Investment appraisal
• What is “Investment”?
• Investment appraisal
– Using quantitative analysis to analyse whether a capital investment is
worthwhile
– All about CAPITAL COST vs NET CASH FLOW
– For strategic or medium term objectives not tactical decisions.
Methods of Investment Appraisal
• Three methods
– Payback
• How many years and months before the initial cost of
the investment is paid back
– Average rate of return (“ARR”)
• The average annual profit as a percentage of the initial
investment. Comparable with ROCE
– Net present value (“NPV”)
• Total return from an investment in today’s money
(taking into account that money received in the future
is worth less than money now)
Payback
• Measures the length of time it takes to pay back the original cost of an
investment in a new printing machine
• Look at initial investment, then annual cash inflows and outflows, for
example with a printing machine costing £750,000
• Use the information in the first table to complete the second
£
Initial cost
Machine A
Year (£)
750,000
Cash in
Net cash
flow per
year
0
Inflows:
Year 1
180,000
1
Year 2
220,000
2
Year 3
250,000
3
Year 4
250,000
4
Year 5
275,000
5
10,000 per year
Total
Maintenance
Cash out
Note the initial investment is deemed to take
place in year 0
Cumulative
Cash Flow
Payback
•
•
Year
Cash out (£)
Cash in (£)
Net cash flow
(£) per year
Cumulative
Cash Flow
0
750,000
0
(750,000)
-750,000
1
10,000
180,000
170,000
-580,000
2
10,000
220,000
210,000
-370,000
3
10,000
250,000
240,000
-130,000
4
10,000
250,000
240,000
110,000
5
10,000
275,000
265,000
375,000
Total
800,000
1,175,000
375,000
750,000
When does the investment of £750,000 get paid back? Add up all the cash flows
cumulatively until you make a profit
The investment is paid back in the 4th year - When in the 4th year?
– Net cash flow in year 4 is £240,000, or £20,000 per month (assume spread
evenly)
– Require £130,000, so need £130,000/£20,000 which is 6.5 months
– So payback is 3 years 6.5 months
Payback
• Shortcut: If cash flows are constant (eg £360,000 per year for a capital cost
of £750,000), then:
Payback = sum invested/net cash flow.
Answer is 2 years and 1 month (how did we work it out?)
• May be given outflows and inflows, or costs and revenues. Need to work
out net cash flow and put into a table
• Always put investment in Year 0, then work out net inflow for the
following years
• Nearly always based on a finite time period
– Most machinery is expected to last a certain time (and is depreciated)
– Note that whilst questions are based on a finite period, some investment may add
value over a longer period, eg opening a new store
• Very Simple Method
Payback example
• A local garage is considering buying a machine which can refill (re-gas) the
air-conditioning units of customer cars. The estimated costs and revenues
are as follows:
Cost of machinery
£10,000
Cost of gas per service
£15
Wages and other costs per service
£15
Price charged per service
£80
• The garage estimates the number of customers requesting the airconditioning service to be:
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
• Calculate the payback period
40
60
60
60
40
30
Payback example answer
• First need to fill in cash out
and cash in, complicated by
needing to calculate
• Make a positive cumulative
Cashflow by the 4th year
• In year 4 cash flow is £3,000
or £250 per month, but we
just need £2,000. So we
need £2,000/£250 months
• Payback is therefore 3 years
8 months
Year
Cash out Cash in Net cash Cumulati
(£)
(£)
flow (£)
ve
0
10,000
0
(10,000) (10,000)
1
1,200
3,200
2,000
(8,000)
2
1,800
4,800
3,000
(5,000)
3
1,800
4,800
3,000
(2,000)
4
1,800
4,800
3,000
1,000
5
1,200
3,200
2,000
3,000
6
900
2,400
1,500
4,500
Total
18,700
23,200
4,500
Average rate of return
• We can calculate when an investment is paid
back, but does that make it worthwhile?
• Really looking for a high rate of return on the
investment (remember Unit 2????)
• Need to make sure the return covers the cost
of borrowing if using a bank loan, or if there
are other better investments
• Use average rate of return (ARR)
return/number of years)
• ARR (%)= (Total netInitial
x 100
investment
Example
Project X
Capital Cost Yr0
Return Yr 1
Return Yr 2
Return Yr 3
Return Yr 4
Return Yr 5
Total Net
Cashflow
CashFlow
-50,000
10,000
10,000
15,000
15,000
20,000
1. Add up Total Net Cashflow (Done -> £20,000)
2. Divide by the number ofyears toget average
return / year
= £20,000 / 5 = £4,000 average return per year
3. ARR% = £4,000 x 100 = 8%
£50,000
20,000
(Total net return/number of years)
X 100
ARR(%) =
Initial investment
What would the ARR% be for the above project with
returns of £20,000 each year (Years 1 to 5)?
ARR
• Calculate for printing machine
• Calculate for air-conditioning machine
Net present value (NPV) – sometimes called
the time value of money or TVM approach
• Quite sophisticated, and only larger businesses will use this
• ARR does not take into account when the cash flows take
place
• Are cash flows received in 5 years worth the same as cash
flows or payments this year?
• Idea is that £1 today has more value than £1 in the future
– This is because of the opportunity cost of money – can do
something with the £1, such as earn interest. Also, money today
is certain, whilst there is always risk about receiving money in
the future
– For example, at an interest rate of 10%, £100 becomes £110
after 1 year
– In this case, the present value of £110 received in a year’s time
is £100
NPV
• If you could earn 10% interest by putting money in the
bank, which of the following would you prefer:
– £1,000 today or £1,150 in 2 year’s time?
– £50 today or £65 in 3 year’s time?
– £1,000 + 10% of £1,000 is £1,100 in a year’s time,
– £1,100 + 10% of £1,100 is £1,210 in 2 year’s time
– Formula is £1,000 x (1 + 10%) x (1+10%) or £1,000 x
(1+10%)2 which is £1,000 x 1.12
– Advanced: general formula is £1 becomes £1 x (1 + r)n
where r is the rate of interest, and n is the number of years
Example Discount Factors
NPV & Discount Factors
• So putting in reverse, what is £1,150 due in 2 years, worth in
today’s money if interest rates are 10%
• Easiest to calculate a discount factor using £1
DF =
•
•
•
•
•
1__ = __1___ = 0.83
(1 + r)n
(1 + 0.10)²
So the present value of every pound in 2 year’s time is £0.98 today,
which means
£1,150 in 2 year’s time is worth £1,150 x 0.83 = £950
10% is called the discount rate and 0.83 is called the discount factor
Present value is future net cash flow times the discount factor
Exam questions will give the discount factor you should use
NPV example
• Simple example:
– Invest in a machine for £100m, with the following cash
inflows and outflows, and with the following discount
factors (based on a discount rate of 10%):
Year
Cash out (£m)
0
1
2
3
Total
100
10
20
30
160
Cash in (£m)
60
80
100
240
Net cash flow
(£m)
(100)
50
60
70
80
Net cash flow
times
Discount factor Present value (£)
1
0.91
0.83
0.75
discount
factor
equals
(100)
46
50
53
48
present value
NPV practice
• NPV of printing machine
Year
Cash out (£)
Cash in (£)
Net cash flow (£)
Discount
factor
0
750,000
0
(750,000)
1
(750,000)
1
10,000
180,000
170,000
0.91
154,700
2
10,000
220,000
210,000
0.83
174,300
3
10,000
250,000
240,000
0.75
180,000
4
10,000
250,000
240,000
0.68
163,200
5
10,000
275,000
265,000
0.62
164,300
Total
800,000
1,175,000
375,000
Present value (£)
86,500
NPV practice
• NPV of printing machine
Year
Cash out (£)
Cash in (£)
Net cash flow (£)
Discount
factor
0
750,000
0
(750,000)
1
(750,000)
1
10,000
180,000
170,000
0.91
154,700
2
10,000
220,000
210,000
0.83
174,300
3
10,000
250,000
240,000
0.75
180,000
4
10,000
250,000
240,000
0.68
163,200
5
10,000
275,000
265,000
0.62
164,300
Total
800,000
1,175,000
375,000
Present value (£)
86,500
NPV
• NPV is particularly useful comparing alternative
projects/investments as follows
£m
Project 1
Project 2
Year
0
1
2
3
4
5
Total
ARR
Net cash flow Discount factor Present value
(100)
1
(100)
20
0.91
18.2
40
0.83
33.2
40
0.75
30.0
40
0.68
27.2
80
0.62
49.6
120
58.2
30%
Discount factor
1
0.91
0.83
0.75
0.68
0.62
Payback
3 years
(100)
80
60
30
20
10
100
25%
(100)
72.8
49.8
22.5
13.6
6.2
64.9
1 year 4 months
• Can also use different discount rates (discount factor) to
take into account riskiness of projects
The 3 methods
Advantages
Disadvantages
Scientific methodology rather than guesswork
Relies on forecasts, which may be inaccurate –
particularly the further into the future they
are made
Easy to understand
Easy to calculate, particularly useful if
comparing many projects
By emphasising the speed of return it is
popular with firms operating in changing
markets
Ignores cash flows which take place after the
payback period has been reached
Hard to establish a payback period – factories
may take longer to pay back than a marketing
campaign, but still be valuable
Values future cash flows the same as present
ones
ARR
Easy to calculate
The result can be compared with the next
best alternative, eg interest rate
Shows true profitability of an investment
A bit harder to calculate than payback
Values all cash inflows and outflows the same,
whenever they take place (including very
uncertain long term forecasts)
NPV
Only method which considers the time value
of money
Only method which gives an answer – positive
NPV means a project is worthwhile
Cash flows a long time in the future are
uncertain (risky) and are given less weight
Conceptually difficult to understand which
bosses may mistrust
Hard to calculate
Depends on the choice of discount rate –
which may be arbitrary
All
Payback