1. 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.

2. 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)

3. 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
Year (£)
Cash in
Cash out
Net cash flow per year
Cumulative Cash Flow 1 2 3 4 5
Total
Note the initial investment is deemed to take place in year 0
Machine A
Initial cost
750,000
Inflows:
Year 1
180,000
Year 2
220,000
Year 3
250,000
Year 4
Year 5
275,000
Maintenance
10,000 per year

4. Net cash flow (£) per year
Payback
Year
Cash out (£)
Cash in (£)
Net cash flow (£) per year
Cumulative Cash Flow
750,000
(750,000)
-750,000 1
10,000
180,000
170,000
-580,000 2
220,000
210,000
-370,000 3
250,000
240,000
-130,000 4
110,000 5
275,000
265,000
375,000
Total
800,000
1,175,000
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

5. Payback Very Simple Method
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

6. 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:
The garage estimates the number of customers requesting the air-conditioning service to be:
Calculate the payback period
Cost of machinery
£10,000
Cost of gas per service
£15
Wages and other costs per service
Price charged per service
£80
Year 1 40
Year 2 60
Year 3
Year 4
Year 5
Year 6 30

7. 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 flow (£)
Cumulative
10,000
(10,000) 1
1,200
3,200
2,000
(8,000) 2
1,800
4,800
3,000
(5,000) 3
(2,000) 4
1,000 5 6
900
2,400
1,500
4,500
Total
18,700
23,200

8. (Total net return/number of years)
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)
ARR (%)= x 100
(Total net return/number of years)
Initial investment

9. (Total net return/number of years)
Example
Add up Total Net Cashflow (Done -> £20,000)
Divide by the number ofyears toget average return / year
= £20,000 / 5 = £4,000 average return per year
ARR% = £4,000 x 100 = 8%
£50,000
(Total net return/number of years)
Initial investment
X 100
ARR(%) =
What would the ARR% be for the above project with returns of £20,000 each year (Years 1 to 5)?

10. ARR Calculate for printing machine
Calculate for air-conditioning machine

11. 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

12. 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, % of £1,000 is £1,100 in a year’s time,
£1, % 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

13. Example Discount Factors

14. 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___ = 0.83
(1 + r)n ( )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

15. 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)
Cash in (£m)
Net cash flow (£m)
Discount factor
Present value (£)
100
(100) 1 10 60 50
0.91 46 2 20 80
0.83 3 30 70
0.75 53
Total
160
240 48
discount
factor
Net cash flow
times
equals
present value

16. NPV practice NPV of printing machine Year Cash out (£) Cash in (£)
Net cash flow (£)
Discount factor
Present value (£)
750,000
(750,000) 1
10,000
180,000
170,000
0.91
154,700 2
220,000
210,000
0.83
174,300 3
250,000
240,000
0.75 4
0.68
163,200 5
275,000
265,000
0.62
164,300
Total
800,000
1,175,000
375,000
86,500

17. NPV practice NPV of printing machine Year Cash out (£) Cash in (£)
Net cash flow (£)
Discount factor
Present value (£)
750,000
(750,000) 1
10,000
180,000
170,000
0.91
154,700 2
220,000
210,000
0.83
174,300 3
250,000
240,000
0.75 4
0.68
163,200 5
275,000
265,000
0.62
164,300
Total
800,000
1,175,000
375,000
86,500

18. NPV
NPV is particularly useful comparing alternative projects/investments as follows
Can also use different discount rates (discount factor) to take into account riskiness of projects £m
Project 1
Project 2
Year
Net cash flow
Discount factor
Present value
(100) 1 20
0.91
18.2 80
72.8 2 40
0.83
33.2 60
49.8 3
0.75
30.0 30
22.5 4
0.68
27.2
13.6 5
0.62
49.6 10
6.2
Total
120
58.2
100
64.9
ARR
30%
25%
Payback
3 years
1 year 4 months

19. The 3 methods Advantages Disadvantages All
Scientific methodology rather than guesswork
Relies on forecasts, which may be inaccurate – particularly the further into the future they are made
Payback
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