©a. ward 2002 capital expenditure appraisal cash flow - revisited accounting rate of return payback...

©A. Ward 2002

Capital Expenditure Appraisal

• Cash Flow - revisited

• Accounting Rate of Return

• Payback Period

• DCF Techniques

• Net Present Value

• Sensitivity Analysis

©A. Ward 2002

Cash Flow Profile

-80

-60

-40

-20

0

20

40

60

80

Investment

Return

NetCashFlow

Time

Major long-term capital investment project.

©A. Ward 2002

Cash Flow Profile

-150

-100

-50

0

50

100

150

Investment

Return

NetCashFlow

Time

Periodic replacement with increasing prices.

©A. Ward 2002

Cash Flow Profile

-80

-60

-40

-20

0

20

40

60

80

InvestmentReturn

NetCashFlow

Time

Investment with cyclical cash flows

©A. Ward 2002

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

• Purchase of Plant or Machinery

• Purchase of Land

• Development of a New Product

• Installation of a New Computer System

• etc.

©A. Ward 2002

Capital Expenditure Appraisal - Objectives

• whether a particular capital expenditure proposal is justified in terms of the expected benefits

• if there are alternative proposals which should be undertaken

©A. Ward 2002

Analysis of Options - Example

Project A Project B Project C

Initial Cost (£) 100000 100000 100000

Expected Cash Inflow (£)

Year 1 15000 30000 30000Year 2 25000 30000 30000Year 3 30000 30000 30000Year 4 30000 30000 30000Year 5 30000 25000 0Year 6 30000 15000 0

Total 160000 160000 120000

©A. Ward 2002

Accounting Rate of Return

• Surplus = Cash Inflow - (Initial Investment - Residual Value)

• Average Investment = (Initial Investment - Residual Value)/2

©A. Ward 2002

Cash Inflow Stream

• 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.

©A. Ward 2002

Payback Period (Breakeven)

Recognises the time value of money

Cash Stream

Time (Years)

-100

-50

0

50

100

0 1 2 3 4 5 6

Project A

Project B

Project C

©A. Ward 2002

Limitations

• Accounting Rate of Return

- Ignores the time value of money

• Payback Period

- Ignores cash after Breakeven

• There has to be a better way! There is!

©A. Ward 2002

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

• Based on Investment Criteria - ignore risk & inflation

©A. Ward 2002

Discounted Cash Flow (DCF)

• 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

©A. Ward 2002

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:

• Solve by spreadsheet or Discount Tables

• Note this ignores future inflation rates. The model allows for varying interest rates per year.

NPVP

r n

( )^1

©A. Ward 2002

Discount Factors

Years 1 2 3 4 5 6 7 8 9 101% 0.990099 0.980296 0.97059 0.96098 0.951466 0.942045 0.932718 0.923483 0.91434 0.9052872% 0.980392 0.961169 0.942322 0.923845 0.905731 0.887971 0.87056 0.85349 0.836755 0.8203483% 0.970874 0.942596 0.915142 0.888487 0.862609 0.837484 0.813092 0.789409 0.766417 0.7440944% 0.961538 0.924556 0.888996 0.854804 0.821927 0.790315 0.759918 0.73069 0.702587 0.6755645% 0.952381 0.907029 0.863838 0.822702 0.783526 0.746215 0.710681 0.676839 0.644609 0.6139136% 0.943396 0.889996 0.839619 0.792094 0.747258 0.704961 0.665057 0.627412 0.591898 0.5583957% 0.934579 0.873439 0.816298 0.762895 0.712986 0.666342 0.62275 0.582009 0.543934 0.5083498% 0.925926 0.857339 0.793832 0.73503 0.680583 0.63017 0.58349 0.540269 0.500249 0.4631939% 0.917431 0.84168 0.772183 0.708425 0.649931 0.596267 0.547034 0.501866 0.460428 0.422411

10% 0.909091 0.826446 0.751315 0.683013 0.620921 0.564474 0.513158 0.466507 0.424098 0.38554311% 0.900901 0.811622 0.731191 0.658731 0.593451 0.534641 0.481658 0.433926 0.390925 0.35218412% 0.892857 0.797194 0.71178 0.635518 0.567427 0.506631 0.452349 0.403883 0.36061 0.32197313% 0.884956 0.783147 0.69305 0.613319 0.54276 0.480319 0.425061 0.37616 0.332885 0.29458814% 0.877193 0.769468 0.674972 0.59208 0.519369 0.455587 0.399637 0.350559 0.307508 0.26974415% 0.869565 0.756144 0.657516 0.571753 0.497177 0.432328 0.375937 0.326902 0.284262 0.24718516% 0.862069 0.743163 0.640658 0.552291 0.476113 0.410442 0.35383 0.305025 0.262953 0.22668417% 0.854701 0.730514 0.624371 0.53365 0.456111 0.389839 0.333195 0.284782 0.243404 0.20803718% 0.847458 0.718184 0.608631 0.515789 0.437109 0.370432 0.313925 0.266038 0.225456 0.19106419% 0.840336 0.706165 0.593416 0.498669 0.419049 0.352142 0.295918 0.248671 0.208967 0.17560220% 0.833333 0.694444 0.578704 0.482253 0.401878 0.334898 0.279082 0.232568 0.193807 0.161506

©A. Ward 2002

Net Present Value of a Cash Stream

To handle a regular or periodic cash stream (in or out):

• 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

©A. Ward 2002

NPV Example

Project A Project B Project C

Initial Cost (£) 100000 100000 100000

Expected Cash Inflow (£)

Year 1 15000 30000 30000Year 2 25000 30000 30000Year 3 30000 30000 30000Year 4 30000 30000 30000Year 5 30000 25000 0Year 6 30000 15000 0

Total 160000 160000 120000

©A. Ward 2002

NPV Example

Year 0 1 2 3 4 5 6DCF 1 0.892857 0.797194 0.71178 0.635518 0.567427 0.506631

Project A -100000 15000 25000 30000 30000 30000 30000PV -100000 13392.86 19929.85 21353.41 19065.54 17022.81 15198.93NPV 5963.393

Project B -100000 30000 30000 30000 30000 25000 15000PV -100000 26785.71 23915.82 21353.41 19065.54 14185.67 7599.467NPV 12905.62

Project C -100000 30000 30000 30000 30000PV -100000 26785.71 23915.82 21353.41 19065.54 0 0NPV -8879.52

©A. Ward 2002

Sensitivity Analysis

• Capital Expenditure Proposals involve assumptions

• Each Assumption can be tested

• The sensitivity of the IRR or NPV can be determined for each assumption

©A. Ward 2002

Sensitivity Analysis - Example

Consider a +/-10% change in initial cost of project

Year 0 1 2 3 4 5 6DCF 1 0.892857 0.797194 0.71178 0.635518 0.567427 0.506631

Project B -100000 30000 30000 30000 30000 25000 15000PV -100000 26785.71 23915.82 21353.41 19065.54 14185.67 7599.467NPV 12905.62 IRR 16.81%



©A. Ward 2002


Consider the effect of a year delay in sales

Or 1 year delay in entire project

Year 0 1 2 3 4 5 6 7DCF 1 0.892857 0.797194 0.71178 0.635518 0.567427 0.506631 0.452349


Project B -100000 0 30000 30000 30000 30000 25000 15000PV -100000 0 23915.82 21353.41 19065.54 17022.81 12665.78 6785.238NPV -5976.65 IRR 12%

Project B -100000 30000 30000 30000 30000 25000 15000PV 0 -89285.7 23915.82 21353.41 19065.54 17022.81 12665.78 6785.238NPV 4737.636 IRR 17%

©A. Ward 2002


Consider interest rate changes

Interest Rate NPV

5% 37159.906% 33209.037% 29436.138% 25830.939% 22383.89

10% 19086.1111% 15929.2712% 12905.6213% 10007.9214% 7229.3815% 4563.68

©a. ward 2002 capital expenditure appraisal cash flow - revisited accounting rate of return payback...

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