the money elsewhere.
With any project, the variables grow increasingly fuzzy as you look out into the future. With a shorter payback period, there's less of a chance that market conditions, interest rates, the economy or other factors affecting your project will drastically change.
Generally, a payback period of three years or less is preferred. Some advisers say that if the payback period is less than a year, the project should be considered essential.
But don't forget the drawbacks of the payback period method. Chiefly, it ignores any benefits that occur after the payback period, so a project that returns $1 million after a six-year payback period is ranked lower than a project that returns zero after a five-year payback. But probably the major criticism is that a straight payback method ignores the time value of money. To get around this problem, you should also consider the net present value of the project, as well as its internal rate of return.
A fairly simple way of gauging your return on an investment in a major project or purchase is the accounting rate of return (ARR). The formula is:
For purposes of this formula, depreciation is calculated very simply, using the straight-line method:
As an example of how ARR works, let's say you're looking at equipment costing $7,500 that is expected to return roughly $2,000 per year for five years. After five years you'll sell the equipment for $500. The depreciation would be ($7,500 - $500) ÷ 5, or $1,400.
Using ARR can give you a quick estimate of the project's net profits, and can provide a basis for comparing several different projects. Under this method of analysis, returns for the project's entire useful life are considered (unlike the payback period method, which considers only the period it takes to recoup the original investment). However, the ARR method uses income data rather than cash flow and it completely ignores the time value of money. To get around this problem, you should also consider the net present value of the project, as well as its internal rate of return.
The net present value method (NPV) of evaluating a major project allows you to consider the time value of money. Essentially, it helps you find the present value in "today's dollars" of the future net cash flow of a project. Then, you can compare that amount with the amount of money needed to implement the project.
If the NPV is greater than the cost, the project will be profitable for you (assuming, of course, that your estimated cash flow is reasonably close to reality). If you have more than one project on the table, you can compute the NPV of both, and choose the one with the greatest difference between NPV and cost.
As an example of how NPV works, imagine you're looking at a project costing $7,500 that is expected to return $2,000 per year for five years, or $10,000 in total. At first glance, the project looks profitable. Under the payback method, it looks as if the project will pay for itself in 3.75 years.
However, using NPV analysis, you can determine that if the discount rate on the project was 10 percent, the value of the expected returns would be $12,078.83. In other words, if you had $7,500.00 today and invested it at 10 percent, after five years you'd wind up with $12,078.83, well above your payback method calculation.
Bear in mind, though, that NPV analysis is generally used to evaluate the project's cash flows, rather than the income from the project that would be shown on an income statement. Why? Because the income statement factors in depreciation, but depreciation is not an out-of-pocket expense.
For instance, if revenue of $10,000 is reduced to $7,000 of income because of a $3,000 depreciation deduction, you still have the use of the full $10,000. So, the cash flow figure of $10,000 is the more instructive one to look at. However, if you are very concerned about the appearance of your income statement (for example, if you anticipate putting the business up for sale or seeking major financing in the future, or if you're under stockholder pressure to show more income) you may decide that the income figure is more appropriate to use.
How do you compute NPV? The easiest way is to use a good financial calculator. If you don't have one, or don't want to take the time to learn how to use one, you can use the present value table contained among the Tools and Forms.
Tools and Forms contains a simple "present value of $1" table that you can use to figure the NPV of your project.
If you are mathematically inclined and have a calculator with exponential functions, you can also use the following formula:
(When using this formula, CFx = cash flow in period x, n = the number of periods, and r = the discount rate.)
Whenever you do time value of money calculations to find a present or future value (such as NPV), you'll need to specify an interest rate, known as the discount rate. Choosing the appropriate discount rate is a very important part of the process.
How can you quickly estimate your cost of borrowing, which is used as the "discount rate," for purposes of analyzing a major purchase decision?
If you are planning to finance the purchase and you know what the interest rate on the loan would be, you can use the rate charged on the loan as the cost of borrowing for the project. Therefore, you would use the loan's rate as the "discount rate" in computing the net present value for the project. (If the rate is variable, you may have to take a guess as to the average rate over the loan period, or do the computation under worst-case and best-case scenarios.)
To fine-tune your calculations, you'll want to account for the fact that interest on business loans is tax-deductible. So, you can multiply the nominal interest rate on the loan by one minus the marginal tax rate for the business, to arrive at the tax-adjusted interest rate.
If the rate on your loan was 8.5 percent and your marginal combined federal and state income tax rate was 40 percent, your tax-adjusted interest rate on the loan would be 5.1 percent (1- 0.40 = 0.60; 0.085 x 0.60 = 0.051).
If you are not financing your purchase, theoretically, you should attempt to compute an average cost of capital for your business that reflects all your current funding sources, including debt and owner's equity. Computing your true cost of capital can be rather time-consuming and complicated, and you'll probably need your accountant's assistance to do it accurately. The calculation depends on a number of economic conditions, opportunity costs, and business risks faced by the company.
What's more, using this figure assumes that additional capital can be obtained from similar sources in the same proportion, and at the same rates. For many small businesses, this may not be a realistic assumption. Instead, you can use your average cost of borrowing as the discount rate.
The following figures reflect the cost to Clear Corporation of borrowing from each external source that it is currently using. We'll assume that Clear's common stock is currently not paying any dividends.
|Funding Source||Amount||% of Total||Interest Rates||Rate Factor|
|Preferred Stock||$250,000||26%||× 8.00%||= 2.08%|
|Bonds||$250,000||26%||× 8.50%||= 2.08%|
|Loans-Community Devel.||$100,000||10%||× 5.50%||= .55%|
|Revolving Loan||$ 75,000||7%||× 11.00%||= .77%|
|Term Loan||$300,000||31%||× 9.75%||= 3.02%|
In this example, the company's average cost of borrowing would be 8.5 percent. Note that interest rates on all loans must first be adjusted to account for tax benefits, as described above.
The internal rate of return (IRR) method of analyzing a major purchase or project allows you to consider the time value of money. Essentially, it allows you to find the interest rate that is equivalent to the dollar returns you expect from your project. Once you know the rate, you can compare it to the rates you could earn by investing your money in other projects or investments.
If the internal rate of return is less than the cost of borrowing used to fund your project, the project will clearly be a money-loser. However, usually a business owner will insist that in order to be acceptable, a project must be expected to earn an IRR that is at least several percentage points higher than the cost of borrowing, to compensate the company for its risk, time, and trouble associated with the project.
As an example of how the internal rate of return works, let's say you're looking at a project costing $7,500 that is expected to return $2,000 per year for five years, or $10,000 in total. The IRR calculated for the project would be 10 percent. If your cost of borrowing for the project is less than 10 percent, the project may be worthwhile. If the cost of borrowing is 10 percent or greater, it won't make sense to do the project (at least from a financial perspective) because, at best, you'll be breaking even.
IRR analysis is generally used to evaluate the project's cash flows, rather than the income from the project that would be shown on an income statement (also known as the profit and loss statement). Why? Because income on a P&L reflects depreciation, but depreciation is not an out-of-pocket expense. For instance, if revenue of $10,000 is reduced to $7,000 of income because of a $3,000 depreciation deduction, you still have the use of the full $10,000. So the cash flow figure of $10,000 is usually the more instructive one to look at.
If you are very concerned about the appearance of your income statement (for example, if you anticipate putting the business up for sale or seeking major financing in the future, or if you're under stockholder pressure for increased income) you may decide that the income figure is more appropriate to use.
How do you compute the IRR? The easiest way is to use a good financial calculator. If you don't have one, or don't want to take the time to learn to use one, you can also use the present value tables located in Tools and Forms.
Among the Tools and Forms is a simple "present value of a series of $1 payments" table that you can use to figure the IRR of your project.
If you want to use the present value tables to calculate the IRR of your project, you must first compute the number to look up in the tables. Do that by dividing your expected net cash outflow for the project by your expected average annual net cash inflow. For example, in our example above, the cost of the project (net cash outflow) was $7,500, and the average annual net cash inflow was $2,000.$7,500
Then, look at the row corresponding to the number of years the project or equipment will be in use (in this case, five). Look across the rows until you find the number that is closest to the result you found (3.8). Then look at the top of the column in which the closest number was found, to see the interest rate that is your IRR (in this case, 10 percent).
One problem with the IRR is that if the expected cash inflows vary greatly from year to year, it's very difficult and time-consuming to calculate the interest rate, though it can be done by using the following math formula.
For those who are mathematically inclined, you can use the following formula (which is very similar to the formula used to find the net present value. The main difference is that in the IRR formula, you must solve for the interest rate, r.
(When using this formula, CFx = cash flow in period x, and n = the number of periods.)
Of the four methods of analyzing a major purchase, which one is the best?
While the payback period method and the accounting rate of return method are the easiest to compute, most accountants would prefer to look at the net present value and the internal rate of return. These methods take into consideration the greatest number of factors, and in particular, they are designed to allow for the time value of money.
If the net present value is negative, or if the internal rate of return is less than the cost of borrowing, the project should be rejected as not financially feasible (unless the project is one that's required by law, such as a safety upgrade).
Occasionally, when you're looking at a number of projects that are competing for your time and money, the NPV and IRR methods will yield different answers to the question, "Which project is best?" Financial experts differ as to which method should be the deciding factor. Your accountant may be able to provide some insight as to which method is more useful in your particular situation.
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