ACCA P4 Advanced Financial Management - 2010 - Study text

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Paper P4

Advanced Financial Management

CHAPTER

Capital investment appraisal

Contents

1 Discounted cash flow: net present value method

2 The time to recover the capital invested: payback

and duration

3 DCF: internal rate of return (IRR) and modified

internal rate of return (MIRR)

4 DCF and taxation

5 DCF and inflation

6 Free cash flow

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Discounted cash flow: net present value method

 Introduction

 Net present value (NPV) method of investment appraisal

 Assumptions about the timing of cash flows

 Changes in working capital and cash flows

 Calculating the NPV of a project

 Discount tables

 Annuities

 Present value of a perpetuity

1 Discounted cash flow: net present value method

1.1 Introduction

An important element of financial management is deciding how to invest funds in

capital projects. The basic principle is that a company should not invest capital

unless the expected return from the investment is expected to exceed the cost of the

funds invested.

Proposed capital expenditure projects can be evaluated using discounted cash flow.

A crucial aspect of DCF is that capital expenditure is assessed by looking at the cash

flows from the investment, not at accounting profits.

You should be familiar with the basic rules of DCF from your earlier studies. This

chapter contains revision material for what you should already know. However, in

your examination, you will be required to take DCF analysis to a more advanced

stage. This chapter explains some advanced aspects of capital investment appraisal.

Other aspects will be dealt with in later chapters.

1.2 Net present value (NPV) method of investment appraisal

With the NPV method of investment appraisal, all the future cash flows from an

investment are converted into a present value, by discounting the cash flow at the

investment cost of capital. This cost of capital is the return required from the

investment.

The discount rate to apply to a cash flow at the end of year n is:

1/(1 + r)

where r is the cost of capital (so that 9% = 0.09, 12.5% = 0.125 and so on).

Cash flows at the beginning of the investment, in Year 0, are already stated at their

present value. The present value of $1 in Year 0 is $1. (The discount factor for Year 0

is 1/(1 + r)

. This has a value of 1.000 for any and every value of r.

Chapter 3: Capital investment appraisal

1.3 Assumptions about the timing of cash flows

The following assumptions are used in DCF about the timing of cash flows:

 The cash flows for each year (or time period) are assumed to occur at the end of

the year (or time period). For example, if it is estimated that cash flows in Year 4

will be $100,000, it is assumed that the $100,000 is a cash inflow on the last day of

Year 4.

 If a cash flow will occur early during a particular year, it is assumed that it will

occur at the end of the previous year. Therefore a cash expenditure early in Year

1, for example, is assumed to occur in Year 0.

If greater accuracy is required for the timing of cash flows, each year can be divided

into shorter time periods, such as three-month periods. The same assumptions

about the timing of cash flows will apply, however, regardless of the length of these

time periods.

1.4 Changes in working capital and cash flows

When there is an increase in working capital, cash inflows are lower than the cash

profit in the same period, by the amount of the increase.

Similarly, when there is a reduction in working capital, cash inflows are higher than

cash profits in the period, by the amount of the reduction.

This rule should be familiar to you from cash flow statements.

In DCF analysis, instead of adjusting the cash profits in the years when working

capital is increased or reduced, the increases or reductions in working capital are

treated as separate cash flow items.

Example

A five-year project will require a working capital investment of $20,000 early in Year

1, and an additional working capital investment of $15,000 early in Year 2. The

adjustments for working capital to the cash flows in each year of the project will be:

Year

0 (20,000)

1 (15,000)

5 35,000

There is a cash inflow at the end of the project because working capital is reduced to

zero, and cash flows exceed cash profits in that year by the amount of the working

capital reduction.

1.5 Calculating the NPV of a project

The net present value (NPV) of a project is the net difference between the present

value of all the costs incurred and the present value of all the cash flow benefits

(savings or revenues).

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 If the present value of benefits exceeds the present value of costs, the NPV is

positive.

 If the present value of benefits is less than the present value of costs, the NPV is

negative.

 The NPV is 0 when the PV of benefits and the PV of costs are equal.

The decision rule is that, ignoring other factors such as risk and uncertainty, and

non-financial considerations, a project is worthwhile financially if the NPV is

positive or zero. It is not worthwhile if the NPV is negative.

The net present value of an investment project is also a measure of the value of the

investment. For example, if a company invests in a project that has a NPV of $2

million, the value of the company should increase by $2 million.

1.6 Discount tables

Discount tables will be provided in your examination. They take away the need to

calculate the value of discount factors

1+ r

()

. The discount factors in the tables are

rounded to three decimal places.

The following example tests your basic understanding of the NPV method and the

use of discount tables. It should also demonstrate that

when the cost of capital is

lower, the NPV is higher

. (And when the cost of capital is higher, the NPV is

lower.)

Example

A company is considering an investment in equipment costing $70,000. Working

capital of $5,000 will also be required early in Year 1. The equipment will have a

resale value of $7,000 at the end of Year 5. The operating profits from the

investment, in cash flows, will be:

Year Cash flow

1 25,000

2 20,000

3 30,000

4 20,000

5 3,000

Required

Using discount tables for the discount factors, calculate the NPV of the project if the

cost of capital is:

(a) 12%, and

(b) 8%.

Chapter 3: Capital investment appraisal

Answer

In this example, the investment in working capital is treated as a cash outflow of

$5,000 in Year 0 (early in Year 1). When the working capital is recovered at the end

of the project (at the end of Year 5, or early in Year 6), this is treated as a Year 5 cash

inflow.

The resale value of the equipment is also a cash inflow at the end of Year 5.

The cash flows for each year are therefore calculated as follows:

Year

Equipment

Working

capital

Cash

profits

Annual cash

flow

$ $ $ $

0 (70,000) (5,000)

(75,000)

25,000

20,000

30,000

20,000

5 7,000 5,000

3,000

15,000

These cash flows should be used to calculate the NPV at (a) 12% and (b) 8%.

Year Cash flow Cost of capital 12% Cost of capital 8%

Discount factor Present value Discount factor Present value

$ $ $

0 (75,000) 1.000

(75,000)

1.000 (75,000)

1 25,000 0.893

22,325

0.926 23,150

2 20,000 0.797

15,940

0.857 17,140

3 30,000 0.712

21,360

0.794 23,820

4 20,000 0.636

12,720

0.735 14,700

5 15,000 0.567

8,505

0.681 10,215

+5,850

+14,025

Conclusion

The NPV is higher when the cost of capital is lower.

1.7 Annuities

An annuity is a constant cash flow for a given number of time periods.

Examples of annuities are:

 $80,000 each year for years 1 – 7

 $50,000 each year for years 6 – 12

 $1,000 each month for months 1 – 36.

Annuity discount factors can be used in DCF investment analysis, mainly to make

the calculations easier and quicker. Instead of discounting a constant annual cash

flow each year by the discount factor for that year, and then adding up the present

values of the annual cash flows, we can multiply the constant annual cash flow by

an annuity factor.

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The annuity factor is simply the sum of the discount factors for all the years in

which the constant annual cash flow occurs.

Annuity discount tables

The cash flows of project might include an annuity. The discount factors for

annuities (‘annuity factors’) are provided in discount tables at the beginning of this

text, and in the examination.

An annuity factor for time periods 1 to n is the sum of the discount factors from time

period 1 to time period n.

Example

You should refer to the annuity factor table at the beginning of this text to check the

discount factors in the following examples.

 The annuity factor for years 1 – 2 at a cost of capital of 8% = 1.783. This is found

from the annuity table, n = 2, discount factor 8%. This annuity factor is the sum

of the discount factors at 8% for years 1, and 2 (0.926 + 0.857).

 The annuity factor for years 1 – 6 at a cost of capital of 10% = 4.355. This is found

from the annuity table, n = 6, discount factor = 10%. This annuity factor is the

sum of the discount factors at 10% for years 1, 2, 3, 4, 5 and 6 (0.909 + 0.826 +

0.751 + 0.683 + 0.621 + 0.564).

 The annuity factor for years 4 – 8 at a cost of capital of 12% is calculated from

annuity tables as follows:

Annuity factor at 12%, Years 1

–

4.968

Annuity factor at 12%, Years 1

–

2.402

Annuity factor at 12%, Years 4

–

2.566

This is the sum of the discount factors at 12% for each of the years 4 to 8. (0.636 +

0.567 + 0.507 + 0.452 + 0.402 = 2.566.)

Formula for calculating an annuity factor

It is useful for the purpose of financial management to be aware of the formula for

an annuity. This is shown at the top of the annuity table:

Annuity factor =

1 - (1+ r)

-n

This formula can be re-arranged, as follows:

Annuity factor =

1−

1+ r

()

⎡

⎣

⎢

⎤

⎦

⎥

For example, the annuity factor for years 1 – 6 at 10% is:

0.10

1−

1.10

()

⎡

⎣

⎢

⎤

⎦

⎥

0.4355

0.10

= 4.355

Chapter 3: Capital investment appraisal

A knowledge of this formula might be useful for calculating an annuity factor when

the cost of capital is not a whole number; for example when the cost of capital is

8.5% or 11.25%.

Example

The expected cash flows for a project to purchase the patent rights to a product are

as follows:

Year

Annual cash

flow

Discount factor at

12%

Present value

$ $

0 (100,000)

1 10,000

2 15,000

–

15 20,000

NPV

If the cost of capital is 12%, the NPV of the project is calculated as follows:

Years

Annuity factor at

12%

–

15 6.811

–

2 1.690

–

15 5.121

Year

Annual cash

flow

Discount factor at

12%

Present value

$ $

0 (100,000) 1.000

(100,000)

1 10,000 0.893

8,930

2 15,000 0.797

11,955

–

15 20,000 5.121

102,420

NPV

+ 23,305

Annuity factors can be used to calculate a ‘breakeven’ or minimum annual cash

flow for a project.

Example

A company is considering an investment of $70,000 in a project. The project life

would be five years.

What must be the minimum annual cash returns from the project to earn a return of

at least 9% per annum, if the returns are a constant amount each year?

Answer

Investment $70,000

Annuity factor at 9%, years 1

–

3.890

The minimum annual cash flow must have a present value of $70,000. The PV of the

returns for the five years is the annual return multiplied by the annuity factor.

Minimum annual return required

= $70,000/3.890 = $17,995.

Paper P4: Advanced Financial Management

1.8 Present value of a perpetuity

A perpetuity is a constant annual cash flow ‘for ever’, or into the long-term future.

In investment appraisal, it might be assumed that there is an annual cash flow in

perpetuity whenever a constant annual cash flow is expected

for a long time into

the future.

The

present value of a perpetuity is: C/r

where:

 C is the constant annual cash flow in perpetuity

 r is the cost of capital: for example 0.08, 0.10 etcetera.

Example

(1) What is the present value of £2,000 in perpetuity, starting in Year 1, if the cost

of capital is 8%?

(2) What is the present value of £5,000 in perpetuity, starting in Year 4, if the cost

of capital is 11%?

Answer

(1)

£2,000

0.08

= £25,000

(2) Year 3 value of perpetuity

£5,000

0.11

= £45, 456

Year 3 discount factor at 11% 0.731

Year 0 (present value) of perpetuity £33,228

Use of perpetuities in financial management

The PV of a perpetuity is used in the dividend valuation model for share valuations,

when there are constant annual dividends. Share valuation methods are explained

in a later chapter.

Chapter 3: Capital investment appraisal

The time to recover the capital invested: payback and duration

 Payback period

 Discounted payback period

 The concept of duration

 Capital investment projects and duration

2 The time to recover the capital invested: payback and

duration

2.1 Payback period

In addition to using NPV as a basis for making investment decisions, a company

might also make their decision partly on the basis of how long it will take to recover

the capital invested from the cash flows of the project.

The simplest method of measuring the time to recover the capital investment is the

payback period. This is the number of years before the cumulative net cash flows

from the project are $0, and the capital invested has been recovered.

A company might establish an investment decision rule, for example, that projects

will not be undertaken unless they have a positive NPV and the payback period is

less than, say, five years.

Example

An investment in a new business venture is expected to have the following cash

flows:

Year

Annual cash

flow

0 (200,000)

1 (40,000)

2 30,000

3 120,000

4 150,000

5 100,000

6 50,000

Paper P4: Advanced Financial Management

The payback period is calculated as follows:

Year

Annual cash

flow

Cumulative

cash flows

$ $

0 (200,000) (200,000)

1 (40,000) (240,000)

2 30,000 (210,000)

3 120,000 (90,000)

4 150,000 60,000

5 100,000 160,000

6 50,000 210,000

Payback occurs during Year 4. Since cash flows are assumed to occur at the payback

period, it could be stated as Year 4. However, it is usual to estimate the payback

period in years and months.

In this example, the cumulative cash flows at the end of Year 3 are $(90,000) and

during Year 4, the cash flows are $150,000. We can therefore estimate that if cash

flows during Year 4 occur at a constant rate, the payback period is:

3 years + [(60,000/150,000) × 12 months) = 3 years and 4.8 months, say 3 years 5

months.

The decision whether or not to invest might depend on whether the NPV of the

project is positive and whether the payback period of 3 years and 5 months is

acceptable.

Criticisms of the payback method of project evaluation

There are two major criticisms of using the payback method to decide whether or

not to undertake a capital investment project.

 The payback period ignores all the cash flows that are expected to occur after the

payback period has been reached. The payback period should never be used on

its own. If it is used at all, it should be used with a method of project evaluation

that assesses the cash flows over the entire life of the project (such as the NPV

method).

 The payback method ignores the time value of money. $1 in a future year has a

lower present value than $1 now. A capital investment is not properly paid back

when the cumulative cash inflows are $0, because the investment needs to earn a

return. A calculation of payback should therefore recognise the opportunity cost

of investing capital. A discounted payback period is a more appropriate measure

of payback than a payback period that ignores the time value of money.

2.2 Discounted payback period

A discounted payback period is calculated in the same way as the ‘ordinary’

payback period, with the exception that the cash flows of the project are converted

to their present value. The discounted payback period is the number of years before

the cumulative NPV of the project reaches $0.

ACCA P4 Advanced Financial Management - 2010 - Study text - Emile Woolf Publishing

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