net present value - examples and exercises - week 4

CC5001 Examples and Exercises Week 4

1

Net Present Value

The apparent costs of a project may appear different when the future value of money is

considered; Discounted Cash Flow (DCF) is one technique which allows us to see future

costs in today's terms, i.e. the Net Present Value (NPV).

Example

Consider the following proposal: "If Amy lends Brian £1500 this year, Brian will repay

Amy £500 next year, the year after, and the year after that." What is this worth? The

apparent value is that £1500 is the same as three times £500, but this does not take account

of the changing values over time. We can also see that Brian is not paying Amy any interest

over this period. A closer examination reveals that there is a difference between the values

of the sums involved. Consider this from Amy’s point of view, and also see what this

means for Brian.

Year 0 1 2 3 4

DCF 10% 1.00 0.91 0.83 0.75 0.68

DCF 12% 1.00 0.89 0.80 0.71 0.64

Note that the value in Year 0 is 1.0 (or 100%), because the value in today’s money is in full

at the present day. We start in Year 0 – we do not reach Year 1 until the following year

(think of birthdays – you are 1 year old on the first anniversary of your birthday).

The proposed loan from Amy’s point of view

Amy needs to consider whether the proposed loan arrangement is worthwhile. The

following calculations, using the recommended DCF values, show that the proposed loan

to Brian does not represent a good use of Amy’s money.

Year Am

y’s

inco

me

£

Am

y’s

ou

tla

y £

Ap

pa

re

nt

va

lue

£

DC

F

10

%

Va

lue

at

10

%

DC

F

DC

F

12

%

Va

lue

at

12

%

DC

F

0 -1500 -1500 1.00 -1500 1.00 -1500

1 500 500 0.91 455 0.89 445

2 500 500 0.83 415 0.80 400

3 500 500 0.75 375 0.71 355

Total 1500 -1500 0 -255 -300

Here, the loan results in a loss for Amy. At a DCF of 10% the NPV is -£255, a loss in real

terms. At a DCF of 12% the NPV is -£300 in real terms, an even greater loss.

It is important to note that we cannot choose a DCF value for the transaction; it would be

wrong for Amy to tell Brian that she would agree to the loan at a lower DCF value. The

DCF values employed are intended to reflect the financial environment; different DCF

calculations are made to test the sensitivity of the proposals to changes in the financial

environment. It would be possible to change the DCF values over the period, if this reflects

what financial experts predict. For example, the recommended DCF for the first two years

could be 8%, growing to 10% over the next two years. Predictions are plagued by

uncertainty, which makes calculations further into the future less reliable than short-term

estimates.

Net

Present

Value


2

The proposed loan from Brian’s point of view

We can now examine how the load appears to Brian. As Brian receives £1500 now, and

repays Amy’s loan without interest over the years ahead, he gains from the loan.

Year Bri

an

’s

inco

me

£

Bri

an

’s

ou

tla

y £

Ap

pa

re

nt

va

lue

£

DC

F

10

%

Va

lue

at

10

%

DC

F

DC

F

12

%

Va

lue

at

12

%

DC

F

0 1500 0 -1500 1.00 1500 1.00 1500

1 -500 500 0.91 -455 0.89 -445

2 -500 500 0.83 -415 0.80 -400

3 -500 500 0.75 -375 0.71 -355

Total 1500 -1500 0 255 300

Here we can see that Amy’s loss is Brian’s gain. The DCF value of 10% leaves Brian

£255 better off; and at a DCF value of 12% Brian’s gain rises to £300.

It is usual in dealing with financial transactions to show the income as positive, and the

outlay as negative. We can see here that the numeric values are exactly the same for

Brian as they were for Amy, except that they are positive for Brian where they were

negative for Amy, and vice versa. Here, the negative values have been indicated with a

minus sign, but other notations use parentheses to indicate a negative number.

Task 4.1

Amy tells Brian that the original loan proposal is not acceptable because of the loss she

would make. Consider the following proposal: "If Amy lends Brian £1500 next year, Brian

will repay Amy £500 this year, next year and the year after." Is this a better option of Amy?

Use the same DCF values of 10% and 12%.

Year 0 1 2 3 4

DCF 10% 1.00 0.91 0.83 0.75 0.68

DCF 12% 1.00 0.89 0.80 0.71 0.64

Check it out…

Burke R (1999) Project Management: Planning and Control Techniques. Wiley,

Chichester: pages 56 - 58.

Cadle J & Yeates D (2001) Project Management for Information Systems, 3rd

Edition, Prentice-Hall, Harlow: pages 90 –91.

Gray CF & Larson EW (2000) Project Management: The Managerial Process,

McGraw-Hill: pages 36 – 37.

Lockyer K & Gordon J (1996) Project Management and Project Network

Techniques, 6th

edition, Prentice-Hall, Harlow: pages 75–93.

Maylor H (2003) Project Management, 3rd

edition, Pearson Education, Harlow:

pages 183 – 188.

Meredith JR & Mantel Jr. SJ (2006) Project Management: A Managerial

Approach, John Wiley & Sons, Asia: pages 52–53, 67–75.

Task 4.1

Check it out…


3

Example

Bumblefist and Dogsbody are a company specialising in the office of office stationery.

They have 10 clerks who generate invoices and letters, many of which are in a standard

format. These clerks have PCs running WordPerfect; these are now out-of-date compared

to PCs with more modern software packages. Management intends to replace these old PCs

with news ones for word processing, setting up a customer database system, and using a

spreadsheet for accounting information. The company has two options under consideration:

(a) to purchase 10 personal computers together with software for £1000 each from

Grabbit Computers

(b) to rent 10 personal computers with software included at £1700 per annum for all 10

machines from Steadfast Equipment Supplies.

If the rental option is pursued then maintenance, again for all machines, is £12 per annum

for the first five years, then £15 per annum for the next five years, and £17.50 for the

following five years. If Bumblefist and Dogsbody elect to purchase, maintenance is

included in the purchase agreement for the first five years, after which the terms are £15 per

annum for the next five years and £17.50 for the following five years, as with the rental

agreement. Whether renting or purchasing, Bumblefist and Dogsbody will need to pay 10%

of the initial purchase price every year in insurance. Bumblefist and Dogsbody expect that

they will replace all the machines in 10 years, by which time they consider that they will

have become worthless.

In order to consider the best option for the company, Net Present Value calculations will

need to be made in order to compare options (a) and (b).

Discounted Cash Flow factors of

(i) 11%, and

(ii) 15%

are used in order to assess the impact of the two proposals. The calculations will show

which option appears to be better value in today's terms.

Read the question carefully in order to calculate the rental and purchase values each

year. Note in particular that the insurance is calculated as 10% of the purchase price; do not

make the mistake of using 10% of the cost of rental.

The DCF values are as follows: Year/

DCF

0 1 2 3 4 5 6 7 8 9

11% 1.00 0.90 0.81 0.73 0.66 0.59 0.53 0.48 0.43 0.39

15% 1.00 0.87 0.76 0.66 0.57 0.50 0.43 0.38 0.33 0.28


4

In this example, all the values are expenditure. For clarity of presentation, neither minus

signs nor parentheses have been used, but it should be remembered that the values below are

negative (i.e. money being spent), and we should aim to minimise expenditure.

Yea

r

Rent Purchase DCF 15% DCF 11%

Basi

c

Main

ten

an

ce

Insu

ran

ce

Tota

l

Basi

c

Insu

ran

ce

Main

ten

an

ce

Tota

l

Rate

at

15%

Ren

t

Bu

y

Rate

at

11%

Ren

t

Bu

y

£ £ £ £ £ £ £ £ £ £ £ £

0 1700 12 1000 2712 10000 1000 11000 1.00 2712 11000 1.0

0

2712 11000

1 1700 12 1000 2712 1000 1000 .87 2359.44 870 .90 2440.80 900

2 1700 12 1000 2712 1000 1000 .76 2061.12 760 .81 2196.72 810

3 1700 12 1000 2712 1000 1000 .66 1789.92 660 .73 1979.76 730

4 1700 12 1000 2712 1000 1000 .57 1545.84 570 .66 1789.92 660

5 1700 15 1000 2715 1000 15 1015 .50 1357.50 507.50 .59 1601.85 598.85

6 1700 15 1000 2715 1000 15 1015 .43 1167.45 436.45 .53 1438.95 537.95

7 1700 15 1000 2715 1000 15 1015 .38 1031.70 385.70 .48 1303.20 487.20

8 1700 15 1000 2715 1000 15 1015 .33 895.95 334.95 .43 1167.45 436.45

9 1700 15 1000 2715 1000 15 1015 .28 760.20 284.20 .39 1058.85 395.85

Tota

ls 1700

0 135

10000

27135 10000 10000 20075 15681.12 15808.80 17689.50 16556.30

On the basis of this information, a decision could go either way, but supporting reasons

should include consideration of factors such as:

reliability of the supplier

availability of help desk support

training costs

likelihood of the equipment becoming obsolete before the end of the ten-year

period

loss of investment opportunities should purchase be chosen,

inflation

difficulty in maintaining the equipment near the end of its life

Further information that could be included in the calculations: any savings that can be

identified; these can be traded-off against the costs, and these savings can also be

evaluated in today's terms if they are expected to occur in the future.

Task 4.2

Consider the proposal: "Charlie will give Alice £100 each year for the next five years

(starting next year), if Alice gives Charlie £500 this year". What is this proposal worth for

Alice and Charlie? Use DCF factors of 10% and 12%. What difference does it make if

Charlie repays Alice £120 each year?

Year 0 1 2 3 4 5

DCF 10% 1.00 0.91 0.83 0.75 0.68 0.62

DCF 12% 1.00 0.89 0.80 0.71 0.64 0.57

Task 4.2


5

Task 4.3

A disposable party hat manufacturer, Chuck Beret, is considering investing in a new

range of personal computer workstations in order to streamline the ordering and hire and

sale of their range of party hats, which include policemen's helmets, nurses' caps, bowler

hats and top hats. The organisation is considering two options, one for rental, and one for

purchase:

option 1 to rent 8 personal computers, including software, etc, at £2250 per annum

for all equipment from Hare and Hatter systems

option 2 to purchase 8 personal computers, with software, etc, for £11000 for all

the equipment from White Rabbit Computers.

If the rental option is pursued, maintenance for all machines will need to be paid at £300

per annum; this does not apply if the purchase option is selected. Insurance will need to

be paid, whether renting or purchasing, at 10% of the purchase price. Chuck Beret plan

to replace the equipment after five years, with the expectation that the new equipment and

software will have reached the end of its useful life.

You are required to analyse the options, using the DCF factors of 11% and 15% from the

table below, and make a recommendation as to which option should be selected. Identify

all factors that you consider relevant to the decision.

DCF Factors

Year 0 1 2 3 4 5 6 7 8

DCF 11% 1.0 .90 .81 .73 .66 .59 .53 .48 .43

DCF 12% 1.0 .89 .80 .71 .64 .57 .51 .45 .40

DCF 15% 1.0 .87 .76 .66 .57 .50 .43 .38 .33

DCF 18% 1.0 .85 .72 .61 .52 .44 .37 .31 .27

Task 4.3


6

Task 4.4

A sports and leisure club, Shuttleworth and Rackett, maintain a database of club

members who book gymnasium equipment, squash and tennis courts, as well as more

unusual pastimes such as fencing, yoga and T'ai Chi. There is also the opportunity to

book sessions with a personal trainer at £20 per hour, or £100 for a full day. Standard

membership costs £200 per calendar year, with a discount of 25% for full-time students.

Club members may use their own equipment, but also have the option of hiring

equipment when a booking is made. In order to deal with club membership, accounts,

booking facilities and hiring equipment, as well as maintenance of facilities and

equipment, Shuttleworth and Rackett have decided to update their computer system. The

club will scrap their existing computer system which is no longer of any value, but can be

removed free of charge if either of the following two options is chosen, both offered by

the same supplier, Computer Concepts.

option 1 to rent 15 personal computers, including software, etc, for £275 per

machine per annum for the first five years, £320 per machine per annum for the next five

years, and £480 per machine per annum thereafter. The cost of maintenance will be £50

per machine per annum throughout.

option 2 to purchase 15 personal computers, with software, etc, for £1750 per

machine. Maintenance will be £360 per annum for all machines for the first five years,

then £480 for the next five years.

Whichever option is chosen, insurance will need to be paid at 15% of the purchase price.

Shuttleworth and Rackett plan to replace the equipment after eight years, when the

equipment will have reached the end of its useful life, and will therefore be considered

worthless.

You are required to analyse the options, using the DCF factors of 11% and 15% from the

table below. Which would be the best option for Shuttleworth and Rackett? Identify all

relevant factors.

DCF Factors

Year 0 1 2 3 4 5 6 7 8

DCF 11% 1.0 .90 .81 .73 .66 .59 .53 .48 .43

DCF 12% 1.0 .89 .80 .71 .64 .57 .51 .45 .40

DCF 15% 1.0 .87 .76 .66 .57 .50 .43 .38 .33

DCF 18% 1.0 .85 .72 .61 .52 .44 .37 .31 .27

Task 4.4


7

Task 4.5

A small to medium sized enterprise (SME) formed by three chemistry graduates, Gray,

Forks and Knight, have won an award for their new power-saving luminous paint, and

now wish to extend their activities to the research and development of other luminous

products. Gray, Forks and Knight have recruited new staff in order to support their

research ideas, and they are now in a position to invest in new computer equipment. Two

options are outlined below.

option 1 to rent 15 computers, including software, etc, at an agreed annual rate per

machine (£320 for the first year, £355 for the next, £390 the following year, then £445

for the year after, and £510 for the final year). This increasing rate has been agreed as it

includes maintenance at no additional charge.

option 2 to purchase 15 computers, with software etc, for £1150 per machine, with

an additional maintenance charge (in the year of purchase: £90 per machine. Charge per

machine for each subsequent year: £100, £110, increasing at the rate of £10 per machine

per year).

The cost of insurance will be 8% of the purchase price, whether renting or purchasing.

Gray, Forks and Knight plan to replace the equipment after five years, with the

expectation that it will have reached the end of its useful life. As approval from the

European Union is required, Gray, Forks and Knight need to provide an analysis of the

options using the DCF factors of 11%, 12%, 15% and 18%, and they have asked you to

undertake this activity.

Use the factors from the table below, and make a recommendation as to whether option 1

or option 2 should be selected. Identify all factors that you consider relevant to the

decision.

DCF Factors

Year 0 1 2 3 4 5 6 7 8

DCF 11% 1.0 .90 .81 .73 .66 .59 .53 .48 .43

DCF 12% 1.0 .89 .80 .71 .64 .57 .51 .45 .40

DCF 15% 1.0 .87 .76 .66 .57 .50 .43 .38 .33

DCF 18% 1.0 .85 .72 .61 .52 .44 .37 .31 .27

Task 4.5


8

Task 4.6

A new company, Midclay and Barland, specialising in independent financial advice, are

planning to set up a computer system to store details about their clients, as well as a web

site with "frequently asked questions" (FAQs) to encourage potential customers.

Midclay and Barland have narrowed the possibilities down to a choice of two (both

proposed by Satisfactory Systems) which they are now evaluating.

option 1 to rent 20 workstations at £400 per machine per annum (the rental

increasing by £50 per machine each year). There is no additional fee for maintenance.

option 2 to purchase 20 workstations for £1500 per machine, with an annual

maintenance charge of £25 per machine starting in the year of purchase.

There is no additional fee for insurance, which has been included in the basic cost of

acquiring the office accommodation. Midclay and Barland have negotiated a deal that

after four years Satisfactory Systems will collect the equipment and pay Midclay and

Barland £500 per workstation, whether the equipment had been rented or purchased.

Satisfactory Systems plan to use these old workstations for spare parts, and a new deal

will then be arranged, as Midclay and Barland plan to replace the equipment at this time.

As financial advisers, Midclay and Barland are keen to establish how the two options

appear over the years ahead, given the variability in interest rates.

You are asked to analyse the options, using the DCF factors of 11%, 12%, 15% and 18%

from the table below. You will need to take into account the income from the collection

of the workstations.

DCF Factors

Year 0 1 2 3 4 5 6 7 8

DCF 11% 1.0 .90 .81 .73 .66 .59 .53 .48 .43

DCF 12% 1.0 .89 .80 .71 .64 .57 .51 .45 .40

DCF 15% 1.0 .87 .76 .66 .57 .50 .43 .38 .33

DCF 18% 1.0 .85 .72 .61 .52 .44 .37 .31 .27

Task 4.6

net present value - examples and exercises - week 4

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