Net present value (NPV) (HL)
Net present value (NPV) is a method of investment appraisal that calculates the real value (rather than the absolute value) of an investment project by discounting (adjusting) the actual value of money received in the future.
The discount rate is a figure used to reduce the future value of money. It is used to establish the present value of cash that is yet to be received by the business. Refer to the table below for various discount factors:
1% | 2% | 3% | 4% | 5% | 6% | 7% | 8% | 9% | 10% | |
Year 1 | 0.9901 | 0.9804 | 0.9709 | 0.9615 | 0.9524 | 0.9434 | 0.9346 | 0.9259 | 0.9174 | 0.9091 |
Year 2 | 0.9803 | 0.9612 | 0.9426 | 0.9246 | 0.9070 | 0.8900 | 0.8734 | 0.8573 | 0.8417 | 0.8264 |
Year 3 | 0.9706 | 0.9423 | 0.9151 | 0.8890 | 0.8638 | 0.8396 | 0.8163 | 0.7938 | 0.7722 | 0.7513 |
Year 4 | 0.9610 | 0.9238 | 0.8885 | 0.8548 | 0.8227 | 0.7921 | 0.7629 | 0.7350 | 0.7084 | 0.6830 |
Year 5 | 0.9515 | 0.9057 | 0.8626 | 0.8219 | 0.7835 | 0.7473 | 0.7130 | 0.6806 | 0.6499 | 0.6209 |
Year 6 | 0.9420 | 0.8880 | 0.8375 | 0.7903 | 0.7462 | 0.7050 | 0.6663 | 0.6302 | 0.5963 | 0.5645 |
Year 7 | 0.9327 | 0.8706 | 0.8131 | 0.7599 | 0.7107 | 0.6651 | 0.6227 | 0.5835 | 0.5470 | 0.5132 |
Year 8 | 0.9235 | 0.8535 | 0.7894 | 0.7307 | 0.6768 | 0.6274 | 0.5820 | 0.5403 | 0.5019 | 0.4665 |
Year 9 | 0.9143 | 0.8368 | 0.7664 | 0.7026 | 0.6446 | 0.5919 | 0.5439 | 0.5002 | 0.4604 | 0.4241 |
Year 10 | 0.9053 | 0.8203 | 0.7441 | 0.6756 | 0.6139 | 0.5584 | 0.5083 | 0.4632 | 0.4224 | 0.3855 |
The net present value (NPV) is the numerical difference between the total values of future net cash flows expressed in today’s (the present) value and the cost of the investment project or decision. In other words, the NPV is found by adding up the discounted values of all future net cash flows and then deducting the cost of the investment project.
NPV = Sum of Present Values – Cost of Investment
So, for example, if the interest rate is 5% per annum, then the present value of receiving $100 in one year’s time is $95.24. This is because investing $95.24 today and earning an annual return of 5% would make the investment valued at $100 in one year’s time. The table above shows that discount rate is 0.9524.
Top tip!
HL students will be given the relevant discount factors in the final examinations within the question paper itself (should the Net Present Value be part of the examination paper). There is no need for teachers or examination officers to photocopy the discount table in the IB Business Management syllabus / guide.
One limitation of the average rate of return (ARR) method of investment appraisal is that it does not consider the future value of net cash flow – money received in five years’ time is not worth the same as the money received today. Hence, the projected future cash flows calculated using the ARR method do not accurately reflect the true value of the investment decision.
By contrast, the NPV figure shows the quantitative value of the overall financial return on an investment decision stated in today’s value of that amount of money. This means that the NPV method of investment appraisal allows managers to consider the opportunity cost of receiving money in the future (acknowledging that future cash flows are worth less than those received today).
The greater the NPV value, the more feasible the investment proposal / decision becomes, based on financial forecasts. However, the longer the investment project under consideration, the less accurate it becomes to project / forecast future net cash flows – and interest rates are more likely to change over the long term.
Worked example
Suppose a large manufacturer is considering whether to spend $800,000 to upgrade its management information system. The projected net cash flow for the 5-year investment is shown below.
Year | Net cash flow ($) |
1 | 100,000 |
2 | 300,000 |
3 | 500,000 |
4 | 300,000 |
5 | 200,000 |
The manufacturer uses a discount rate of 10%. These are shown in the table below. The first step in calculating the NPV is to determine the discounted value of the net cash flow for each year. This is done by multiplying the nominal value of the net cash flow by the discount factor as shown in the table below:
Year | Net cash flow ($) | Discount factor | Discounted net cash flow ($) |
1 | 100,000 | 0.9091 | 90,910 |
2 | 300,000 | 0.8264 | 247,920 |
3 | 500,000 | 0.7513 | 375,650 |
4 | 300,000 | 0.6830 | 204,900 |
5 | 200,000 | 0.6209 | 124,180 |
The next step is to then calculate the sum of the discounted net cash flow, i.e., 90,910 + 247,920 + 375,650 + 204,900 + 124,180 = $1,043,560. This figure is known as the cumulative discounted net cash flow.
To determine the net present value, we minus the cost of the investment from the value of the cumulative discounted net cash flow.
Net present value = $1,043,560 – 800,000 = $243,560
This represents the real value, or present value, of the investment.
All things being equal, as the NPV figure is positive, the investment is financially worthwhile.
Advantages of net present value (NPV)
The NPV method accounts for the future movements of cash flows from an investment project or decision. By showing these future cash flows expressed in today’s monetary value, it helps managers to make more informed decisions.
The NPV method of investment appraisal is more realistic than the ARR, especially for projects that are medium to long term (as the future value of money is worth less than the same amount received today).
It enables managers and decision makers to make more informed comparisons between projects of varying durations and with different discount rates on their various investments projects / decisions.
Disadvantages of net present value (NPV)
- It is difficult to accurately predict future net cash flows, especially for projects that are medium to long term. Changes in the external business environment (such as a financial crisis or an economic recession) can void such predictions.
- The NPV is more difficult and time consuming to calculate, yet may still prove to be inaccurate given there are so many factors that can change a firm’s net cash flow figures for each time period in an investment appraisal.
- Choosing an accurate discount rate (discount factor) can be subjective at times. Whilst many decision makers choose the rate that reflects the interest rate and/or inflation rate, these can vary significantly over the course of an investment project.
ATL Activity - The real costs of raising children
This is a fun and memorable activity to introduce the topic of investment appraisal - or to use as a plenary to this topic in the syllabus. Although parents don’t see their children as an ‘investment’, this ATL Activity highlights the need to consider finances as part of the family planning process, similar to the way an organization must consider all associated costs in an investment decision.
So, what are the real costs of raising children? List as many items of expenditure on children that parents might need to spend their money on. You may choose to use a spreadsheet to present your results.
Some of the expenses that parents might need to fund include a combination of the following:
Food, drinks and groceries – from baby nappies (diapers) and milk powder to lunch boxes for school
Compulsory education (kindergarten, primary and secondary schooling) - costs may include: uniforms, stationery and textbooks; private education, such as boarding school, will obviously inflate the costs for parents
Private tuition – such as private music lessons or academic tuition for public exams
Holidays – additional costs of flights, accommodation, catering and entertainment
Health care services
Hobbies – children’s sporting and leisure activities can prove expensive for parents
Tertiary education: University fees as well as maintenance costs, such as rent for housing/accommodation
Driving lessons
Deposit on a car
Deposit for first home
Funds for a gap year.
Extension inquiry task
Ask students to do some research using online sources to substantiate the costs of raising children in a country of their choice.
Students could be asked to compile the list of all known expenditures in raising a child. They can record this list in a spreadsheet, and populate this with an estimate of the amount of money their parent(s) has/have spent on each item. You may be rather shocked by the results!
Again, although parents do not see their children as 'investments' that need to generate a 'return', this idea is that effective family planning needs to consider the real financial costs of raising children.
Top tip!
Remember to always express your calculations and answers in the correct unit of measurement.
the payback period is expressed in time (years and months)
the ARR is expressed as a percentage (to 2 decimal places), and
the NPV is expressed as a monetary value (to 2 decimal places).
Top tip!
Evaluation of investment appraisal methods (PBP, ARR & NPV)
This section of the syllabus only considers three quantitative investment appraisal techniques (the PBP, ARR and NPV). In reality, managers often consider the use of qualitative techniques to judge whether an investment project is worth pursuing. For example, they may want to gauge whether the investment decision is aligned with the organization’s mission and vision statements, its corporate culture, and external factors such as the state of the economy. Ultimately, it is important to consider qualitative factors too when making investment decisions.
Click the tab below for an exam practice question on this topic. SL students are encouraged to attempt these questions, except for Question (b) (iii) which is HL only.
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