investment appraisals: estimating uncertainty and exchange rates

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© Copyright QinetiQ Limited 2010

Investment Appraisals: Estimating Uncertainty and Exchange Rates

Paul Duvall Principal Consultant HVR Practice – Through Life Cost Modelling0117 952 8456

Dr Mark GilmourConsultantHVR Practice – Through Life Cost Modelling0117 952 8462

Society for Cost Analysis and Forecasting

9 February 2010

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Sub-Title?

Cost Uncertainty – do we need pure mathematics in IA?

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Contents

1. Introduction

2. Developing assumptions− Every day decisions

3. Assessing Uncertainty

4. Modelling Uncertainty

5. Modelling Foreign Exchange

6. Correlation

A Case Study …

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Investment Appraisals – Common Errors

• Poor Evidence for estimates

• Poor Audit Trail

• Arbitrary Uncertainty Ranges applied (+/-10%)

• No justification for cost spread

• Source: MoD Cost Assurance Guidance 20090626

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…a Case Study…

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CRBS – “In-Service”

CBS Description Non / Recurring

1 Purchase Cost NR2 Insurance R3 Road Licence R4 MOT R5 Road Rescue Membership R6 Spares R7 Fuel R8 Consummables R9 Preventative Maintenance R

10 Unscheduled Maintenance R11 Upgrade (new radio/sat nav etc) NR12 Manual NR13 Tools NR14 Management Cost R15 Parking Fees R16 Disposal Cost NR

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Example CBS

1 structural integrity 20 personnel T&S costs2 Support System Installation 21 Facilities Management - Indirect Support3 power supply upgrade 22 Utilities4 infrastructure modifications 23 disposal5 Buildings 24 CPO (financial)6 Admin - demo 25 equipment costs7 Project / Programme Management 26 equipment costs8 Project / Programme Management 27 equipment costs9 Support (outsourced) 28 equipment costs10 Facility support 29 equipment costs11 manpower 30 equipment costs12 admin - manuf 31 Maintenance Trainer13 admin - in service 32 spares pool 114 unit - exec layer 33 spares pool 215 unit personnel #1 34 additional training16 Fuel 35 T&S costs17 trainers 36 support18 training costs 37 R&D investment19 maintainers

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CLS CBS

Manufacturer Supplied Breakdown

V F1 Inventory Management 20% 80%2 Logs Man System 100%3 Supply & Support 100% 0%4 Sub-contractor's CLS 10% 90%5 Repairs 100% 0%6 Replenishment Spares 100% 0%7 Consumable Spares 100% 0%8 STTE Maintenance 100% 0%9 SW Support 10% 90%

10 CLS Management 10% 90%11ProgManagement 0% 100%12 Training Support 80% 20%13 Obsolescence 0% 100%14 Risk 14% 86%

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Developing Assumptions – Behaviour of the estimate?


1 Purchase Cost NR2 Insurance R3 Road Licence R4 MOT R5 Road Rescue Membership R6 Spares R7 Fuel R8 Consummables R9 Preventative Maintenance R

10 Unscheduled Maintenance R11 Upgrade (new radio/sat nav etc) NR12 Manual NR13 Tools NR14 Management Cost R15 Parking Fees R16 Disposal Cost NR


TLC (Constant)

1 Purchase Cost NR Fixed2 Insurance R Fixed3 Road Licence R Fixed4 MOT R Fixed5 Road Rescue Membership R Fixed6 Spares R Increasing7 Fuel R Fixed8 Consummables R Fixed9 Preventative Maintenance R Increasing

10 Unscheduled Maintenance R Increasing11 Upgrade (new radio/sat nav etc) NR Fixed12 Manual NR Fixed13 Tools NR Fixed14 Management Cost R Fixed15 Parking Fees R Fixed16 Disposal Cost NR Fixed

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Developing Assumptions – Behaviour of the estimate


TLC (Constant) Outturn

1 Purchase Cost NR Fixed N/A2 Insurance R Fixed Hi3 Road Licence R Fixed ML4 MOT R Fixed ML5 Road Rescue Membership R Fixed ML6 Spares R Increasing Hi7 Fuel R Fixed ML8 Consummables R Fixed ML9 Preventative Maintenance R Increasing Hi

10 Unscheduled Maintenance R Increasing Hi11 Upgrade (new radio/sat nav etc) NR Fixed ML12 Manual NR Fixed ML13 Tools NR Fixed ML14 Management Cost R Fixed ML15 Parking Fees R Fixed ML16 Disposal Cost NR Fixed ML


TLC (Constant) Outturn Uncertainty

Range1 Purchase Cost NR Fixed N/A Fixed2 Insurance R Fixed Hi Increasing3 Road Licence R Fixed ML Increasing4 MOT R Fixed ML Increasing5 Road Rescue Membership R Fixed ML Increasing6 Spares R Increasing Hi Increasing7 Fuel R Fixed ML Increasing8 Consummables R Fixed ML Increasing9 Preventative Maintenance R Increasing Hi Increasing

10 Unscheduled Maintenance R Increasing Hi Increasing11 Upgrade (new radio/sat nav etc) NR Fixed ML Increasing12 Manual NR Fixed ML Increasing13 Tools NR Fixed ML Increasing14 Management Cost R Fixed ML Increasing15 Parking Fees R Fixed ML Fixed16 Disposal Cost NR Fixed ML Fixed

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Review – “sanity check”

• Developed a Cost Breakdown Structure of 16 line items

•16 assumptions – Non-Rec/Recurring Cost

•16 assumptions – behaviour of constant cost through life

•16 assumptions – behaviour of cost relative to escalation

•16 assumptions – behaviour of uncertainty range (fixed or variable)

Assuming the CBS is a given

64 assumptions made BEFORE any estimate developed

Are they Catalogued?

Are they Auditable?

Are they Robust?

Will they withstand Scrutiny?

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Case Study SPE

64 items of estimated data or assumptions

CBS Description 2010 2011 2012 2013 2014 2015

1 Purchase Cost 60002 Insurance 500 500 500 500 500 5003 Road Licence 170 170 170 170 170 1704 MOT 45 45 45 45 45 455 Road Rescue Membership 100 100 100 100 100 1006 Spares 300 350 400 450 5007 Fuel 2000 2000 2000 2000 2000 20008 Consummables 30 30 30 30 30 309 Preventative Maintenance 100 150 150 200 200

10 Unscheduled Maintenance 200 200 200 200 200 20011 Upgrade (new radio/sat nav etc) 300 20012 Manual 1513 Tools 5014 Management Cost15 Parking Fees 200 200 200 200 200 20016 Disposal Cost -1000

9310 3945 3945 3795 3895 2945£27,835

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Where to apply uncertainty?

CBS Description 2010 2011 2012 2013 2014 2015 Total1 Purchase Cost 6000 6,0002 Insurance 500 500 500 500 500 500 3,0003 Road Licence 170 170 170 170 170 170 1,0204 MOT 45 45 45 45 45 45 2705 Road Rescue Membership 100 100 100 100 100 100 6006 Spares 300 350 400 450 500 2,0007 Fuel 2000 2000 2000 2000 2000 2000 12,0008 Consummables 30 30 30 30 30 30 1809 Preventative Maintenance 100 150 150 200 200 80010 Unscheduled Maintenance 200 200 200 200 200 200 1,20011 Upgrade (new radio/sat nav etc) 300 200 50012 Manual 15 1513 Tools 50 5014 Management Cost15 Parking Fees 200 200 200 200 200 200 1,20016 Disposal Cost -1000 -1,000

Total 9310 3945 3945 3795 3895 2945 £27,835

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Assessing Uncertainty - Annually?

CBS Description 2010 2011 2012 2013 2014 2015

1 Purchase Cost 60002 Insurance 500 500 500 500 500 5003 Road Licence 170 170 170 170 170 1704 MOT 45 45 45 45 45 455 Road Rescue Membership 100 100 100 100 100 1006 Spares 300 350 400 450 5007 Fuel 2000 2000 2000 2000 2000 20008 Consummables 30 30 30 30 30 309 Preventative Maintenance 100 150 150 200 200

10 Unscheduled Maintenance 200 200 200 200 200 20011 Upgrade (new radio/sat nav etc) 300 20012 Manual 1513 Tools 5014 Management Cost15 Parking Fees 200 200 200 200 200 20016 Disposal Cost -1000

9310 3945 3945 3795 3895 2945£27,835

Min 90% 88% 86% 84% 82% 80%Max 150% 105% 115% 120% 125% 130%

Min 8,379 3,472 3,393 3,188 3,194 2,356 23,981ML 9,310 3,945 3,945 3,795 3,895 2,945 27,835

Max 13,965 4,142 4,537 4,554 4,869 3,829 35,895

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Assessing Uncertainty – Line Item?

CBS Description 2010 2011 2012 2013 2014 2015 Total Min Max Min ML Max

1 Purchase Cost 6000 6,000 90% 125% 5,400 6,000 7,5002 Insurance 500 500 500 500 500 500 3,000 80% 120% 2,400 3,000 3,6003 Road Licence 170 170 170 170 170 170 1,020 100% 110% 1,020 1,020 1,1224 MOT 45 45 45 45 45 45 270 100% 110% 270 270 2975 Road Rescue Membership 100 100 100 100 100 100 600 100% 110% 600 600 6606 Spares 300 350 400 450 500 2,000 75% 150% 1,500 2,000 3,0007 Fuel 2000 2000 2000 2000 2000 2000 12,000 90% 120% 10,800 12,000 14,4008 Consummables 30 30 30 30 30 30 180 50% 150% 90 180 2709 Preventative Maintenance 100 150 150 200 200 800 80% 150% 640 800 1,200

10 Unscheduled Maintenance 200 200 200 200 200 200 1,200 80% 150% 960 1,200 1,80011 Upgrade (new radio/sat nav etc) 300 200 500 90% 150% 450 500 75012 Manual 15 15 95% 105% 14 15 1613 Tools 50 50 90% 110% 45 50 5514 Management Cost15 Parking Fees 200 200 200 200 200 200 1,200 80% 150% 960 1,200 1,80016 Disposal Cost -1000 -1,000 125% 90% -1,250 -1,000 -900

9310 3945 3945 3795 3895 2945 £27,835 23899 27835 35570

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Assessing Uncertainty - Detailed

CBS Description 2010 2011 2012 2013 2014 2015

1 Purchase Cost 90% 6000 125% 6,0002 Insurance 90% 500 110% 88% 500 115% 86% 500 120% 84% 500 125% 82% 500 130% 80% 500 135% 3,0003 Road Licence 100% 170 100% 100% 170 102% 100% 170 105% 100% 170 109% 100% 170 114% 100% 170 120% 1,0204 MOT 98% 45 105% 98% 45 107% 98% 45 110% 98% 45 114% 98% 45 119% 98% 45 125% 2705 Road Rescue Membership 90% 100 125% 92% 100 125% 94% 100 128% 96% 100 130% 98% 100 132% 100% 100 135% 6006 Spares 60% 300 100% 65% 350 125% 70% 400 150% 75% 450 175% 80% 500 200% 2,0007 Fuel 90% 2000 110% 90% 2000 112% 90% 2000 114% 90% 2000 116% 90% 2000 118% 90% 2000 120% 12,0008 Consummables 90% 30 105% 92% 30 115% 94% 30 125% 96% 30 150% 98% 30 175% 100% 30 200% 1809 Preventative Maintenance 95% 100 110% 90% 150 120% 85% 150 130% 80% 200 140% 75% 200 150% 800

10 Unscheduled Maintenance 90% 200 105% 88% 200 115% 86% 200 125% 84% 200 150% 82% 200 175% 80% 200 200% 1,20011 Upgrade (new radio/sat nav etc) 90% 300 150% 90% 200 150% 50012 Manual 90% 15 125% 1513 Tools 90% 50 125% 5014 Management Cost15 Parking Fees 80% 200 150% 80% 200 150% 80% 200 150% 80% 200 150% 80% 200 150% 80% 200 150% 1,20016 Disposal Cost 125% -1000 90% -1000

2010 2011 2012 2013 2014 20158,380 9,310 11,215 3,455 3,945 4,586 3,441 3,945 4,741 3,294 3,795 4,752 3,373 3,895 5,159 2,164 2,945 4,630

24,107 27,835 35,083

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Methods Summarised

Min ML Max Hi-Lo "Mean"Annual 23,981 27,835 35,895 11,914 28,536

Line Item 23,899 27,835 35,570 11,671 28,468Detailed 24,108 27,835 35,083 10,975 28,422

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Uncertainty Output?

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

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Correlation

1 2 3 6Purchase Cost 1 1 0.7 0 -0.1Insurance 2 0.7 1 0 ?Road Licence 3 0 0 1 0Spares 6 -0.1 ? 0 1

Correlation = an assumption based on an assumption?

Looking at a few line items in the Case Study…

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2 Foreign Exchange(Focus on $/£)

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DASA/DESA advice

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

FY09/10 FY10/11 FY11/12 FY12/13 FY13/14

MaxML

MinLinear (Min)

Linear (Max)

Uncertainty Range = +/-45% from FY12/13

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Correlation in Foreign Exchange

09/10 10/11 11/12 12/13 13/14 14/1509/10 1 0.710/11 0.7 1 0.711/12 0.7 1 0.712/13 0.7 1 0.713/14 0.7 1 0.514/15 0.5 1

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$/£ Sep 99 – Jan 10

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

Sep-9

9

Mar-00

Sep-0

0

Mar-01

Sep-0

1

Mar-02

Sep-0

2

Mar-03

Sep-0

3

Mar-04

Sep-0

4

Mar-05

Sep-0

5

Mar-06

Sep-0

6

Mar-07

Sep-0

7

Mar-08

Sep-0

8

Mar-09

Sep-0

9

$/UK £

MeanMode

MedianMin

Max

Source - HM Revenue and Customs: https://www.uktradeinfo.com/index.cfm?task=exchange&lastcountry=usa

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1.200

1.400

1.600

1.800

2.000

2.200

Max

Median

Mean

Min

Spread around Annual Mean: 5% (01/02) to 35% 08/09

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Historic Trend Analysis

Note: £:$

Reviewing trend from 1987 - maximum any year has differed is -17% (2007 : 0.4998 GBP = 1 USD)+15% (2001 : 0.6609 GBP = 1 USD). Over twenty three years: 14 have seen weaker sterling, and 9 stronger. The difference has been less than 10% in 18 years, and greater in only 5.

1.000

2.000

3.000

4.00019

48

1950

1952

1954

1956

1958

1960

1962

1964

1966

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

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Review

• 3-point estimates triple the quantity of cost line items

• Each estimate needs to be an auditable assumption

• Assessing costs prior to importing into SW packages is informative

• Paucity of data is the enemy of detailed analysis

• Correlation of data is building assumptions on assumptions

Therefore..?

• The number of assumptions should be minimised

• Uncertainty analysis should be based similarly on few assumptions

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Summary

“Complexity is not desirable in a cost model. The cost, labour hours, and schedule required to set up and provide data for a complex model may prohibit its effective and timely use in the decision process. Although some analyses will inevitably require complex models, complexity in itself does not lend credibility to a model or its results.”

(UK MINISTRY OF DEFENCE: 20070129- Guidelines For Estimating and Assurance Issue 1 – U)

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investment appraisals: estimating uncertainty and exchange rates

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