Toolbox 7: Economic Feasibility Assessment Methods

Dr. John C. Wright

MIT - PSFC

05 OCT 2010

Introduction We have a working definition of sustainability We need a consistent way to calculate energy costs This helps to make fair comparisons Good news: most energy costs are quantifiable Bad news: lots of uncertainties in the input data

Interest rates over the next 40 years Cost of natural gas over the next 40 years Will there be a carbon tax?

Todays main focus is on economics Goal: Show how to calculate the cost of energy in

cents/kWhr for any given option Discuss briefly the importance of energy gain

3

Basic Economic Concepts

Use a simplified analysis

Discuss return on investment and

inflation

Discuss net present value

Discuss levelized cost

4

The Value of Money The value of money changes with time 40 years ago a car cost $2,500 Today a similar car may cost $25,000 A key question How much is a dollar n years

from now worth to you today? To answer this we need to take into account Potential from investment income while

waiting Inflation while waiting

5

Present Value Should we invest in a power plant? What is total outflow of cash during the plant

lifetime? What is the total revenue income during the

plant lifetime Take into account inflation Take into account rate of return Convert these into todays dollars Calculate the present value of cash outflow Calculate the present value of revenue

6

Net Present Value Present value of cash outflow: PVcost Present value of revenue: PVrev Net present value is the difference

NPV = PVrev PVcost

For an investment to make sense

NPV > 0

7

Present Value of Cash Flow $100 today is worth $100 today obvious How much is $100 in 1 year worth to you today? Say you start off today with $Pi Invest it at a yearly rate of iR%=10% One year from now you have $(1+ iR)Pi=$1.1Pi Set this equal to $100 Then

This is the present value of $100 a year from now

8

$100 $100Pi = = = $90.911 1+ iR .1

Generalize to n years $P n years from now has a present value to

you today of

( )

This is true if you are spending $P n years fronow

This is true for revenue $P you receive n yearsfrom now

Caution: Take taxes into account iR=(1-iTax)iTot

PPV( )P =1+ i nR

9

m

The Effects of Inflation Assume you buy equipment n years from now that costs

$Pn Its present value is

( )

However, because of inflation the future cost of the equipment is higher than todays price

If iI is the inflation rate then

PPV( )P nn = 1+ i nR

P i(1 )nn I= + Pi

10

The Bottom Line Include return on investment and inflation $Pi n years from now has a present value to

you today of

Clearly for an investment to make sense

11

n1+ iPV I = P 1+ i iR

i iR I>

Costing a New Nuclear Power Plant

Use NPV to cost a new nuclear power plant

Goal: Determine the price of electricity that

Sets the NPV = 0

Gives investors a good return

The answer will have the units cents/kWhr

12

Cost Components

The cost is divided into 3 main parts

Total = Capital + O&M + Fuel

Capital: Calculated in terms of hypothetical overnight cost

O&M: Operation and maintenance Fuel: Uranium delivered to your door Busbar costs: Costs at the plant No transmission and distribution costs

13

Key Input Parameters

Plant produces Pe = 1 GWe

Takes TC = 5 years to build

Operates for TP = 40 years

Inflation rate iI = 3%

Desired return on investment iR = 12%

14

Capital Cost

Start of project: Now = 2000 year n = 0

Overnight cost: Pover = $2500M

No revenue during construction

Money invested at iR = 12%

Optimistic but simple

Cost inflates by iI = 3% per year

15

Construction Cost TableYear Construction Present

Dollars Value

2000 500 M 500 M

2001 515 M 460 M

2002 530 M 423 M

2003 546 M 389 M

2004 563 M 358 M

16

Mathematical Formula Table results can be written as

Sum the series

17

T -c nP iover 1+PV I CAP = T i1

C Rn=0 1+

Pover 1BTCPV CAP = = $2129MTC 1B 1+ iB = =I 0.91961+ iR

Operations and Maintenance

O&M covers many ongoing expenses

Salaries of workers

Insurance costs

Replacement of equipment

Repair of equipment

Does not include fuel costs

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Operating and Maintenance Costs

O&M costs are calculated similar to capital cost

One wrinkle: Costs do not occur until operation starts in 2005

Nuclear plant data shows that O&M costs in 2000 are about

P MOM = $95 /yr O&M work the same every year

19

Formula for O&M Costs During any given year the PV of the O&M costs

are

The PV of the total O&M costs are

20

n( )n 1+ iPV I OM = P OM 1+ iR

T +C P

T -1

PV ( )nOM = PVOMn=TC

C P+ 1 1+nT T i = P IOM

n T= C 1+ iR

1BT= =POMB C P

T $750 1B M

Fuel Costs Cost of reactor ready fuel in 2000 KF = $2000/ g Plant capacity factor fc = 0.85 Thermal conversion efficiency I = 0.33 Thermal energy per year

Fuel burn rate B k= 1.08 106 Whr /kg Yearly mass consumption

21

( )( )( )

f Pc eT (0.85) 106kWe 8760hr

W 2.26 1010th = = = WhrI 0.33

WM kth 2.09 104F = = gB

k

k

Fuel Formula Yearly cost of fuel in 2000

P KF F= =MF $41.8M /yr

PV of total fuel costs

22

BTC

1 PPV T F F= =P B $330M 1B

Revenue

Revenue also starts when the plant begins operation

Assume a return of iR = 12%

Denote the cost of electricity in 2000 by COE measured in cents/kWhr

Each year a 1GWe plant produces

W W 74.6 108e t= =I h kWhr

23

Formula for Revenue The equivalent sales revenue in 2000 is

The PV of the total revenue

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( )( )COE (We c) COE f PeTPR = = = ( )$74.6 COE100 100

( ) T

C 1 B 1B

P P

PV T

R R= =P $(74.6M ) COE C

1B

M

1

TT BB

B

Balance the Costs Balance the costs by setting NPV = 0

PVR c= +PV ons PVOM +PVF

This gives an equation for the required COE

25

100 P 1 1BTCOE = + C

over T T P +Pf Pc eT T C P

OM FC B B 1

= 3.61 + 1.27 + 0.56 = 5.4 cents /kWhr

Potential Pitfalls and Errors

Preceding analysis shows method

Preceding analysis highly simplified

Some other effects not accounted for

Fuel escalation due to scarcity

A carbon tax

Subsidies (e.g. wind receives 1.5 cents/kWhr)

26

More More effects not accounted for Tax implications income tax, depreciation Site issues transmission and distribution

costs Cost uncertainties interest, inflation rates O&M uncertainties mandated new

equipment Decommissioning costs By-product credits heat Different fc base load or peak load?

27

Economy of Scale An important effect not included Can be quantified Basic idea bigger is better Experience has shown that

Typically

28

C Ccap ref PB

ref = P P e ref Pe

B x 1/3

Why?

Consider a spherical tank

Cost v Material v Surface area: C Rr 4Q 2

Power v Volume: P Rr (4 / 3)Q 3

COE scaling: C P/ 1r r/ 1R /P1/3 Conclusion:

This leads to plants with large output power

29

1BCcap Pe = C Pref ref

The Learning Curve

Another effect not included

The idea build a large number of identical units

Later units will be cheaper than initial units

Why? Experience + improved construction

Empirical evidence cost of nth unit

C Cn = 1nC

f = improvement factor / unit: o

ln fC xln 2

f 0.85 C = 0.23

30

An example Size vs. Learning

Build a lot of small solar cells (learning curve)?

Or fewer larger solar cells (economy of scale)?

Produce a total power Pe with N units

Power per unit: pe = Pe/N

Cost of the first unit with respect to a known reference

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1Bp N1B

C C ref1 = =ref C p Nref ref

Example cont. Cost of the nth unit

Total capital cost: sum over separate units

If we want a few large units Its a close call need a much more accurate calculation

C CN1 B

C C refn r= =1n C ef n N

BN N N N1 1 NC C= =C ref cap n ref nC xC refref n dn

1n n= =1 1 N N

C N 1C= ref ref N NB C r B C

1 C

B C>

32

BC

Dealing With Uncertainty

Accurate input data o accurate COE estimate Uncertain data o error bars on COE Risk v size of error bars Quantify risk o calculate COE standard deviation Several ways to calculate V, the standard deviatiation

Analytic method

Monte Carlo method

Fault tree method

We focus on analytic method

33

The Basic Goal

Assume uncertainties in multiple pieces of data

Goal: Calculate V for the overall COE including all uncertainties

Plan:

Calculate V for a single uncertainty Calculate V for multiple uncertainties

34

The Probability Distribution Function

Assume we estimate the most likely cost for a given COE contribution.

E.g. we expect the COE for fuel to cost C = 1 cent/kWhr Assume there is a bell shaped curve around this value The width of the curve measures the uncertainty This curve P(C) is the probability distribution function It is normalized so that its area is equal to unity

dP C( )dC = 1

0

The probability is 1 that the fuel will cost something

35

The Average Value The average value of the cost is just

The normalized standard deviation is defined by

A Gaussian distribution is a good model for P(C)

d

C C= P ( )C dC0

1 d0( )

1/2

T = C C 2 P ( )C dCC

( )( )

( )( )

C C 2 1 P C = 1/2 exp 2Q TC 2 TC 2

36

Multiple Uncertainties

Assume we know C and for each uncertain cost.

The values of C are what we used to determine COE.

Specically the total average cost is the sum of the separate costs:

C Tot =

Cj Pj (Cj )dCj = C j . j

The total standard deviation is the root of quadratic sum of the separate contributions (assuming independence of the Cj ) again normalized to the mean:

(C j j )2 jTot =

j C j

Uncertainties

37 SE T-6 Economic Assessment

Multiple Uncertainties

An Example

We need weighting - why?

Low cost entities with a large standard deviation do not have much eect of the total deviation

Consider the following example Ccap = 3.61, c = 0.1 CO&M = 1.27, OM = 0.15 Cfuel = 0.56, f = 0.4

Uncertainties Nuclear Power

38 SE T-6 Economic Assessment

An Example

Example Continued

The total standard deviation is then given by (c C cap)2 + ( OMC 2 2 O&M ) + (f C fuel )

= C cap + C O&M + C fuel

0.130 + 0.0363 + 0.0502 = = 0.086

5.4

Large f has a relatively small eect.

Why is the total uncertainty less than the individual ones? (Regression to the mean)

Uncertainties Nuclear Power

39 SE T-6 Economic Assessment

Example Continued

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Toolbox 1OutlineIntroductionBasic Economic ConceptsThe Value of MoneyPresent ValueNet Present ValuePresent Value of Cash FlowGeneralize to n yearsThe Effects of InflationThe Bottom LineCosting a New Nuclear Power PlantCost ComponentsKey Input ParametersCapital CostConstruction Cost TableMathematical FormulaOperations and MaintenanceOperating and Maintenance CostsFormula for O&M CostsFuel CostsFuel FormulaRevenueFormula for RevenueBalance the CostsPotential Pitfalls and ErrorsMoreEconomy of ScaleWhy?The Learning CurveAn example Size vs. LearningExample cont.Dealing With UncertaintyThe Basic GoalThe Probability Distribution FunctionThe Average Value