Table of Contents
Type: Assignment | Subject: Finance | Level: Undergraduate | Word Count: ~2,270 words
This model assignment was produced by an Essays UK specialist as reference material for learning purposes only. For support in this field, see our finance writers.
Overview: This worked assignment appraises a proposed new production line using net present value, internal rate of return and the payback period. It demonstrates how to build a relevant cash-flow forecast, discount it correctly and present the workings in clearly labelled tables before reaching a reasoned investment recommendation.
Capital investment decisions are among the most significant that any business will make. Because they typically involve large, often irreversible outlays of cash in exchange for benefits that accrue over several years, the quality of the appraisal process has a direct bearing on the long-term value of the firm (Arnold, 2013). This model assignment demonstrates how a typical undergraduate capital-budgeting question can be answered to a high standard. It works through the appraisal of a proposed new production line for a fictional manufacturer, Meridian Components Ltd, applying three complementary techniques: net present value (NPV), internal rate of return (IRR) and the payback period. The purpose is not simply to arrive at a single figure, but to show how relevant cash flows are identified, how the time value of money is incorporated, how the results of each method are interpreted, and how a defensible recommendation is constructed from the evidence. The figures used throughout are illustrative and have been chosen to keep the arithmetic transparent, so that the method rather than the data remains the focus. Readers should treat the document as reference material that models good practice in presentation, structure and reasoning.
Meridian Components Ltd, a mid-sized engineering firm, is considering installing a new production line to manufacture a precision component for which management anticipates growing demand. The finance department has gathered the estimates set out below, which form the basis of the appraisal. As with any forecast these figures carry uncertainty, and the assumptions are stated explicitly so that the analysis can be reproduced and challenged.
Only incremental, future cash flows that arise as a direct consequence of accepting the project are relevant to the decision (Horngren, Datar and Rajan, 2015). Depreciation is deliberately excluded because it is a non-cash accounting allocation rather than a cash flow, while any costs already incurred, such as a feasibility study, would be treated as sunk and therefore irrelevant (Atrill and McLaney, 2019; Dyson and Franklin, 2020).
Three techniques are applied so that their results can be compared and the limitations of each exposed. The first two are discounted cash flow (DCF) methods, which recognise that a pound received in the future is worth less than a pound received today; the third is a simpler measure of liquidity and risk.
NPV discounts every expected cash flow back to its present value using the firm’s cost of capital and then subtracts the initial outlay. A positive NPV indicates that the project is expected to earn a return above the cost of capital and therefore adds value to the business; the decision rule is to accept any project with a positive NPV (Watson and Head, 2019). NPV is widely regarded as the theoretically superior method because it uses all of a project’s cash flows, accounts for the time value of money and is expressed in absolute monetary terms, consistent with the objective of shareholder wealth maximisation (Brealey, Myers and Allen, 2020; Ross, Westerfield and Jordan, 2019).
The IRR is the discount rate at which the NPV of a project equals zero; in other words, it is the breakeven rate of return implied by the project’s cash flows. The decision rule is to accept a project when its IRR exceeds the cost of capital. Because the relationship between the discount rate and NPV is non-linear, the IRR is usually estimated by linear interpolation between a rate that produces a positive NPV and one that produces a negative NPV (Pike, Neale and Linsley, 2018).
The payback period measures the time taken for cumulative cash inflows to recover the initial investment. Managers value it as an intuitive indicator of liquidity and risk, since projects that return cash quickly expose the firm to less uncertainty. Its principal weaknesses are that, in its basic form, it ignores the time value of money and disregards all cash flows arising after payback has been achieved (Drury, 2018).
The first step is to construct the annual operating cash flows from the contribution and fixed-cost assumptions. Sales volumes are expected to rise as the product becomes established in the market and then to taper as competition increases. Multiplying the forecast volume by the £20 contribution per unit and deducting the £40,000 of fixed cash costs produces the net operating cash flow for each year, as set out below.
| Item | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
|---|---|---|---|---|---|
| Sales volume (units) | 8,000 | 9,500 | 10,500 | 10,000 | 8,500 |
| Contribution @ £20/unit (£) | 160,000 | 190,000 | 210,000 | 200,000 | 170,000 |
| Fixed cash costs (£) | (40,000) | (40,000) | (40,000) | (40,000) | (40,000) |
| Net operating cash flow (£) | 120,000 | 150,000 | 170,000 | 160,000 | 130,000 |
These operating flows are then combined with the capital items to give the net cash flow for each year. The £450,000 machinery cost and the £50,000 of working capital appear as outflows in year 0, while the recovery of working capital (£50,000) and the residual value of the machinery (£40,000) are added to the year 5 operating flow. The resulting net cash flows, shown below, form the single input used by all three appraisal techniques.
| Cash flow (£) | Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
|---|---|---|---|---|---|---|
| Machinery | (450,000) | – | – | – | – | – |
| Working capital | (50,000) | – | – | – | – | 50,000 |
| Operating cash flow | – | 120,000 | 150,000 | 170,000 | 160,000 | 130,000 |
| Residual value | – | – | – | – | – | 40,000 |
| Net cash flow (£) | (500,000) | 120,000 | 150,000 | 170,000 | 160,000 | 220,000 |
Each net cash flow is multiplied by the appropriate discount factor at the 10% cost of capital. The discount factor for year n is 1 ÷ (1 + r)n; these factors can be read from present value tables or calculated directly. The present values are then summed to give the NPV.
| Year | Net Cash Flow (£) | Discount Factor @ 10% | Present Value (£) |
|---|---|---|---|
| 0 | (500,000) | 1.0000 | (500,000) |
| 1 | 120,000 | 0.9091 | 109,092 |
| 2 | 150,000 | 0.8264 | 123,960 |
| 3 | 170,000 | 0.7513 | 127,721 |
| 4 | 160,000 | 0.6830 | 109,280 |
| 5 | 220,000 | 0.6209 | 136,598 |
| Net Present Value (£) | +106,651 | ||
The project produces a net present value of approximately +£106,651. Because this is comfortably positive, the investment is expected to generate a return in excess of the 10% cost of capital and to increase the wealth of the firm by that amount in today’s terms. The present values also show how heavily later cash flows are discounted: the year 5 inflow of £220,000 is worth only £136,598 once the time value of money is applied. On the NPV criterion alone, the production line should be accepted.
To estimate the IRR, the NPV is recalculated at two trial discount rates chosen to bracket zero. A rate of 15% yields a positive NPV, while a rate of 20% yields a negative NPV, so the IRR must lie between the two.
| Year | Net Cash Flow (£) | DF @ 15% | PV @ 15% (£) | DF @ 20% | PV @ 20% (£) |
|---|---|---|---|---|---|
| 0 | (500,000) | 1.0000 | (500,000) | 1.0000 | (500,000) |
| 1 | 120,000 | 0.8696 | 104,352 | 0.8333 | 99,996 |
| 2 | 150,000 | 0.7561 | 113,415 | 0.6944 | 104,160 |
| 3 | 170,000 | 0.6575 | 111,775 | 0.5787 | 98,379 |
| 4 | 160,000 | 0.5718 | 91,488 | 0.4823 | 77,168 |
| 5 | 220,000 | 0.4972 | 109,384 | 0.4019 | 88,418 |
| Net Present Value (£) | +30,414 | (31,879) | |||
Linear interpolation is then used to approximate the rate at which NPV would be zero:
IRR ≈ 15% + [30,414 ÷ (30,414 + 31,879)] × (20% − 15%) = 15% + 2.44% ≈ 17.4%
The estimated IRR of roughly 17.4% is well above the 10% cost of capital, which again supports acceptance. It is important to recognise that interpolation gives only an approximation: because the NPV profile is a curve rather than a straight line, the interpolated figure differs slightly from the true IRR, and the error grows as the gap between the trial rates widens. Choosing trial rates close to the true rate therefore improves accuracy (Lumby and Jones, 2015).
The payback period is found by accumulating the net cash flows year by year until the initial outlay is recovered.
| Year | Net Cash Flow (£) | Cumulative Cash Flow (£) |
|---|---|---|
| 0 | (500,000) | (500,000) |
| 1 | 120,000 | (380,000) |
| 2 | 150,000 | (230,000) |
| 3 | 170,000 | (60,000) |
| 4 | 160,000 | 100,000 |
| 5 | 220,000 | 320,000 |
The cumulative cash flow turns positive during year 4. By the end of year 3, £440,000 of the £500,000 outlay has been recovered, leaving £60,000 outstanding at the start of year 4. Dividing this by the year 4 inflow of £160,000 gives 0.38 of a year, so the payback period is approximately 3.4 years (about three years and four to five months). If the time value of money is taken into account, the discounted payback period — based on the present values calculated earlier — extends to approximately 4.2 years, because the discounted inflows are smaller and therefore take longer to accumulate to £500,000.
The three methods point consistently towards acceptance, but each tells a slightly different part of the story. The positive NPV of £106,651 and the IRR of 17.4% are two sides of the same coin: a positive NPV at a 10% discount rate necessarily implies an IRR above 10%, and the sizeable gap between the IRR and the cost of capital signals a comfortable margin of safety. For a single, conventional project of this kind — one with an initial outflow followed by a series of inflows — NPV and IRR will always give the same accept-or-reject signal (Brealey, Myers and Allen, 2020).
The payback period adds a different dimension. A simple payback of around 3.4 years means that more than two-thirds of the project’s life must elapse before the outlay is recovered, and the discounted payback of roughly 4.2 years is longer still. Whether this is acceptable depends on management’s attitude to risk and on any internal payback target the company applies. A firm operating in a fast-moving market, or one facing liquidity constraints, might regard a four-year discounted payback as a concern even though the NPV is strongly positive.
Where the methods conflict — for example, when ranking mutually exclusive projects of different sizes or with different cash-flow patterns — NPV should take precedence, because it measures the absolute contribution to shareholder wealth, whereas the IRR, expressed as a percentage, can mislead by favouring smaller projects with higher returns but lower total value (Watson and Head, 2019). In this instance, however, no such conflict arises, and all three indicators reinforce one another.
The conclusions rest on a number of assumptions that should be acknowledged. First, the cash flows are single-point estimates. Sales volumes, the contribution per unit and fixed costs are all forecasts, and relatively small changes in these variables can have a large effect on the NPV. A fuller analysis would apply sensitivity or scenario analysis to establish how robust the recommendation is — for instance, by calculating the percentage fall in annual contribution that would reduce the NPV to zero (Arnold, 2013).
Second, the appraisal assumes a constant 10% discount rate throughout the project’s life, whereas the cost of capital may change as interest rates and the firm’s risk profile evolve. Third, taxation and inflation have been excluded for simplicity; in practice, capital allowances, corporation tax on operating profits and the erosion of real cash flows by inflation would all need to be modelled, and their omission means the figures presented here overstate the position to some degree. Fourth, the IRR method carries well-known technical limitations, including the possibility of multiple IRRs where cash flows change sign more than once, and an implicit assumption that interim cash flows are reinvested at the IRR rather than at the cost of capital (Pike, Neale and Linsley, 2018; Brigham and Ehrhardt, 2017).
Finally, investment decisions should never be reduced to financial metrics alone. Strategic fit, the effect on product quality and customer relationships, environmental and regulatory considerations, and the availability of finance and management capacity are all relevant to the final decision but fall outside the scope of a purely quantitative appraisal (McLaney, 2017).
On the basis of the quantitative analysis, Meridian Components Ltd should proceed with the new production line. The project generates a positive net present value of approximately £106,651, an internal rate of return of about 17.4% — some seven percentage points above the cost of capital — and recovers its initial outlay within the project’s life on both an undiscounted and a discounted basis. Taken together, these results indicate that the investment is expected to add value to the firm. The recommendation should, however, be treated as conditional: before committing funds, management would be well advised to test the sensitivity of the NPV to the key assumptions, to incorporate the effects of tax and inflation, and to weigh the non-financial factors noted above. This model assignment has illustrated how the core capital-budgeting techniques are applied, how their workings are best presented in clearly labelled tables, and how a reasoned recommendation is built from the evidence rather than simply asserted. It is intended solely as reference material to support students in developing their own understanding of investment appraisal.
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