# Net present value

Other Versions
Spanish
Making the correct calculations when buying machinery. June 24, 2002

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.