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Net present value (NPV) (HL)

Net present value (NPV) (HLonly), (AO3 and AO4)

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.

YearNet cash flow ($)
1100,000
2300,000
3500,000
4300,000
5200,000

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:

YearNet cash flow ($)Discount factorDiscounted net cash flow ($)
1100,0000.909190,910
2300,0000.8264247,920
3500,0000.7513375,650
4300,0000.6830204,900
5200,0000.6209124,180
  • 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.

Exam Practise Question

 Exam Practise Question - Juke’s Retro Arcade Games (J-RAG)

Encourage SL students to also attempt these questions, except for Question (b) (iii) which is HL only.

Juke’s Retro Arcade Games (J-RAG)

Juke’s Retro Arcade Games (J-RAG) is a partnership owned by brothers Jake and Luke that trades second-hand games, including popular games consoles and arcade games from the 1980s. The business has a single store in a popular location, and hires 15 part-time workers, most of whom attend the local university. Whilst this creates great flexibility, J-RAG struggles with staff retention, especially during the spring each year as the students who work at the business need time to prepare for their exams.

The business also has an outdated computer system so struggles with accurate stock control management. J-RAG’s accountant has also advised that the business needs to improve its financial and human resources record keeping, such as a secure database of employee details and payment records. Therefore, the brothers are considering whether to invest in a new computerised system to improve its operational efficiency. The cost of the investment is forecast to be $140,000 with an expected lifespan of five years. Alternatively, they could use the money to hire two full time workers which is expected to minimise disruptions caused by high labour turnover.

The forecasted net cash flows from the investment in the computerised system are given below. The partnership uses a 4% discount factor (HL only).

Year

Net cash flow ($)

Discount factor

1

45,000

0.9615

2

50,000

0.9246

3

55,000

0.8890

4

45,000

0.8548

5

40,000

0.8219

(a)  (i)

Define the term partnership.

[2 marks]

(a)  (ii)

Define the term labour turnover.

[2 marks]

(b)  (i)

Calculate the payback period for the proposed investment project.

[2 marks]

(b)  (ii)

Calculate the average rate of return (ARR) for the proposed investment project.


[2 marks]

(b)  (iii)

Calculate the net present value for the proposed investment project.

[2 marks]

(c)

Evaluate whether J-RAG should invest in the new computerised system. Use information from the case study and both quantitative and qualitative considers in your answer.



[10 marks]

 Teacher only box

Answers

(a)  (i)  Define the term partnership[2 marks]

A partnership is a form of business ownership where two to twenty people collectively own the organization. In this case, brothers Jake and Luke own J-RAG as a partnership.

Award [1 mark] if there is some understanding of ‘partnership’ shown, although the answer might lack clarity.

Award [2 marks] if ‘partnership’ is clearly defined, similar to the example above. Application is not required to gain full marks.

(a)  (ii)  Define the term labour turnover[2 marks]

Labour turnover measures the number of workers who leave an organization expressed as a percentage of the size of the workforce, per time period (usually each year).

Award [1 mark] if there is some understanding of ‘labour turnover’ shown, although the answer might lack clarity.

Award [2 marks] if ‘labour turnover’ is clearly defined, similar to the example above. Application is not required to gain full marks.

(b)  (i)  Calculate the payback period for the proposed investment project.  [2 marks]

Payback period (PBP) calculations:

Year

Annual NCF

Cumulative NCF

1

45,000

2

50,000

95,000

3

55,000

150,000

4

45,000

195,000

5

40,000

235,000

  • At the end of Year 2, there is a shortfall of $45,000.

  • By the end of Year 3, the cumulative net cash flow ($150,000) is greater than the investment cost ($140,000). Hence, the PBP must occur between Year 2 and Year 3.

  • In Year 3: $45,000 / ($55,000 / 12) = 4,583.33 = 9.82 months.

  • Hence, the payback period is 2 years and 10 months.

Award [1 mark] if the PBP is correct but there is no working out shown or the correct procedure is used but with an incorrect answer.

Award [2 marks] if the correct PBP is given with the working out shown.

(b)  (ii)  Calculate the average rate of return for the proposed investment project.  [2 marks]

  • ARR  =  $95,000 / 5 years = $19,000 per year

  • ARR  =  $19,000 / $140,000

  • ARR  =  13.57%

Award [1 mark] if the ARR is correct but there is no working out shown or the correct procedure is used but with an incorrect answer.

Award [2 marks] if the correct ARR is given with the working out shown.

(b)  (iii)  Calculate the net present value for the proposed investment project.  [2 marks]

The NPV is calculated by taking away the cost of the investment project from the sum of the present values for the duration of the project. The higher the NPV, the more attractive the investment project.

Year

Annual NCF

Discount factor

Discounted NCF

1

45,000

0.9615

43,267.50

2

50,000

0.9246

46,230.00

3

55,000

0.889

48,895.00

4

45,000

0.8548

38,466.00

5

40,000

0.8219

32,876.00

Total

209,734.50

  • Cumulative NCF = $209,734.50

  • Cost = $140,000.00

  • Hence, NPV = $69,734.50

Award [1 mark] if the NPV is correct but there is no working out shown or the correct procedure is used but with an incorrect answer.

Award [2 marks] if the correct NPV is given with the working out shown.

(c)  Evaluate whether J-RAG should invest in the new computerised system. Use information from the case study and both quantitative and qualitative considers in your answer.  [10 marks]

Relevant financial factors could include:

  • A relatively long payback period of 3 years and 10 months (especially given that the project is expected to last 5 years before the computerized system needs to be upgraded).
  • The ARR of 13.57% is high (and likely to be significantly higher than interest rates in the economy, so there is an opportunity cost to just leaving any spare cash in the bank.
  • However, J-RAG should also consider the reliability of the forecasted financial data, especially as they are projecting figures for the next five years.
  • There also needs to be consideration of the opportunity cost of the $140,000 that could be used for investment. For example, there is the possibility of using this money for the partners to hire two full-time workers, which would help to minimize the impact of the high labour turnover at J-RAG.
  • Accept any other relevant financial / quantitative factor, written in the context of the case study.

Non-financial factors that could be considered by the partners regarding the investment in a new computerized computer system could include:

  • Consideration of whether the human resource issues are more of a priority than the need for a new computerized system.
  • The state of the economy – people are less likely to spend money on arcade consoles and games if there is a recession, for example.
  • The degree of competition in the local area (J-RAG operates in a rather niche market).
  • Expected changes in interest rates.
  • The impact on human resources, e.g. staff training, staff morale (retention is already an issue for J-RAG).
  • Accept any other relevant non-financial / qualitative factor, written in the context of the case study.

Award [1 - 2 marks] if the answer is vague, generalized or lacks substance.

Award [3 - 4 marks] if the answer shows some understanding of the demands of the question. There is some relevant application of the case study and figures calculated in Question (b), although the answer lacks depth / analysis.

Award [5 - 6 marks] if the answer shows understanding of the demands of the question. There is relevant application of the case study and figures calculated in Question (b), although the answer lacks balance. Award up to [6 marks] if only financial or non-financial factors are considered.

Award [7 - 8 marks] if the answer shows good understanding of the demands of the question. There is detailed consideration of both relevant numerical and non-numerical factors in relation to J-RAG’s investment decision. However, evaluation is limited if attempted.

Award [9 - 10 marks] if there is a balanced discussion of relevant numerical and non-numerical factors in relation to whether J-RAG should invest in the new computerized system to improve its stock (inventory) control and operational efficiency. Appropriate terminology and examples from the case study have been used effectively. There is evidence of critical and evaluative thinking.

Click here to download a PDF version of this exam practice question for use with students.

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