In this workshop, we will look at techniques that enable managers to appraise, or weigh up, investment in long-lasting assets by relating the initial outlay to the future revenue. These techniques are used by businesses both to assess specific investments and to decide between alternative investments. Companies take these decisions very seriously because they involve large amounts of resources and once made they cannot be reversed.

Buglear, John. Quantitative Methods for Business (p. 261). Taylor and Francis. Kindle Edition.

**Upon successful completion of this assignment, you will be able to:**

- Assess the financial viability of alternative solutions.

- Review the file title Investment Analysis and complete the five questions at the end of the file. Be show to show your work. You may do the work in excel but be sure your answers are clearly highlighted and that the formulas work within the excel document.

Investment Analysis

Almost every organization at one time or another has to take decisions about making investments. These decisions may involve something as big as the construction of a new plant or something more mundane like the purchase of a new piece of machinery. One of the main difficulties that managers face when taking these sorts of decisions is that the cost of making the investment is incurred when the plant is built or the machine is purchased, yet the income which it is intended to help generate arises in the future, perhaps over many years.

In this workshop we will look at techniques that enable managers to appraise, or weigh up, investment in long-lasting assets by relating the initial outlay to the future revenue. These techniques are used by businesses both to assess specific investments and to decide between alternative investments. Companies take these decisions very seriously because they involve large amounts of resources and once made they cannot be reversed.

We will begin with the accounting rate of return method then we will consider the payback period approach, and finally the more sophisticated discounting techniques. Despite the differences between them they all involve the determination of single figures that summarize the financial appeal of an investment project.

**The Accounting Rate of Return **

Generally, a rate of return expresses the return or profit resulting from the use of assets such as machinery or equipment in terms of the expenditure involved in purchasing them, usually in percentage terms. You will find that accountants make extensive use of these types of summary measure; look at a business newspaper or a company report and you will probably find reference to measures like the ROCE (Return on Capital Employed). These measures are used by companies to indicate how effectively they have managed the assets under their control.

The accounting rate of return, often abbreviated to ARR, is the use of this approach to weigh up the attraction of an investment proposal. To apply it we need to establish the average (mean) profit per year and divide that by the average level of investment per year.

To calculate the average profit per year we add up the annual profits and divide by the number of years over which the investment will help generate these revenues. Having said that, the profit figures we use must be profits after allowing for *depreciation*. Depreciation is the spreading of the cost of an asset over its useful life. The simplest way of doing this is to subtract the residual value of the asset, which is the amount that the company expects to get from the sale of the asset when it is no longer of use, from the purchase cost of the asset and divide by the number of years of useful life the asset is expected to have. This approach is known as straight-line depreciation and it assumes that the usefulness of the asset, in terms of helping to generate profits, is reasonably consistent over its useful life.

To work out the average level of investment, we need to know the cost of the asset and the residual value of the asset. The average investment value is the difference between the initial cost and the residual value divided by two, in other words we split the difference between the highest and lowest values of the asset while it is in use. After dividing the average return by the average investment we multiply by 100 so that we have a percentage result. The procedure can be represented as:

Accounting rate of return = __average annual return__ * 100

Average annual investment

where

average annual investment = __(purchase cost – residual value)__

2

**Example 1**

The Budisha Bus Company is thinking of purchasing a new luxury coach to sustain its prestige client business. The purchase cost of the vehicle, including licence plates and delivery, is £120,000. The company anticipates that it will use the vehicle for five years and be able to sell it at the end of that period for £40,000. The revenue the company expects to generate using the coach is as follows:

By the end of year |
Net profit before depreciation (£) |

1 |
30,000 |

2 |
30,000 |

3 |
30,000 |

4 |
25,000 |

5 |
20,000 |

What is the accounting rate of return for this investment?

The average annual profit before depreciation is:

__(30,000+30,000+30,000 + 25,000+20,000)__ = __135,000__ = 27,000

5 5

From this amount we must subtract the annual cost of depreciation, which is:

__(120,000 – 40,000)__ = __80,000__ = 16,000

5 5

The annual average profit after depreciation is: 27000 — 16000 = £11000

The average annual investment is:

__(120,000 – 40,000)__ = __80,000__ = 40,000

2 2

The accounting rate of return is:

__11,000__ * 100= 27.5%

40,000

Should the company in Example 1 regard the accounting rate of return for this project as high enough to make the investment worth its while? In practice they would compare this figure to accounting rates of return for alternative investments that it could make with the same money, or perhaps they have a company minimum rate that any project has to exceed to be approved.

The accounting rate of return is widely used to evaluate investment projects. It produces a percentage figure which managers can easily compare to interest rates and it is essentially the same approach to future investment as accountants take when working out the ROCE (Return on Capital Employed) to evaluate a company’s past performance.

The critical weakness in using the accounting rate of return to appraise investments is that it is completely blind to the timing of the initial expenditure and future income. It ignores what is called the time value of money. The value that an individual or business puts on a sum of money is related to when the money is received; for example if you were offered the choice of a gift of £1000 now or £1000 in two year’s time you would most likely prefer the cash now. This may be because you need cash now rather than then, but even if you have sufficient funds now you would still be better off having the money now because you could invest the money in a savings account and receive interest on it.

The other investment appraisal techniques we shall examine have the advantage of bringing the time element into consideration. The other difference between them and the accounting rate of return approach is that they are based on net cash flows into the company, which are essentially net profits before depreciation.

**Payback Period**

The payback period approach to investment appraisal does take the timing of cash flows into account and is based on a straightforward concept – the time it will take for the net profits earned using the asset to cover the purchase of the asset. We need only accumulate the negative (expenditure) and positive (net profits before depreciation) cash flows relating to the investment over time and ascertain when the cumulative cash flow reaches zero. At this point the initial outlay on the asset will have been paid back.

**Example 2**

Work out the payback period for the investment proposal being considered by the Budisha Bus Company in Example 1.

The net cash flows associated with the acquisition of the luxury coach can be summarized as follows:

End of Year |
Cost/Receipt |
Net Cash Flow (£) |
Cummulative Cash Flow (£) |

0 |
Cost of Coach |
-120000 |
-120000 |

1 |
Net profit before depreciation |
30000 |
-90000 |

2 |
Net profit before depreciation |
30000 |
-60000 |

3 |
Net profit before depreciation |
30000 |
-30000 |

4 |
Net profit before depreciation |
25000 |
-5000 |

5 |
Net profit before depreciation |
20000 |
15000 |

5 |
Sale of coach |
40000 |
55000 |

Payback is achieved in year 5. We can be more precise by adding the extra cash flow required after the end of year four to reach zero cumulative cash flow (£5000) divided by the net cash flow received by the end of the fifth year (£20,000):

Payback period = 4 + __5000 __= 4.25 years

20000

Note that in the net cash flow column of the table in Example 2 the initial outlay for the coach has a negative sign to indicate that it is a flow of cash out of the business. You will find that accountants use round brackets to indicate an outflow of cash, so where we have written − 120000 for the outgoing cash to buy the coach an accountant would represent it as (120000).

The payback period we found in Example 2 might be compared with a minimum payback period the company required for any investment or with alternative investments that could be made with the same resources.

The payback period is a simple concept for managers to apply and it is particularly appropriate when firms are very sensitive to risk because it indicates the time during which they are exposed to the risk of not recouping their initial outlay. A cautious manager would probably be comfortable with the idea of preferring investment opportunities that have shorter payback periods.

The weakness of the payback approach is that it ignores cash flows that arise in periods beyond the payback period. Where there are two alternative projects it may not suggest the one that performs better overall.

**Example 3**

Gravura Print specialize in precision graphics for the art poster market. To expand their business they want to purchase a flying-arm stamper. There are two manufacturers that produce such machines: Smeshnoy and Pazorna. The cash flows arising from the two ventures are expected to be as follows:

Smeshnoy machine

End of Year |
Cost/Receipt |
Net Cash Flow (£) |
Cummulative Cash Flow (£) |

0 |
Cost of Coach |
-30000 |
-30000 |

1 |
Net profit before depreciation |
7000 |
-23000 |

2 |
Net profit before depreciation |
8000 |
-15000 |

3 |
Net profit before depreciation |
8000 |
-7000 |

4 |
Net profit before depreciation |
7000 |
0 |

5 |
Net profit before depreciation |
7000 |
7000 |

5 |
Sale of coach |
5000 |
12000 |

Pazorna machine

End of Year |
Cost/Receipt |
Net Cash Flow (£) |
Cummulative Cash Flow (£) |

0 |
Cost of Coach |
-30000 |
-30000 |

1 |
Net profit before depreciation |
12000 |
-18000 |

2 |
Net profit before depreciation |
12000 |
-6000 |

3 |
Net profit before depreciation |
6000 |
0 |

4 |
Net profit before depreciation |
2000 |
2000 |

5 |
Net profit before depreciation |
1000 |
3000 |

5 |
Sale of coach |
2000 |
5000 |

In Example 3 the payback period for the Smeshnoy machine is four years and for the Pazorna machine three years. Applying the payback period criterion we should choose the Pazorna machine, but in doing so we would be passing up the opportunity of achieving the rather higher returns from investing in the Smeshnoy machine.

A better approach would be to base our assessment of investments on all of the cash flows involved rather than just the earlier ones, and to bring into our calculations the time value of money. Techniques that allow us to do this adjust or discount cash flows to compensate for the time that passes before they arrive. The first of these techniques that we shall consider is the net present value.

**Net Present Value **

The net present value (NPV) of an investment is a single figure that summarizes all the cash flows arising from an investment, both expenditure and receipts, each of which have been adjusted so that whenever they arise in the future it is their current or present value that is used in the calculation. Adjusting, or discounting them to get their present value means working out how much money would have to be invested now in order to generate that specific amount at that time in the future.

To do this we use the same approach as we would to calculate the amount of money accumulating in a savings account. We need to know the rate of interest and the amount of money initially deposited. The amount in the account at the end of one year is the original amount deposited plus the rate of interest, r, applied to the original amount:

Amount at the end of the year = Deposit + (Deposit * r)

We can express this as:

Amount at the end of the year = Deposit * (1 + r)

If the money stays in the account for a second year:

Amount at the end of the second year = Deposit * (1 + r) * (1 + r) = Deposit * (1 + r)2

**Example 4 **

If you invested £1000 in a savings account paying 5% interest per annum, how much money would you have in the account after two years?

Amount at the end of the first year = 1000 * (1 + 0.05) = £1050

If we invested £1050 for a year at 5%, at the end of one year it would be worth:

1050* (1 + 0.05) = £1102.5

We can combine these calculations:

Amount at the end of the second year = 1000 * (1 + 0.05)2

=1000 * (1.05)2

= 1000 * 1.1025

= £1102.5

In general if we deposit an amount in an account paying an annual interest rate r for n years, the amount accumulated in the account at the end of the period will be:

Deposit * (1 + r)n

The deposit is, of course, the sum of money we start with, it is the present value (PV) of our investment, so we can express this procedure as:

Amount at the end of year n = PV * (1 + r)n

This expression enables us to work out the future value of a known present value, like the amount we deposit in an account. When we assess investment projects we want to know how much a known (or at least expected) amount to be received in the future is worth now. Instead of knowing the present value and wanting to work out the future, we need to reverse the process and determine the present value of a known future amount. To obtain this we can rearrange the expression we used to work out the amount accumulated at the end of a period:

Present Value (PV) = __Amount at the end of year n__

(1 + r)n

**Example 5**

You are offered £1000 to be paid to you in two years’ time. What is the present value of this sum if you can invest cash in a savings account paying 5% interest per annum?

Present value = __ 1000__ = __ 1000__ = __ 1000__ = 907.029

(1+0.05)2 1.052 1.1025

The present value of £1000 received in two years’ time is £907.03, to the nearest penny. In other words, if you invested £907.03 at 5% now in two years’ time the amount would be worth

Amount at the end of year two = 907.03 *(1 – 0.05)2 = 907.03 * 1.1025

= £1000.00 to the nearest penny

When companies use net present value (NPV) to assess investments they discount future cash flows in the same way as we did in Example 5, but before they can do so they need to identify the appropriate rate of interest to use. In Example 5 we used 5% as it was a viable alternative that in effect reflected the opportunity cost of not receiving the money for two years, that is, the amount you have had to forego by having to wait.

The interest, or discount, rate a company uses is likely to reflect the opportunity cost, which may be the interest it could earn by investing the money in a bank. It may also reflect the prevailing rate of inflation and the risk of the investment project not working out as planned.

**Example 6 **

What is the net present value of the proposed investment in a luxury coach by the Budisha Bus Company in Example 2. Use a 10% interest rate.

The cash flows involved in the project were:

End of Year |
Net Cash Flow (£) |
Discount Factor |
PV ( to the nearest £) |

0 |
-120000 |
1.00 |
-120,000 |

1 |
30000 |
0.91 |
27,273 |

2 |
30000 |
0.83 |
24,793 |

3 |
30000 |
0.75 |
22,539 |

4 |
25000 |
0.68 |
17,075 |

5 |
20000 |
0.62 |
12,418 |

5 |
40000 |
0.62 |
24,837 |

Discount Rate |
10% |
Net Present Value |
8,936 |

The net present value of the project in Example 8.11 is £8936. The initial outlay of £120,000 in effect purchases future returns that are worth £128,936. Because the discount rate used is in effect a threshold of acceptable returns from a project, any opportunity that results in a positive NPV such as in Example 6 should be approved and any opportunity producing a negative NPV should be declined.

**The Internal Rate of Return **

A fourth investment appraisal method widely used by businesses is the internal rate of return (IRR). It is closely related to the net present value approach; indeed the internal rate of return is the discount rate at which the total present value of the cash flows into a business arising from an investment precisely equals the initial outlay. To put it another way, the internal rate of return is the discount rate that would result in a net present value (NPV) of zero for the investment. Because the concept of discounting is at the heart of both NPV and IRR they are known as discounted cash flow (DCF) methods.

Finding the internal rate of return for a project is a rather hit and miss affair. We try out one discount rate and if the result is a positive NPV we try a higher discount rate; if the result is negative, we try a lower discount rate.

**Example 7 **

Find the internal rate of return for the proposed luxury coach purchase by the Budisha Bus Company project in Example 2.

We know from Example 6 that if we apply a discount rate of 10% the net present value of the project is £8936. Since this is positive the internal rate of return will be higher, so we might try 15%:

End of Year |
Net Cash Flow (£) |
Discount Factor |
PV ( to the nearest £) |

0 |
-120000 |
1.00 |
-120,000 |

1 |
30000 |
0.87 |
26,087 |

2 |
30000 |
0.76 |
22,684 |

3 |
30000 |
0.66 |
19,725 |

4 |
25000 |
0.57 |
14,294 |

5 |
20000 |
0.50 |
9,944 |

5 |
40000 |
0.50 |
19,887 |

Discount Rate |
15% |
Net Present Value |
-7,379 |

This negative NPV suggest that the internal rate of return is not as high as 15%. One of the advantages of using a spreadsheet like Excel is that one can try changing the discount rate and quickly find a desired value.

End of Year |
Net Cash Flow (£) |
Discount Factor |
PV ( to the nearest £) |

0 |
-120000 |
1.00 |
-120,000 |

1 |
30000 |
0.89 |
26,642 |

2 |
30000 |
0.79 |
23,660 |

3 |
30000 |
0.70 |
21,011 |

4 |
25000 |
0.62 |
15,549 |

5 |
20000 |
0.55 |
11,047 |

5 |
40000 |
0.55 |
22,094 |

Discount Rate |
12.61% |
Net Present Value |
2.43 |

The NPV at the discount rate of 10% was just under £9000 so the discount rate that will yield an NPV of zero is about 12.61%. Often it is sufficient to find an approximate value of the IRR, as we have done in

If you need a precise value you can try several discount rates and plot them against the resulting NPV figures for the project.

**Example 8 **

The net present values for the coach purchase by the Budisha Bus Company were calculated using different discount rates. The results are:

Discount Rate |
Net Present Value |

10% |
8936 |

12% |
1989 |

13% |
-1267 |

15% |
-7379 |

Plot these and with a scatterplot and use Excel’s trendline function to calculate the equation of the line.

Solve for x to determine the discount rate that produces a NPV of zero. Set Y equal to zero and solve for X.

Y = -326273 x + 41354

0 = -326273 x + 41354

326273x = 41354

X = 41354/ 326273 = 12.67%

The result we obtained in Example 8 could be used to assess the coach purchase in comparison with other investment opportunities open to the company, or perhaps the cost of borrowing the money to make the investment, if they needed to do so. In general, the higher the internal rate of return, the more attractive the project.

The internal rate of return and the net present value methods of investment appraisal are similar in that they summarize all the cash flows associated with a venture and are therefore superior to the payback method. They also take the time value of money into account and are therefore superior to the accounting rate of return approach.

The drawback of the internal rate of return technique compared to the net present value method is that the IRR is an interest rate, a relative amount, which unlike the NPV gives no idea of the scale of the cash flows involved. Both IRR and NPV are rather laborious to calculate.

Companies may well use the fairly basic approach of the payback period as the threshold that any proposed investment must meet, and then use either NPV or IRR to select from those that do.

Problems:

1. A young aspiring DJ has saved up £4000 to buy the equipment she needs. She anticipates that the equipment will last for five years, after which it will be obsolete and have no disposal value. During these five years she believes she can use it to earn the following amounts, after allowing for her own wages and costs of travelling to clubs and events:

1 1200

2 1800

3 2000

4 2000

5 2000

(a) Work out the accounting rate of return for the investment, allowing for depreciation of one-fifth of the cost of the equipment per year.

(b) Find the payback period for the investment.

2. An advertisement offers a time share investment in a luxury apartment in the Algarve region of Portugal. Investors can purchase the use of the apartment for an eight week period each year to rent out to tourists. The cost of the time share is £ 15,000 for five years and it is claimed that the net rental income will be £4000 per year.

(a) What is the payback period for the investment?

(b) What is the net present value of the investment to an investor who would otherwise be able to earn 5% on their money?

(c) In the small print of the advertisement, it says “a service charge of £1000 per annum is charged for the cleaning and general maintenance of the property.” Work out how this will alter the net present value of the investment.

3. After a bad accident, Anton receives a large sum in compensation. He is thinking about using it in a stretch limousine to hire out for special occasions. The cost of the limousine is £ 100,000. Anton is due to retire in six years, at which stage he thinks he will be able to sell the limousine for £ 40,000. The net cash inflows for the venture, after allowing for the driver’s wages and other direct expenses are:

1 10,000

2 15,000

3 20000

4 20000

5 15000

6 15000

(a) Find the payback period for this venture.

(b) Calculate the net present value using a discount rate of 8%,

4. Ricky Sadovnik, a geologist, discovered a deposit of decorative stone during a holiday in Scotland. He wants to establish a quarry to extract the stone and sell it to gardeners. The owner of the land is prepared to allow him to open and operate a quarry on the site for five years for a fee of £150,000. In addition he must landscape the site at the end of the period, at a cost of £50,000. Ricky intends to hire the digging equipment for the quarry. The net cash flows from the sale of the stone are predicted to be:

End of year Net cash flow (£)

1 30,000

2 50,000

3 60,000

4 60,000

5 60,000

6 60,000

(a) Determine the net present value for this project based on a discount rate of 15%.

(b) Find the net present value using a discount rate of 10%.

(c) Determine the internal rate of return for the project.

5. A Russian businessman offers a major Japanese car manufacturer an eight-year lease on a disused tank factory in Southern Russia. The company could refit the factory and use it to manufacture low cost recreational off road vehicles for the holiday car-hire market in Southern Europe. The total cost of the investment , including the lease and the installation of the equipment is $ 55 million. Once the plant is operational, the following cash flows are expected:

End of year Net cash flow ($millions)

1 8

2 12

3 15

4 20

5 20

6 10

7 10

8 5

At the end of the eighth year the lease would expire. The disposal value of the equipment is likely to be $5 m.

(a) Determine the net present value for this project based on a discount rate of 20%.

(b) Determine the internal rate of return for the project.

Net Present Value

0.1 0.12 0.13 0.15 8936 1989 -1267 -7379

We are a professional custom writing website. If you have searched a question and bumped into our website just know you are in the right place to get help in your coursework.

Yes. We have posted over our previous orders to display our experience. Since we have done this question before, we can also do it for you. To make sure we do it perfectly, please fill our Order Form. Filling the order form correctly will assist our team in referencing, specifications and future communication.

1. Click on the “**Place order** tab at the top menu or “**Order Now**” icon at the
bottom and a new page will appear with an order form to be filled.

2. Fill in your paper’s requirements in the "**PAPER INFORMATION**" section
and click “**PRICE CALCULATION**” at the bottom to calculate your order
price.

3. Fill in your paper’s academic level, deadline and the required number of pages from the drop-down menus.

4. Click “**FINAL STEP**” to enter your registration details and get an account
with us for record keeping and then, click on “**PROCEED TO CHECKOUT**”
at the bottom of the page.

5. From there, the payment sections will show, follow the guided payment process and your order will be available for our writing team to work on it.

August 16, 2022

August 16, 2022