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How does net present value account for the time value of money, and how is a project's NPV calculated and interpreted?

Calculate the net present value of a project using discount factors and use it to make an investment decision

A focused answer to the H2 Principles of Accounting outcome on net present value. The time value of money, discounting future cash flows with given factors, the NPV decision rule, and why NPV is the most rigorous appraisal method.

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  1. What this dot point is asking
  2. The answer
  3. Examples in context
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What this dot point is asking

SEAB wants you to calculate the net present value (NPV) of a project using discount factors and to use it to make an investment decision. NPV is the most theoretically sound appraisal method because it is the only common one that fully accounts for the time value of money. The central insight is that cash received in the future is worth less than cash today, so future inflows must be discounted before they can be fairly compared with the cost incurred now.

The answer

The time value of money

A dollar today is worth more than a dollar in the future because today's dollar can be invested to earn a return, and because future cash carries risk and is eroded by inflation. To compare cash flows arising at different times, each is converted to its present value by discounting at the firm's cost of capital.

Discounting

The present value of a future cash flow is found by multiplying it by a discount factor:

Present value=future cash flow×discount factor,discount factor=1(1+r)n\text{Present value} = \text{future cash flow} \times \text{discount factor}, \qquad \text{discount factor} = \frac{1}{(1 + r)^n}

where rr is the cost of capital and nn the number of years. In exams the discount factors are usually given, so the work is to apply them and sum the results.

The NPV calculation and decision rule

NPV is the sum of the present values of all cash flows, including the negative outlay at time zero:

NPV=∑(cash flow×discount factor)−initial outlay\text{NPV} = \sum \big(\text{cash flow} \times \text{discount factor}\big) - \text{initial outlay}

The decision rule is simple:

  • NPV positive - accept; the project earns more than the cost of capital and adds value.
  • NPV negative - reject; it earns less than the cost of capital.
  • Choosing between projects - pick the higher (positive) NPV.

Why NPV is the best method

NPV uses all the cash flows over the project's life and weights them by when they occur. Unlike payback (which ignores timing's value and post-payback flows) and the accounting rate of return (which uses profit, not cash, and ignores timing), NPV gives a single figure for the value added in today's money, making it the benchmark appraisal method.

Examples in context

Example 1. Two projects, same total cash. Two projects each return \300,000$ in total over five years for the same outlay, but one front-loads its cash and the other back-loads it. Payback and the accounting rate of return might rank them similarly, but NPV favours the front-loaded project because its earlier cash is discounted less heavily. Only NPV captures this timing advantage, which is why it is the preferred method when cash-flow patterns differ.

Example 2. A marginal project. A firm computes an NPV of just +\190ona on a \100 000100\,000 project. Technically the project adds value and should be accepted, but the wafer-thin margin means a small error in the cash-flow estimates or the discount rate could turn it negative. NPV thus prompts sensitivity analysis: the figure is a decision basis, but its size signals how much confidence to place in it.

Try this

Q1. A cash inflow of \50,000arisesinyear2;thediscountfactoris arises in year 2; the discount factor is 0.826$. Find its present value. [2 marks]

  • Cue. 50\,000 \times 0.826 = \41,300$.

Q2. Present value of inflows is \210,000andtheoutlayis and the outlay is \200 000200\,000. State the NPV and the decision. [2 marks]

  • Cue. NPV = 210\,000 - 200\,000 = +\10,000$; positive, so accept the project.

Q3. Explain why NPV is preferred to the payback period. [3 marks]

  • Cue. NPV accounts for the time value of money by discounting and uses all the cash flows over the whole life, giving the value added; payback ignores timing's value and all cash flows after the payback point.

Exam-style practice questions

Practice questions written in the style of SEAB exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Original8 marksA project costs \100\,000nowandreturnsnetcashinflowsof now and returns net cash inflows of \40 00040\,000, \50\,000and and \30 00030\,000 in years 1 to 3. The cost of capital is 10%10\%, with discount factors 0.9090.909, 0.8260.826 and 0.7510.751. (a) Calculate the net present value. (b) State whether the project should be accepted.
Show worked answer →

Discount each future inflow to its present value, then subtract the initial outlay.

Year Cash flow Discount factor Present value
0 (100,000) 1.000 (100,000)
1 40,000 0.909 36,360
2 50,000 0.826 41,300
3 30,000 0.751 22,530
NPV 190

Present value of inflows = 36\,360 + 41\,300 + 22\,530 = \100,190$.

NPV = 100\,190 - 100\,000 = +\190$.

(b) The NPV is positive (+\190),sotheprojectshouldbe∗∗accepted∗∗:itearnsareturnabovethe), so the project should be **accepted**: it earns a return above the 10%costofcapital,adding cost of capital, adding \190190 of value in present terms. The margin is small, so the decision is sensitive to the estimates.

Markers reward discounting each inflow, summing to \100,190,anNPVof, an NPV of +\190190, and acceptance because the NPV is positive.

Original6 marksExplain the time value of money and why net present value is considered superior to the payback period as an appraisal method.
Show worked answer →

The time value of money is the principle that a dollar received today is worth more than a dollar received in the future, because today's dollar can be invested to earn a return, and because of risk and inflation. Future cash flows are therefore discounted to their present value using a discount factor based on the cost of capital.

Net present value (NPV) is considered superior to payback for two main reasons:

  1. It accounts for the time value of money. By discounting, NPV recognises that distant cash flows are worth less than near ones, which payback ignores.

  2. It uses all the cash flows over the whole project life and gives a clear measure of the value added in absolute terms, whereas payback ignores everything after the payback point and measures only speed of recovery.

A positive NPV means the project earns more than the cost of capital and adds value. Markers reward defining the time value of money, the discounting principle, and the two reasons NPV beats payback (time value plus use of all cash flows).

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