Capital Expenditure Appraisal
©A. Ward 2002
•
Cash Flow - revisited
•
Accounting Rate of Return
•
Payback Period
•
DCF Techniques
•
Net Present Value
•
Sensitivity Analysis
Cash Flow Profile
Major long-term capital investment project.
Net
Cash
Flow
80
60
40
20
0
Time
-20
-40
-60
-80
©A. Ward 2002
Investment
Return
Cash Flow Profile
Periodic replacement with increasing prices.
Net
150
Cash
Flow 100
50
0
Time
-50
-100
-150
©A. Ward 2002
Investment
Return
Cash Flow Profile
Investment with cyclical cash flows
Net
Cash
Flow
80
60
40
20
0
Time
-20
-40
-60
-80
©A. Ward 2002
Investment
Return
Capital Expenditure - Definition
“Funds spent in the expectation of securing a
stream of benefits, which may take some time to
start flowing and which may last for some years.”
The amount spent is very often substantial.
©A. Ward 2002
Capital Expenditure - Examples
©A. Ward 2002
•
Purchase of Plant or Machinery
•
Purchase of Land
•
Development of a New Product
•
Installation of a New Computer System
•
etc.
Capital Expenditure Appraisal Objectives
©A. Ward 2002
•
whether a particular capital expenditure
proposal is justified in terms of the
expected benefits
•
if there are alternative proposals which
should be undertaken
Analysis of Options - Example
Project A Project B Project C
Initial Cost (£)
100000
100000
100000
15000
25000
30000
30000
30000
30000
30000
30000
30000
30000
25000
15000
30000
30000
30000
30000
0
0
160000
160000
120000
Expected Cash Inflow (£)
Year
Year
Year
Year
Year
Year
Total
©A. Ward 2002
1
2
3
4
5
6
Accounting Rate of Return
•
Surplus = Cash Inflow - (Initial Investment - Residual Value)
•
Average Investment = (Initial Investment - Residual Value)/2
©A. Ward 2002
Cash Inflow Stream
©A. Ward 2002
•
Total net cash flow is identical
•
Pattern of cash inflow is different
•
There is less risk associated with cash
received early, compared to that received
later
•
The earlier that cash is received the quicker
it can be recycled into new cash generating
ventures (or used to pay-off debts)
•
Accounting Rate of Return ignores the time
value of money.
Payback Period (Breakeven)
Recognises the time value of money
©A. Ward 2002
Limitations
•
Accounting Rate of Return
- Ignores the time value of money
•
Payback Period
- Ignores cash after Breakeven
•
©A. Ward 2002
There has to be a better way! There is!
Discounted Cash Flow (DCF)
•
Basic Principle is that the value of money changes with
time.
Example :
£100 invested at 10% interest rate
is worth £110 in 1 year, £121
Thus £100 now is worth just the same as £121 next year
•
©A. Ward 2002
Based on Investment Criteria - ignore risk & inflation
Discounted Cash Flow (DCF)
©A. Ward 2002
•
Decision :
•
Is it worth making a £100 “investment”
now to generate a £130 of future value at
the end of 2 years?
•
To answer we need to make a Net Present
Value calculation
Net Present Value (NPV)
•
Given an interest rate of 10% what investment now will give
a future value of £130 in 2 years time?
? invested now is worth ?*(1+0.1) in 1 years time
?*(1+0.1) becomes worth ?*(1+0.1)*(1+0.1) in 2 years time
Hence ?*(1+0.1)*(1+0.1) = £130
? = £107.44
©A. Ward 2002
Net Present Value (NPV)
•
In General
•
The Net Present Value of a return of £P in n years time with
a prevailing interest rate of r% is given by:
P
NPV 
(1  r )^ n
•
Solve by spreadsheet or Discount Tables
•
Note this ignores future inflation rates. The model allows for
varying interest rates per year.
©A. Ward 2002
Discount Factors
Years
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
15%
16%
17%
18%
19%
20%
©A. Ward 2002
1
0.990099
0.980392
0.970874
0.961538
0.952381
0.943396
0.934579
0.925926
0.917431
0.909091
0.900901
0.892857
0.884956
0.877193
0.869565
0.862069
0.854701
0.847458
0.840336
0.833333
2
0.980296
0.961169
0.942596
0.924556
0.907029
0.889996
0.873439
0.857339
0.84168
0.826446
0.811622
0.797194
0.783147
0.769468
0.756144
0.743163
0.730514
0.718184
0.706165
0.694444
3
0.97059
0.942322
0.915142
0.888996
0.863838
0.839619
0.816298
0.793832
0.772183
0.751315
0.731191
0.71178
0.69305
0.674972
0.657516
0.640658
0.624371
0.608631
0.593416
0.578704
4
0.96098
0.923845
0.888487
0.854804
0.822702
0.792094
0.762895
0.73503
0.708425
0.683013
0.658731
0.635518
0.613319
0.59208
0.571753
0.552291
0.53365
0.515789
0.498669
0.482253
5
0.951466
0.905731
0.862609
0.821927
0.783526
0.747258
0.712986
0.680583
0.649931
0.620921
0.593451
0.567427
0.54276
0.519369
0.497177
0.476113
0.456111
0.437109
0.419049
0.401878
6
0.942045
0.887971
0.837484
0.790315
0.746215
0.704961
0.666342
0.63017
0.596267
0.564474
0.534641
0.506631
0.480319
0.455587
0.432328
0.410442
0.389839
0.370432
0.352142
0.334898
7
0.932718
0.87056
0.813092
0.759918
0.710681
0.665057
0.62275
0.58349
0.547034
0.513158
0.481658
0.452349
0.425061
0.399637
0.375937
0.35383
0.333195
0.313925
0.295918
0.279082
8
0.923483
0.85349
0.789409
0.73069
0.676839
0.627412
0.582009
0.540269
0.501866
0.466507
0.433926
0.403883
0.37616
0.350559
0.326902
0.305025
0.284782
0.266038
0.248671
0.232568
9
0.91434
0.836755
0.766417
0.702587
0.644609
0.591898
0.543934
0.500249
0.460428
0.424098
0.390925
0.36061
0.332885
0.307508
0.284262
0.262953
0.243404
0.225456
0.208967
0.193807
10
0.905287
0.820348
0.744094
0.675564
0.613913
0.558395
0.508349
0.463193
0.422411
0.385543
0.352184
0.321973
0.294588
0.269744
0.247185
0.226684
0.208037
0.191064
0.175602
0.161506
Net Present Value of a Cash
Stream
To handle a regular or periodic cash stream (in or out):
©A. Ward 2002
•
Determine the periodic cash flow
•
Convert each cash flow to the net present
value
•
Sum all present values to give Net Present
Value of Stream
NPV Example
Project A Project B Project C
Initial Cost (£)
100000
100000
100000
15000
25000
30000
30000
30000
30000
30000
30000
30000
30000
25000
15000
30000
30000
30000
30000
0
0
160000
160000
120000
Expected Cash Inflow (£)
Year
Year
Year
Year
Year
Year
Total
©A. Ward 2002
1
2
3
4
5
6
NPV Example
Year
DCF
©A. Ward 2002
0
1
2
1 0.892857 0.797194
3
4
5
6
0.71178 0.635518 0.567427 0.506631
Project A
PV
NPV
-100000
15000
25000
30000
30000
30000
30000
-100000 13392.86 19929.85 21353.41 19065.54 17022.81 15198.93
5963.393
Project B
PV
NPV
-100000
30000
30000
30000
30000
25000
15000
-100000 26785.71 23915.82 21353.41 19065.54 14185.67 7599.467
12905.62
Project C
PV
NPV
-100000
30000
30000
30000
30000
-100000 26785.71 23915.82 21353.41 19065.54
-8879.52
0
0
Sensitivity Analysis
©A. Ward 2002
•
Capital Expenditure Proposals involve
assumptions
•
Each Assumption can be tested
•
The sensitivity of the IRR or NPV can be
determined for each assumption
Sensitivity Analysis - Example
Consider a +/-10% change in initial cost of project
Year
DCF
©A. Ward 2002
0
1
2
1 0.892857 0.797194
3
4
5
6
0.71178 0.635518 0.567427 0.506631
Project B
PV
NPV
-100000
30000
30000
30000
30000
25000
15000
-100000 26785.71 23915.82 21353.41 19065.54 14185.67 7599.467
12905.62
IRR
16.81%
Project B
PV
NPV
-110000
30000
30000
30000
30000
25000
15000
-110000 26785.71 23915.82 21353.41 19065.54 14185.67 7599.467
2905.619
IRR
13.00%
Project B
PV
NPV
-90000
30000
30000
30000
30000
25000
15000
-90000 26785.71 23915.82 21353.41 19065.54 14185.67 7599.467
22905.62
IRR
21.31%
Sensitivity Analysis - Example
Consider the effect of a year delay in sales
Or 1 year delay in entire project
Year
DCF
©A. Ward 2002
0
1
2
1 0.892857 0.797194
3
4
5
6
7
0.71178 0.635518 0.567427 0.506631 0.452349
Project B
PV
NPV
-100000
30000
30000
30000
30000
25000
15000
-100000 26785.71 23915.82 21353.41 19065.54 14185.67 7599.467
12905.62
IRR
16.81%
Project B
PV
NPV
-100000
-100000
-5976.65
0
30000
30000
30000
30000
25000
15000
0 23915.82 21353.41 19065.54 17022.81 12665.78 6785.238
IRR
12%
Project B
PV
NPV
0
4737.636
-100000
30000
30000
30000
30000
25000
15000
-89285.7 23915.82 21353.41 19065.54 17022.81 12665.78 6785.238
IRR
17%
Sensitivity Analysis - Example
Consider interest rate changes
Interest Rate
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
15%
©A. Ward 2002
NPV
37159.90
33209.03
29436.13
25830.93
22383.89
19086.11
15929.27
12905.62
10007.92
7229.38
4563.68