Net Present Value (NPV) shows the cash value return from the investment with taking discounting into consideration.
Why is Net Present Value (NPV) of a project important?
Net Present Value (NPV) gives today’s numerical cash value of the estimated future Net Cash Flows (or Net Profits) resulting from an investment considering the time value of money as it employs the discounting concept. Or simply, net earnings in USD$ from the investment adjusted for inflation.
It uses discounted Cash Flows. Discounted Cash Flows are present values of future Cash Flows.
How to calculate Net Present Value (NPV)?
STEP 1: Multiply the discount factors by Net Cash Flows in each year. Net Cash Flow in Year 0 is never discounted because it is expressed in today’s values already.
STEP 2: Sum up all the Discounted Net Cash Flows.
STEP 3: Subtract the Initial Cost of Investment from the Sum of Discounted Net Cash Flows to give Net Present Value (NPV).
The Initial Cost of Investment which is the original amount invested in the project is also often referred to as the principal. Net Present Value (NPV) is the sum of all Discounted Net Cash Flows minus the Initial Cost of Investment:
Net Present Value (NPV) = Sum of Discounted Net Cash Flows – Initial Cost of Investment
Where:
Net Cash Flows = Cash Inflows – Cash Outflows
Problems may occur when forecasting the future because no one can predict what external forces will affect cash flows. This can make cash flow projections inaccurate. Therefore, managers must take this into consideration.
Example of calculating Net Present Value (NPV)
A business is thinking about purchasing a new machine at a cost of USD$5,000,000. The machine is going to be used for four years to produce products. The rate of discount to be used was set by the manager at 10% as inflation in the country was forecasted by the central bank to be around 10% in the next few years. The annual Net Cash Flows are showed below. What is the Net Present Value (NPV) for this investment?
Let’s multiply discount factors by Net Cash Flows in each year:
In Year 0, the Net Cash Flow is -USD$5,000,000. This is the Initial Cost of Investment. Cash Flows in Year 0 are not discounted as they are already expressed in their present values. The present value in Year 0 is always 1, and this is not included in the Discount Table below.
In Year 1, the Net Cash Flow is USD$2,000,000.
In Year 2, the Net Cash Flow is USD$2,000,000.
In Year 3, the Net Cash Flow is USD$2,000,000.
In Year 4, the Net Cash Flow is USD$3,000,000.
| Present Value of USD$1 | |||||||||||||
| Year: | 1% | 2% | 3% | 4% | 5% | 6% | 7% | 8% | 9% | 10% | 12% | 14% | |
| 1 | 0.990 | 0.980 | 0.971 | 0.962 | 0.952 | 0.943 | 0.935 | 0.926 | 0.917 | 0.909 | 0.893 | 0.877 | |
| 2 | 0.980 | 0.961 | 0.943 | 0.925 | 0.907 | 0.890 | 0.873 | 0.857 | 0.842 | 0.826 | 0.797 | 0.769 | |
| 3 | 0.971 | 0.942 | 0.915 | 0.889 | 0.864 | 0.840 | 0.816 | 0.794 | 0.772 | 0.751 | 0.712 | 0.675 | |
| 4 | 0.961 | 0.924 | 0.888 | 0.855 | 0.823 | 0.792 | 0.763 | 0.735 | 0.708 | 0.683 | 0.636 | 0.592 | |
| 5 | 0.951 | 0.906 | 0.863 | 0.822 | 0.784 | 0.747 | 0.713 | 0.681 | 0.650 | 0.621 | 0.567 | 0.519 | |
| 6 | 0.942 | 0.888 | 0.837 | 0.790 | 0.746 | 0.705 | 0.666 | 0.630 | 0.596 | 0.564 | 0.507 | 0.456 | |
| 7 | 0.933 | 0.871 | 0.813 | 0.760 | 0.711 | 0.665 | 0.623 | 0.583 | 0.547 | 0.513 | 0.452 | 0.400 | |
| 8 | 0.923 | 0.853 | 0.789 | 0.731 | 0.677 | 0.627 | 0.582 | 0.540 | 0.502 | 0.467 | 0.404 | 0.351 | |
| 9 | 0.914 | 0.837 | 0.766 | 0.703 | 0.645 | 0.592 | 0.544 | 0.500 | 0.460 | 0.424 | 0.361 | 0.308 | |
| 10 | 0.905 | 0.820 | 0.744 | 0.676 | 0.614 | 0.558 | 0.508 | 0.463 | 0.422 | 0.386 | 0.322 | 0.270 | |
| 11 | 0.896 | 0.804 | 0.722 | 0.650 | 0.585 | 0.527 | 0.475 | 0.429 | 0.388 | 0.350 | 0.287 | 0.237 | |
| 12 | 0.887 | 0.788 | 0.701 | 0.625 | 0.557 | 0.497 | 0.444 | 0.397 | 0.356 | 0.319 | 0.257 | 0.208 | |
| 13 | 0.879 | 0.773 | 0.681 | 0.601 | 0.530 | 0.469 | 0.415 | 0.368 | 0.326 | 0.290 | 0.229 | 0.182 | |
| 14 | 0.870 | 0.758 | 0.661 | 0.577 | 0.505 | 0.442 | 0.388 | 0.340 | 0.299 | 0.263 | 0.205 | 0.160 | |
| 15 | 0.861 | 0.743 | 0.642 | 0.555 | 0.481 | 0.417 | 0.362 | 0.315 | 0.275 | 0.239 | 0.183 | 0.140 | |
| 16 | 0.853 | 0.728 | 0.623 | 0.534 | 0.458 | 0.394 | 0.339 | 0.292 | 0.252 | 0.218 | 0.163 | 0.123 | |
| 17 | 0.844 | 0.714 | 0.605 | 0.513 | 0.436 | 0.371 | 0.317 | 0.270 | 0.231 | 0.198 | 0.146 | 0.108 | |
| 18 | 0.836 | 0.700 | 0.587 | 0.494 | 0.416 | 0.350 | 0.296 | 0.250 | 0.212 | 0.180 | 0.130 | 0.095 | |
| 19 | 0.828 | 0.686 | 0.570 | 0.475 | 0.396 | 0.331 | 0.277 | 0.232 | 0.194 | 0.164 | 0.116 | 0.083 | |
| 20 | 0.820 | 0.673 | 0.554 | 0.456 | 0.377 | 0.312 | 0.258 | 0.215 | 0.178 | 0.149 | 0.104 | 0.073 |
In Year 1, the Discounted Net Cash Flow is USD$1,820,000.
In Year 2, the Discounted Net Cash Flow is USD$1,660,000.
In Year 3, the Discounted Net Cash Flow is USD$1,500,000.
In Year 4, the Discounted Net Cash Flow is USD$2,040,000.
When you sum up all the Discounted Net Cash Flows, the total Discounted Net Cash Flows equal to USD$1,820,000 + USD$1,660,000 + USD$1,500,000 + USD$2,020,000 which gives USD$7,000,000.
The Net Present Value (NPV) for this project can now be calculated:
Net Present Value (NPV) = USD$7,000,000 – USD$5,000,000
Net Present Value (NPV) = USD$2,000,000
What does this result mean?
The Net Present Value (NPV) of USD$2,000,000 means that this investment earns USD$2,000,000 in today’s money values. The Net Present Value (NPV) is positive. The discounted Net Cash Flows are greater than the original investment and they are enough to cover the initial investment. Therefore, this investment project is worth pursuing.
Comment on the result of Net Present Value (NPV)
Net Present Value (NPV) is an investment appraisal method that solves the problem of trying to compare projects with different Average Rates of Return (ARR) and Payback Periods (PBP). It considers both the size of the Net Cash Flows and the timing of them. It does this by discounting those cash flows.
1. Which projects are worth investing in?
The Net Present Value (NPV) will be positive (NPV>0), if the discounted Net Cash Flows are higher than the initial cost of investment. A positive Net Present Value (NPV) means that the project is worthwhile because the cost of tying up the firm’s capital is compensated by the Net Cash Flows that result from the investment.
Projects with Net Present Value (NPV)>0 are theoretically worth pursuing when it comes to cash returns.
2. Which project is the best to invest in?
When comparing projects with each other, select those with the highest Net Present Values (NPV), so you will earn the most money adjusted for inflation. The higher the Net Present Value (NPV), the more the project is worth in terms of today’s cash compared to its cost.
3. Which projects are not worth investing in?
The Net Present Value (NPV) will be negative (NPV<0), if the discounted Net Cash Flows are lower than the initial cost of investment. A negative Net Present Value (NPV) means that the project is not worthwhile because the cost of tying up the firm’s capital is not compensated by the Net Cash Flows that result from the investment.
Projects with Net Present Value (NPV)<0 are theoretically not worth pursuing when it comes to cash returns.
4. What’s the today’s value of future earnings from the investment?
The business is expecting to receive USD$3,000 in Net Cash Flows in three years’ time. The current inflation rate in the country is 10%. What is the present value of that USD$3,000? After applying the Discount Factor of 0.751, the Net Present Value (NPV) of USD$3,000 is USD$2,250 as of today.
5. What to consider when thinking about returns from investment in the present terms?
The Net Present Value (NPV) of future money depends mainly on two things: inflation rate / interest rate and time. Risk may also be considered
a.) Inflation rate / Interest rate. The lower the rate of inflation / the rate of interest, the more value future cash has in today’s money. But, the higher the rate of inflation / the rate of interest, the less value future cash has in today’s money. If the rate of inflation / the rate of interest in a country increase, the business will be forced to discount its future Net Cash Flows at a higher rate. This will decrease the amount of Net Present Value (NPV) received. If the rate of inflation / the rate of interest in a country decrease, the business will gladly discount its future Net Cash Flows at a lower rate. This will increase the amount of Net Present Value (NPV) received.
b.) Time. It is important to calculate the present value of money in order to distinguish between the yields of investments over different time periods. The shorter into the future cash is received, the more value it has today. So, the shorter the time period of the project, the higher the Net Present Value (NPV) of that future amount of money received from that project. But, the longer into the future cash is received, the less value it has today. So, the longer the time period of the project, the lower Net Present Value (NPV) of that future amount of money received from that project.
c.) Risk. If the project is high risk and the value of money is expected to be much lower in the future, the firm will discount future expected earnings to a greater extent. If the project is low risk and the value of money is expected to be much higher in the future, the firm will discount future expected earnings to a lesser extent.
6. When will the investment become profitable?
The investment will be profitable when Net Present Value (NPV) becomes positive (NPV>0). Let’s take a look at three different scenarios:
- NPV>0. If NPV is positive, then the project earns more than the discount rate. The project will be considered.
- NPV=0. If NPV is zero, then the project earns exactly the discount rate. The project will or will not be considered. The rate when Net Present Value (NPV) equals zero is called Internal Rate of Return (IRR). Internal Rate of Return (IRR) gives the rate of discount that yields Net Present Value (NPV) of zero considering the time value of money as it employs the discounting concept.
- NPV<0. If NPV is negative, then the project earns less than the discount rate. The project will not be considered.
7. Should the business invest or save money in the bank?
If you decide to save money instead of investing, with higher saving rate, the more money you will receive in the future. With lower saving rate, the less money you will receive in the future.
Will a business choose to receive USD$100 today or USD$105 in a year really depends on having the alternatives or not?
A. Invest. If the business has no other investment opportunities, it is worth waiting one year to earn 5%. However, if there is something else that the business could do with USD$100 that would earn more than 5%, then the business should invest instead of saving.
B. Do not invest. If the investment yields NPV=0 at the discount rate of 1%, and the bank pays 5% on fixed deposits, then the business should save money in the bank instead of investing. It is because the business would earn more, so it should save.
8. Should the business borrow money to invest?
If you borrow money to invest with higher interest rate, then the less value future cash has in today’s terms, hence you should expect lower Net Present Value (NPV). If you borrow money to invest with lower interest rate, then the more value future cash has in today’s terms, hence you should expect higher Net Present Value (NPV).
So, the business will adopt a cut-off rate or criterion rate when looking at the interest cost of borrowing the capital to finance the investment. The cut-off rate is usually determined using the interest rate (the cost of borrowing money), or by the expected return of other projects. For example, if it costs 5% to borrow money from the bank, the business will avoid all the projects that are expected to return less than 5% per year, and accept all the projects that are expected to return more than 5% per year.
If the investment yields NPV=0 at the interest rate is 5%, then the business will only borrow funds with the interest cost of less than 5%.
9. Should the Opportunity Cost be considered when calculating Net Present Value (NPV)?
The Net Present Value (NPV) places a monetary value on cash earnings arising from the capital investment. This creates the opportunity cost – what is sacrificed, lost or foregone as a result of making the particular decision while not choosing to make other decisions.
For the Net Present Value (NPV), the discount rate used to bring future Net Cash Flows back to their present value is the discount rate equivalent to the interest that would have been received had the money been saved in the bank, or the interest that has to be paid by the business had the money been borrowed from the bank.
So, two things are the opportunity cost when the Net Present Value (NPV) is considered:
- The interest lost on the sum that would have been saved. Because businesses are likely to invest their capital in the project, what is foregone by having to wait for earnings arising from the investment is the interest paid on the saved capital.
- The interest lost on the sum that would have been borrowed. Because businesses are likely to borrow their capital to invest in the project, what is foregone by having to wait for earnings arising from the investment is the interest paid on the borrowed capital.
10. Do internal finance also have an opportunity cost?
The rate of interest should also be used to discount future returns from the investment project even for internal sources of finance. This is because internal sources of finance also have the opportunity cost. The internal money that the business has could have been used for another purpose to earn higher returns, or simply be left as a deposit in the bank.
Net Present Value (NPV) – Evaluation
Net Present Value (NPV) is a very popular method of evaluating investment projects comparing the numerical value of investment projects while taking into consideration the time value of money. It should be considered together with Discounted Payback Period which considers project lengths and cash-flow timings while also taking into consideration the time value of money. And, with Internal Rate of Return (IRR) which considers a percentage rate of return taking into consideration the time value of money.
Advantages of Net Present Value (NPV) include:
- Easy to calculate and use. Assessing the value of Net Present Value (NPV) calculations is simple. A positive Net Present Value (NPV) which is NPV>0 means that the project is worthwhile because the cost of tying up the firm’s capital is compensated by the Net Cash Flows that result from the investment.
- Considers time value of money. Net Present Value (NPV) does consider discounting. It brings to the present value the future Net Cash Flows. The timing of the Net Cash Flows and the size of them (their amounts) in arriving at the final appraisal are taken into consideration. Therefore, Net Present Value (NPV) is helpful in evaluating investment projects as it compares project monetary returns from investment while taking the time value of money into account.
- The rate of discount can be varied. Net Present Value (NPV) assumes that the value of money is affected by interest rates – the rate at which businesses borrow money from banks and other lending institutions to pay for their investments. Varying the rate of discount when discounting Net Cash Flows allow for considering different economic circumstances. Net Present Value (NPV) shows you what your investment would have earned in an alternative investment regime. For example, if you borrow money with higher interest rate, then the less value future cash has in today’s terms, hence you should expect lower Net Present Value (NPV).
- Allows to compare projects. Managers can compare Net Present Value (NPV) of a particular project with other alternative projects. Also, they can put different projects in rank order. The results can be used by the business to ‘screen out’ the best projects, those with the most positive Net Present Value (NPV). Managers will always be looking for the highest monetary returns from their investments. Net Present Value (NPV) can also help to eliminate projects that bring no returns, or very little returns. When more than one project is being appraised, the firm should choose the one that produces the highest NPV.
Disadvantages of Net Present Value (NPV) include:
- Not comprehensive enough to make final investment decisions. Net Present Value (NPV) should only be regarded as one of the methods to assess competing investments. It could be used as a screening tool to include and eliminate certain projects based on their monetary cash returns, but it is inappropriate as a basis for making any sophisticated investment decisions. The results can only be compared with other projects, if two projects have the same initial capital investment. As the results of the Net Present Value (NPV) method are expressed in USD$, projects of different sizes cannot really be compared with one another. It is because a large project worth USD$5,000,000 may a have higher Net Present Value (NPV) than a small project worth USD$500,000, but the latter may have much higher profitability on a percentage basis. Net Present Value (NPV) does not give a percentage rate of return, so it usually is not considered by itself.
- Complex for longer projects. Calculations of Discounted Net Cash Flows can be very complex for multi-million-dollar projects lasting for many years. What is more, the numerical results might be difficult to comprehend by business managers who are not that good with numbers.
- The final result depends on the rate of discount used. Even a small change in the discount rate can lead to significant changes in the discounted value of future Net Cash Flows. The results are very much determined by the accuracy of the discount rate selected. Any inaccurate discount rates arising from wrong expectation may lead to incorrect Net Present Value (NPV). Hence, managers will be exposed to making incorrect decision on the project’s viability. Therefore, the businesses should notover rely on Net Present Value (NPV) figure itself, but should additionally consider other methods of Quantitative Investment Appraisal.
In summary, remember that Investment Appraisal is evaluating the profitability or desirability of an investment project. There are two ways to do it. Quantitative Investment Appraisal is using techniques to study the financial issues of investment (think quantity in terms of percentages and money). And, Qualitative Appraisal which is studying non-financial issues that may impact an investment decision (think quality and impact).
