In the second part of our guide,

**S****enior Lecturer in Finance at Warrington School of Management, Jim Stockton**further examines the different techniques used in Investment Decision Making.

**Introduction**

My previous article on capital budgeting described the context and purpose of capital budgeting. It set out the commercial reasoning that justified business investment in large projects and the acquisition of fixed assets-for example expanding capacity in the form of new factories, machinery, vehicles. I also alluded to four capital investment appraisal (CIA) techniques in common commercial use. These are:-

- Payback (PB)
- Accounting Rate of Return (ARR)
- Net Present Value (NPV)
- Internal Rate of Return (IRR)

I also posed the following question in my last article. If I offered you £10,000 now or £10,000 in a year’s time, which would you choose? The answer may be obvious to you but have a think about why-there are a number of issues involved (at least three) all of which will help in your understanding of capital investment appraisal techniques. I will return to this when I consider the NPV and IRR investment appraisal techniques later in this article.

But first let’s get started on Payback (for readers getting worried about complex explanations and lots of numbers, stick with it-the principles are not difficult and I will try to keep all the examples uncomplicated).

**Case study example**

Fred Ltd is considering investing £24,000 in a new machine to expand production of his Mark 3 widget which is sold to breweries to be used in the ale making process. The Finance Manager has estimated the revenues and costs associated with investment and converted them to actual cash flows-basically cash in and cash out. The Operations Manager at Fred Ltd reckons the new machine will last 4 years and then be scrapped with no residual value.

We have, therefore, the following financial profile:-

**Year Cash flow Comments**

0 (£24,000)* Purchase of machine today =Year 0

1 £10,000 Sales less cost of sales as cash flow

2 £10,000 Sales less cost of sales as cash flow

3 £10,000 Sales less cost of sales as cash flow

4 £10,000 Sales less cost of sales as cash flow

*brackets indicate cash out i.e. spend

Thus we have captured the basic financial information need to apply our CIA techniques

**Payback (PB)**

This is the most simple of all the CIA techniques and is very popular with non-financial managers for that reason. However it has some significant shortcomings. Let’s explain.

PB calculates the number of years that it will take a project-in this case a new machine-for the cash flows received to payback the original investment. By inspecting the cash flows, you should be able to see that the £24,000 investment is repaid sometime between years 2 and 3 as the cumulative cash flow at the end of year 2 is (£4,000). This is calculated as minus £24,000 plus £10,000 plus £10,000. At the end of year 3 the cumulative cash flow is £6,000 as a further £10,000 has been received. Assuming the cash flows occur evenly over the year, then the

**Payback period is just under 2½ years**(there is a formula to calculate this precisely but remember what I said regarding spurious accuracy in my previous article).
The managers at Fred Ltd can now compare this project payback period with other proposals or with a hurdle payback period set previously-all investment in new machinery must pay back in less than three years, for example. In this case, the project passes the test.

The advantages of this technique are as follows:-

- Payback is a useful measure of risk (liquidity) as uncertainty increases the further you go into the future
- Payback is a fairly straightforward technique that most managers can understand and apply
- Payback can be used a screening device to weed out projects that do not meet pre-set criteria-e.g. projects of this type must pay back in under three years

However it has some serious limitations which are:-

- Payback ignores any cash flows after the payback point is reached
- Payback ignores a project’s overall profitability
- Payback ignores the time value of money

I will return to the concept of the “time value of money” later (so don’t worry about that for now).

**Accounting Rate of Return (ARR)**

Accounting Rate of Return as the name suggests uses accounting data related to the average profits of a project (rather than cash flows) so it will include non-cash items such as depreciation in its financial figures.

As an example, let’s assume a project similar to the one discussed above costing £24,000 but with a three year life.

An annual profit statement is then estimated something like this:-

£ per annum | |
---|---|

Sales | 20000 |

Materials | (2000) |

Labour | (3000) |

Specific overheads | (3000) |

Depreciation | (8000) |

Project profit | 2000 |

To calculate the ARR, you simply take the average annual profit of the project-let’s assume £2,000 as above and divide by the average investment-again let’s assume £24,000, as above, to yield an accounting rate of return of

**8.3%**(£2,000/£24,000)
Companies will often specify a hurdle ARR which projects must exceed. If this were set at 10% for example then the above investment proposal would be rejected.

The advantages of this technique are as follows:-

- ARR is easy to understand
- It uses data easily obtainable from the accounting system

However, like PB, it has some serious limitations which are:-

- ARR uses accounting data which can be distorted by accounting conventions e.g. changing depreciation periods
- ARR does not consider the time value of money-i.e. when are the cash returns generated? Clearly early returns are preferable to later returns (yes I will get to a fuller explanation of this shortly)
- ARR could produce identical output in terms of percentage returns but the averaging process eliminates important information as to when those returns are generated-see example below-project B is clearly preferable as it has earlier returns thus reducing risk but the ARR for both projects is identical.

**Comparison of 2 projects each costing £24,000 with average profits of £2000 per annum**

Project | A | B |
---|---|---|

Year 1 | £2000 | £4000 |

Year 2 | £2000 | £1000 |

Year 3 | £2000 | £1000 |

ARR% | 8.3 | 8.3 |

As a result of the drawbacks regarding both PB and ARR, more contemporary techniques which remedy some of these defects were developed, most importantly, to take account of the time value of money (OK, time I explained this, I know).

**The time value of money**

Going back to the question I posed above (remember?). If I offered you £10,000 now or £10,000 in a year’s time, which would you choose? The answer may be obvious to you but have a think about why-there are a number of issues involved (at least three) all of which will help in your understanding of capital investment appraisal techniques.

I would offer three reasons to take the money now:-

- to limit risk-I may not be around in a year’s time so grab the opportunity now
- to maintain the purchasing power of the cash-inflation will eat away at it over a year and you may not still be able to buy something you needed as the price has risen
- to invest now and earn interest. If, in a fantasy world, given where interest rates are currently, you invested £10,000 now at 10% you would have £11,000 in a year’s time-this essentially indicates the time value of money which is further enhanced by the compounding effect. £11,000 invested at 10% for a further year would grow to £12,100. Reversing the logic, a sum of £12,100 receivable in two years’ time has a present value of £10,000. This is known as discounting. Discount tables are generally available to use to work out present values so the basic maths are:-

- £12,100 x discount factor for 10% rec’d in two years’ time gives a present value of £10,000
- £12,100 x 0.8264 (this is the discount factor) =
**£10,000**

This principle is the backbone of the Net Present Value and Internal Rate of Return C.I.A. methodologies and, as such, remedies the principal defects of PB and ARR. (Just think about it for a while if it does not sink in straight away).

**Net Present Value (NPV)**

The Net Present Value technique thus embodies the time value of money into its working methodology crucially recognising earlier financial returns have greater value than later returns when discounted to the present. The technique also recognises that money invested in a business has a cost-it is not free. Just think if you had £10,000 would you leave it under the mattress or invest it? If you invest in a risk free government bond (or a building society) you could earn between 3% and 5% at no risk (assuming the UK as a country does not go the way of Argentina and default on its borrowings!)

If you decide to take on extra risk and invest in a small firm you will want a much higher return to compensate you for accepting that risk say 10%. That will mean the firm will need to identify projects that will generate a higher return than 10% in order to keep you invested. In the same way, if a small firm borrows from the bank at 10%, it will need to invest that cash in projects earning more than 10% to make the financing decision economically rational. This, in simple terms, equates to the firm’s

**cost of capital**and is represented by the appropriate discount rate. A firm has no free cash as it always must satisfy its shareholders expected returns to keep the shareholder invested as shareholders always have alternative investment opportunities.
Let’s go back to our previous example-Fred Ltd and assume Fred Ltd has a cost of capital of 10%-the NPV workings are:-

**Year Cash flow Discount factor @10% Present value**

**(taken from tables)**

0 (£24,000)* x 1.00 (as it’s spend today) = (£24,000)

1 £10,000 x 0.909** = £9,090

2 £10,000 x 0.826** = £8,260

3 £10,000 x 0.751** = £7,510

4 £10,000 x 0.683** = £6,830

**Net Present Value = +£7,690**

*brackets indicate cash out or spend

** notice-the further away in time the smaller the discount factor thus reflecting the time value of money concept

The NPV disclosed above is positive and is shown as a + therefore. This indicates that the investment earns more than 10% and exceeds Fred’s cost of capital and therefore will add to shareholder value. The investment should proceed on financial grounds.

The converse is also true-if the Net Present Value disclosed was negative-that would mean that the project earns less than 10% and is less than the 10% cost of capital of the firm-it should not proceed as it would destroy shareholder value.

The advantages of the NPV methodology are:-

- NPV takes account of the time value of money
- It takes into account all cash flows associated with the project
- NPV remedies many of the defects associated with PB and ARR

It does have some drawbacks however:-

- NPV may appear complicated and difficult to understand to non-financial managers (don’t underestimate this!)
- It relies on the ability of managers to accurately predict future cash flows

Well, if you have got this far you are doing well-I will finally consider the Internal Rate of Return or IRR (briefly, you will be pleased to read).

**Internal Rate of Return (IRR)**

The Internal Rate of Return is closely linked to NPV as a CIA technique. Its purpose is to identify where the NPV of a project is equal to zero i.e. it is neither positive nor negative. If you recall from the NPV example above, the NPV was positive at £7,690 at a discount rate of 10% which implies an IRR of more than 10% on the project. But what is the %IRR? Well, using trial and error, we repeat the NPV calculation using a higher discount rate. I have done the calculation (sparing you the workings) and found that, at a 25% discount rate, the NPV of the project is negative at -£384.

Hopefully, by looking at the two results, you can see that the IRR of the project is going to be closer to 25% than 10% given the financial values disclosed. IRR uses a formula (which I will spare you but it’s not that complex) based on a statistical technique called linear interpolation (which says if you know two points on a line you can plot any values in between). This discloses an IRR result of 24.28% for the project which fits with our earlier “gut feel”.

How does this help decision making? Well, it enables the manager to compare projects by establishing an IRR for each and also allows comparison with the cost of funds (the cost of capital) used to finance the project. Over-simplifying, would you borrow at 10% to finance a project earning you 24.28%? Looks a no-brainer but remember to assess the risk (it could be argued that risk could be taken into account by adding another 5% to the cost of capital making 15%-in which case the project still “wipes its face”.

The advantages of IRR methodology are:-

- Like NPV, IRR takes account of the time value of money
- Like NPV, it takes account of all relevant cash flows
- Like NPV, an allowance for risk can be built into the discount factor
- Unlike NPV, IRR discloses an absolute % value so projects of different financial sizes can be compared. Larger projects will tend to generate higher NPVs but may have lower IRRs. IRR therefore allows a more accurate comparison of different projects to aid decision making.

However, as always, there are disadvantages:-

- IRR can appear complex and difficult to understand for non-financial managers
- It has some technical defects when estimated cash flows are very irregular (I’ll spare you that explanation.)

**Summary**

If you have reached this far well done! Some final summarising points are:-

- CIA is a key aid to assist in decision making for competing business investment proposals
- CIA involves forecasting the future-a difficult task especially the further out you go
- If your inputs to CIA techniques are poor, your output will also be poor (remember G.I.G.O)
- There are various techniques which can be used in CIA-all have advantages and disadvantages
- Money received tomorrow is less valuable than money received today (the time value of money)

At the end of the day, CIA is all about selecting business projects to invest in using scarce financial resources and choosing the optimum project which will maximise the profits of the business and therefore enhance shareholder value.

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