PJ
August 21 2006
Pall Jensson, Professor
Faculty of Engineering
University of Iceland
pall@hi.is
Profitability Assessment Model
Reykjavik, Iceland, August 21, 2006
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PJ
August 21 2006
1. Introduction
This paper describes a computer model of profitability analysis. It has been developed with
investments in small and middle scale industries in mind. The computer model has been used
widely in feasibility studies in Iceland as well as other countries. It should also be mentioned
that the model forms the basis for a course on profitability assessment. There the participants
actually develop the model themselves during the course.
A profitability analysis model as described in here can be defined as a simulation model of an
initial investment and subsequent operations. The cash flow from operations must be
estimated carefully on the basis of a thorough business plan. The cash flow and the
development of balance sheet is then simulated over the lifetime of the investment. The model
is based on given assumptions which are deterministic, however random variables (for
example normally distributed) reflecting uncertain factors can easily be added. The time unit
is a year, so we have a deterministic, yearly simulation of company operations. A typical
example of a cash flow series calculated by a model like this could look as Fig. 1 shows.
Cash Flow Series
300.0
200.0
100.0
0.0
2005
2007
2009
2011
2013
2015
-100.0
-200.0
Total Cash Flow & Capital
-300.0
-400.0
Net Cash Flow & Equity
-500.0
Fig. 1: An example of Cash Flow Series for a planned investment
The model can be used in many ways besides evaluating investment projects. It is a kind of a
laboratory allowing studies of for example taxation, dividend payments, etc. What-if
questions can be asked to analyse different company policies or governmental regulations.
Several companies in Iceland have actually used a model of this type as a yearly or quarterly
cash flow forecasting system.
The main components of the model are shown in Fig. 2. The discussion in the following is
organized in sections according to this structure. Each component is implemented in a
separate Excel sheet in the same workbook.
In the case used in this description we will assume one year of construction and investment,
and after that 10 years of operational lifetime. These assumptions can of course be changed
easily in the Excel model.
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PJ
August 21 2006
The Excel Model for Profitability Analysis
Model Components
Assumptions
Summary
Results and
Sensitivity
Investment
Revenue
Operating Costs
Scenario Summary
Sensitivity Chart
Investment
Revenue and Costs
Investment and
Financing
Investment
Depreciation
Financing
Repayment
Interest
Operating
Statement
Depreciation
Interest
Revenue and Costs
Taxation
Appropriation of profit
Taxes
Net Profit/Loss
Stock
Dividend
Cash Flow
Operating Surplus
Paid Taxes
Repaym. & Interest
Paid Dividend
Balance Sheet
Work.Cap.Changes
Assets (Current, Fixed)
Debt (Short, Long)
Equity (Shares, Other)
Cash Movements
Cash Flow
Profitability
Measures
Project, Equity:
Net Present Value
Internal Rate of Return
Financial Ratios
Graphs and Charts
NPV
IRR
Profitability (NPV, IRR)
Financial Ratios
Cost Breakdown
Fig. 2: The main components of the Profitability Model
and their relationships
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PJ
August 21 2006
2. Assumptions and Results
This component of the model is for the input of the assumptions for the calculations to follow.
Also, the main results of the profitability analysis are shown here. If needed, additional
assumptions sheets can be inserted before this sheet for details like for example a breakdown
of the Investment Costs and of Operational Costs, as is done in our case study. The colour
code used is blue for input cells and yellow for results. We note that all subsequent
components are based on these assumptions sheets and contain only formulas but no input
cells at all.
In the left part of the Assumptions and Results Summary sheet the assumptions are stated,
including the investment costs. The top section to the right also includes the main results, i.e.
the Net Present Value (NPV) and the Internal Rate of Return (IRR) for the project, so that
these can be seen on the same sheet as the main assumptions.
The case study used here is based on the following assumptions regarding investment costs:
Initial Costs Estimates
Case Study Example
Traditional Method
estimating contingencies:
Most likely
Buildings:
estimate
Land, roads etc
20 MUSD
Water wells & ditches
5
"
Farm house & Store
20
"
Contingencies
5
"
Buildings Total:
50
"
Equipment:
Construct ponds
Tanks
Pumps & pipes
Feeding Equipment
Contingencies
Equipment Total:
Other Investment:
Consultation
Design
Contingencies
Other Inv. Total:
Total Investment:
130
10
15
25
20
200
"
"
"
"
"
"
10
35
5
50
"
300
"
"
"
The totals of these estimates, for buildings 50 MUSD, equipment 200 MUSD and other
investment 50 MUSD, is brought to the top of the Assumptions and Results Summary sheet.
Another estimation method, addressing the uncertainties in a more advanced way, the Three
Point Method, is described in Supplement 1.
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PJ
August 21 2006
The Operational Cost Estimates are as follows:
Operational Costs Estimates
Case Study Example
Variable Costs:
Raw Materials
Labour Cost
Transportation
Variable Cost Total
1.4 KUSD/ton
1.2
"
0.4
"
3
"
Fixed Costs:
Maintenance
Housing
Management
Sales
Fixed Costs Total
5 MUSD/year
3
9
"
3
"
20
"
The cost estimate totals are brought to the Summary sheet shown below.
The Summary of Assumptions and Results of model calculations looks like this:
Assumptions and Results
2005
Investment:
Buildings
Equipment
Other
Total
Financing:
Working Capital
Total Financing
Equity
Loan Repayments
Loan Interest
Operations:
Sales Quantity
Sales Price
Variable Cost
Fixed Cost
Inventory Build-up
Debtors
Creditors
Income Tax
Dividend
Depreciation Buildings
Depreciation Equipm.
Depreciation Other
Loan Managem. Fees
100%
100%
100%
100%
100%
100%
100%
100%
25%
15%
18%
30%
4%
15%
20%
2%
Discounting Rate
Planning Horizon
50 MUSD
200
"
50
"
300
"
NPV of Cash Flow
Internal Rate
Capital/Equity
145
"
after 10 years
445
"
30%
6 years
12%
2006
2007
2008
ton/year
5.0
10.0
15.0
KUSD/ton
6.0
12.0
14.0
3 KUSD/ton
20 MUSD/year
45
of turnover
of variable cost
of taxable profit
of profit after tax
15%
10 years
Total Cap.
139.1
21.0%
Equity
158.1
26.3%
6.5
2009
20.0
15.0
2010
20.0
15.0
Colour Code:
Blue: Assumptions
Yellow: Results
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August 21 2006
3. Investments and Financing
Next component of the model is called Investment and Financing. First there is the assumed
breakdown of the investment cost into Buildings, Equipment and Other Investment
(Engineering and Diverse Start-up Costs).
Depreciation is calculated in this analysis mainly with the purpose of getting an accurate
estimate of income tax. The depreciation is calculated here with the straight-line method.
Buildings are depreciated by 4 % each year, machines by 15 % and other investment by 20 %.
Note that equipment is only depreciated by 90% down to 10% of original value.
Financing is assumed to be paid equity on one hand, which is 30% of the total capital, and the
drawdown of a single loan on the other hand. In our case the repayment period of this loan is
only 6 years with a one year grace period (year 2006) and the loan interest is 12 %. The
calculation of interest is based on the principal at the end of the last year. We assume a loan
management fee of 2%.
In our case study the total investment is assumed to be 300 MUSD; however the total capital
needed is higher. The difference is the estimated need for Working Capital, the method to do
that estimate will be described later.
Investment
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
1
2
3
4
5
6
7
8
9
10
50.0
200.0
50.0
300.0
48.0
170.0
40.0
258.0
46.0
140.0
30.0
216.0
44.0
110.0
20.0
174.0
42.0
80.0
10.0
132.0
40.0
50.0
0.0
90.0
38.0
20.0
0.0
58.0
36.0
20.0
0.0
56.0
34.0
20.0
0.0
54.0
32.0
20.0
0.0
52.0
30.0
20.0
0.0
50.0
0.0
2.0
30.0
10.0
42.0
2.0
30.0
10.0
42.0
2.0
30.0
10.0
42.0
2.0
30.0
10.0
42.0
2.0
30.0
10.0
42.0
2.0
30.0
0.0
32.0
2.0
0.0
0.0
2.0
2.0
0.0
0.0
2.0
2.0
0.0
0.0
2.0
2.0
0.0
0.0
2.0
Investment and Financing
Investment:
Buildings
Equipment
Other
Booked Value
Depreciation:
Depreciation Buildings 4%
Depreciation Equipm. 15%
Depreciation Other
20%
Total Depreciation
Financing:
Equity
Loans
30%
70%
445
133.5
311.5
Repayment
6
Principal
Interest
12%
Loan Managem. Fees 2%
311.5
0.0
6.2
0.0
311.5
37.4
51.9
259.6
37.4
51.9
207.7
31.2
51.9
155.8
24.9
6
51.9
103.8
18.7
51.9
51.9
12.5
51.9
0.0
6.2
0.0
0.0
0.0
0.0
0.0
0.0
2015 Total
0.0
0.0
0.0
20.0
180.0
50.0
250.0
445
134
312
0
312
168
480
PJ
August 21 2006
4. Operating Statement
This component has the purpose of calculating the Revenue and Costs year by year, the
Income Tax and other taxes, and the Appropriation of Profit. When we have subtracted Total
Production Costs from the Revenue we reach the line called Operating Surplus, which is the
basis for cash flow calculation in the next section. Note that we assume here that Diverse
Taxes are zero.
Total depreciation was calculated in the previous section. Stock movements are calculated as
changes in the Stock under Current Assets on Balance Sheet, which in turn is based on the
Inventory build-up, see the Assumptions and Results Summary sheet.
Subtracting all these items (except adding stock movement) brings us to the Operating
Gain/Loss. From that we subtract Interest of loans calculated in the previous component. This
gives us the Profit before Tax, and we enter the tax calculations.
The tax law in many countries allows loss to be transferred over several years. In our case the
loss transfer is allowed. Income Tax Basis is calculated from Profit before Tax and Loss
Transfer. This gives us the Taxable Profit and the Income Tax for corporations is in our case
study 18% of that. Net Worth Tax is zero according to the case study assumptions. Net Worth
is defined as the Total Capital (bottom line of Balance Sheet) minus Equity plus Taxes
Payable.
Appropriation of Profit is determined in the line called Total Dividend. The conditions in our
case study are that Profit after Tax is high enough and that Profit and Loss Balance on the
Balance Sheet allows payment of dividend. In the case shown here the Total Dividend is 30%
of the Profit after Tax, under the above-mentioned conditions. This can of course be adjusted
at will. Finally Net Profit/Loss is calculated and added to the Profit and Loss Balance on
Balance Sheet.
Operations
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
Total
0.0
0.0
5.0
6.0
30.0
10.0
12.0
120.0
15.0
14.0
210.0
20.0
15.0
300.0
20.0
15.0
300.0
20.0
15.0
300.0
20.0
15.0
300.0
20.0
15.0
300.0
20.0
15.0
300.0
170.0
20.0
15.0
300.0 2,460.0
0.0
0.0
0.0
0.0
60.0
20.0
0.0
-50.0
30.0
20.0
0.0
70.0
45.0
20.0
0.0
145.0
60.0
20.0
0.0
220.0
60.0
20.0
0.0
220.0
60.0
20.0
0.0
220.0
60.0
20.0
0.0
220.0
60.0
20.0
0.0
220.0
60.0
20.0
0.0
220.0
555.0
60.0
200.0
20.0
0.0
0.0
220.0 1,705.0
0.0
0.0
45.0
42.0
-47.0
42.0
28.0
42.0
103.0
42.0
178.0
42.0
178.0
32.0
188.0
2.0
218.0
2.0
218.0
2.0
218.0
45.0
250.0
2.0
218.0 1,500.0
6.2
-6.2
37.4
-84.4
37.4
-9.4
31.2
71.9
24.9
153.1
18.7
159.3
12.5
175.5
6.2
211.8
0.0
218.0
0.0
218.0
174.4
0.0
218.0 1,325.6
-6.2
0.0
0.0
0.0
-6.2
0.0
-6.2
-90.6 -100.0
0.0
0.0
0.0
0.0
0.0
0.0
-84.4
-9.4
0.0
0.0
-84.4
-9.4
-28.1
0.0
0.0
0.0
71.9
21.6
50.3
0.0
124.9
22.5
0.0
130.6
39.2
91.4
0.0
159.3
28.7
0.0
130.6
39.2
91.4
0.0
175.5
31.6
0.0
143.9
43.2
100.8
0.0
211.8
38.1
0.0
173.7
52.1
121.6
0.0
218.0
39.2
0.0
178.8
53.6
125.1
0.0
218.0
39.2
0.0
178.8
53.6
125.1
0.0
218.0
238.6
39.2
0.0
0.0
178.8 1,087.0
356.1
53.6
125.1
730.9
Operations Statement
Sales
Price
Revenue
Variable Cost
Fixed Cost
Diverse Taxes
Operating Surplus
3
20
0%
Inventory Movement
Depreciation
Operating Gain/Loss
Interest
Profit before Tax
Loss Transfer
Taxable Profit
Income Tax
Net Worth Tax
Profit after Tax
Dividend
Net Profit/Loss
0
18%
0%
30%
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PJ
August 21 2006
5. Balance Sheet
This component of the model might seem of little value as it is in particular the cash flow
series that is of interest for profitability evaluation. However, it gives a more complete picture
to be able to follow the forecasted development of the balance sheet. Also, financial ratios can
be calculated. Finally the balance sheet is used in the model as a verification tool as many
logical errors would result in a difference between Total Assets on one hand and Total Debt
and Capital on the other hand (both these lines are shown with double underlining below).
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
138.8
0.0
0.0
138.8
300.0
438.8
52.9
7.5
45.0
105.4
258.0
363.4
6.6
30.0
45.0
81.6
216.0
297.6
48.3
52.5
45.0
145.8
174.0
319.8
149.6
75.0
45.0
269.6
132.0
401.6
237.4
75.0
45.0
357.4
90.0
447.4
325.1
75.0
45.0
445.1
58.0
503.1
412.2
75.0
45.0
532.2
56.0
588.2
542.0
75.0
45.0
662.0
54.0
716.0
669.1
75.0
45.0
789.1
52.0
841.1
796.2
75.0
45.0
916.2
50.0
966.2
Debts
Dividend Payable
Taxes Payable
Creditors
15%
Next Year Repayment
Current Liabilities
Long Term Loans
Total Debt
0.0
0.0
0.0
0.0
0.0
311.5
311.5
0.0
0.0
9.0
51.9
60.9
259.6
320.5
0.0
0.0
4.5
51.9
56.4
207.7
264.1
21.6
0.0
6.8
51.9
80.2
155.8
236.0
39.2
22.5
9.0
51.9
122.6
103.8
226.4
39.2
28.7
9.0
51.9
128.8
51.9
180.7
43.2
31.6
9.0
51.9
135.7
0.0
135.7
52.1
38.1
9.0
0.0
99.2
0.0
99.2
53.6
39.2
9.0
0.0
101.9
0.0
101.9
53.6
39.2
9.0
0.0
101.9
0.0
101.9
53.6
39.2
9.0
0.0
101.9
0.0
101.9
Equity
Profit & Loss Balance
Total Capital
133.5
-6.2
127.3
133.5 133.5
-90.6 -100.0
42.9
33.5
133.5
-49.7
83.8
133.5
41.7
175.2
133.5
133.2
266.7
133.5
233.9
367.4
133.5
355.5
489.0
133.5
480.6
614.1
133.5
605.7
739.2
133.5
730.9
864.4
438.8
363.4
319.8
401.6
447.4
503.1
588.2
716.0
841.1
966.2
Balance Sheet
Assets
Cash Account
Debtors
Stock
Current Assets
Fixed Assets
Total Assets
Debts and Capital
0
25%
0
0
297.6
Financial Ratios are calculated according to common accounting traditions. Later all the ratios
will be presented graphically. Here we will only give few comments on the interpretation of
the ratios.
The two first ratios, the profit ratios, some times show a decreasing trend after the middle of
the lifetime. This is not because profits are getting smaller but because the capital in the
nominators is increasing as profit and loss balance grows.
The liquidity ratios are high through all the lifetime and debt service coverage, which is cash
flow after taxes divided by repayment and interest of loans, is acceptable. The debt ratios are
also well in order.
8
PJ
August 21 2006
Financial Ratios
Profit+Interest/Debt+Capital
Profit/Shareh. Capital
Revenue/Debt+Capital
Capital/Debt+Capital
Net Current Ratio
Liquid Current Ratio
Total Capital/Equity
0%
0%
7%
12%
1.7
1.0
0.3
8%
0%
33%
11%
1.4
0.6
0.3
35%
100%
71%
26%
1.8
1.3
0.6
56%
100%
94%
44%
2.2
1.8
1.3
44%
75%
75%
60%
2.8
2.4
2.0
42%
54%
67%
73%
3.3
2.9
2.8
43%
47%
60%
83%
5.4
4.9
3.7
37%
37%
51%
86%
6.5
6.1
4.6
Most of these ratios are presented graphically in Fig. 3 and 4.
Financial Ratios 1
120%
Prof it+Interest/Debt+Capital
100%
Prof it/Shareh. Capital
Revenue/Debt+Capital
80%
60%
40%
20%
0%
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
-20%
Fig. 3: Financial Ratios, part 1
Financial Ratios 2
10.0
9.0
Net Current Ratio
8.0
Liquid Current Ratio
7.0
Total Capital/Equity
6.0
5.0
4.0
3.0
2.0
1.0
0.0
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Fig. 4: Financial Ratios, part 2
9
30%
29%
42%
88%
7.7
7.3
5.5
26%
24%
36%
89%
9.0
8.6
6.5
PJ
August 21 2006
6. Cash Flow
The Cash Flow calculation begins with the Operating Surplus from Operating Statement in
previous section. Debtor and Creditor changes are calculated on basis of Debtors and
Creditors on the Balance Sheet, giving Cash Flow before Taxes. Note that Debtor and
Creditor changes can not be calculated until the Balance Sheet is ready.
Taxes are paid the year after they are calculated, and subtracting these gives us Cash Flow
after Taxes. This together with the total invested capital (equity and loan) is of interest as a
measure of the profitability of the project regardless of how it will be financed, see later.
Interest and repayment of loans (calculated earlier) are now subtracted and the resulting line is
called Net Cash Flow. This will be used later to measure the profitability of the equity.
Finally Cash Movements are found by adding to Net Cash Flow the difference between
Financing (Drawdown of Equity and Loans) and Capital Expenditure, i.e. the Working
Capital, and subtracting Paid Dividend. The Cash Movements are then added to the Cash
Account on Balance Sheet, see later.
Cash Flow
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
Total
Cash Flow
Operating Surplus
Debtor Changes
Creditor Changes
Cash Flow before Tax
0.0
0.0
0.0
0.0
-50.0
-7.5
9.0
-48.5
70.0
-22.5
-4.5
43.0
145.0
-22.5
2.3
124.8
220.0
-22.5
2.3
199.8
220.0
0.0
0.0
220.0
220.0
0.0
0.0
220.0
220.0
0.0
0.0
220.0
220.0
0.0
0.0
220.0
220.0
0.0
0.0
220.0
220.0
0.0
0.0
220.0
1,705.0
-75.0
9.0
1,639.0
Paid Taxes
Cash Flow after Tax
0.0
0.0
0.0
-48.5
0.0
43.0
0.0
124.8
0.0
199.8
22.5
197.5
28.7
191.3
31.6
188.4
38.1
181.9
39.2
180.8
39.2
180.8
199.4
1,439.6
6.2
0.0
-6.2
37.4
0.0
-85.9
37.4
51.9
-46.3
31.2
51.9
41.7
24.9
51.9
122.9
18.7
51.9
126.9
12.5
51.9
126.9
6.2
51.9
130.3
0.0
0.0
181.9
0.0
0.0
180.8
0.0
0.0
180.8
174.4
311.5
953.7
0.0
145.0
138.8
0.0
0.0
-85.9
0.0
0.0
-46.3
0.0
0.0
41.7
21.6
0.0
101.4
39.2
0.0
87.7
39.2
0.0
87.8
43.2
0.0
87.1
52.1
0.0
129.8
53.6
0.0
127.1
53.6
0.0
127.1
302.5
145.0
796.2
Interest
Repayment
Net Cash Flow
Paid Dividend
Financing - Expenditure
Cash Movement
Source and Allocation is an optional section and will be described in a Supplement 2.
There are two important cash flow related ratios that will be described here. The Debt Service
Ratio is defined each year as Cash Flow after Tax divided by Repayment and Interest of
Loans. This should preferably be greater than 1.5, ensuring that each year the cash flow is
enough for payments of loans. The Loan Life Cover Ratio is defined each year as Net Present
Value of Cash Flow after Tax for the rest of the lifetime divided by the Principals of loans
that year. This should also be greater than 1.5, ensuring that future cash flow is enough to pay
back the loan.
10
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August 21 2006
Debt Service Coverage
Loan Value 10 years
8% 810.3
Loan Value 5 years
8% 344.7
Principal
311.5
Loan Life Cover Ratio 10 years2.6
0.0
875.1
372.2
311.5
2.8
0.5
1.5
993.7 1030.2
450.5 443.6
259.6 207.7
3.8
5.0
2.6
987.8
354.3
155.8
6.3
2.8
867.1
182.9
103.8
8.4
3.0
738.9
3.2
606.7
0.0
466.9
0.0
322.3
0.0
167.4
51.9
14.2
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
These cash flow related ratios are shown graphically on Fig. 5.
Cash Flow Ratios
16
14
12
10
8
6
4
2
0
Debt Service Coverage
Loan Lif e Cover Ratio 10 years
20
05
20
06
20
07
20
08
20
09
20
10
20
11
20
12
20
13
20
14
20
15
Acceptable LLCR and DSC
Fig. 5: Cash Flow related Ratios
7. Profitability Calculations
This component of the model calculates the profitability of the investment. Two measures are
used in the model: The Net Present Value (NPV) with a discounting factor chosen by the user
and the Internal Rate of Return (IRR). The theoretical background for this can be found in
textbooks. These measures are calculated for the following cash flow series:
1. Total Capital invested and Cash Flow after Taxes
2. Equity and Net Cash Flow
The NPV and IRR are calculated for all years through the lifetime. By this we are able to see
the development of the accumulated discounted cash flow and impact of lifetime on IRR. This
becomes clearer when studying the graphs of NPV and IRR on Fig. 6 and 7.
11
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August 21 2006
Profitability
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
Total
Profitability Measurements
NPV and IRR of Total Cash Flow
Cash Flow after Taxes
0.0 -48.5
43.0 124.8 199.8 197.5 191.3 188.4 181.9 180.8 225.8 1,484.6
311.5
Loans
311.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
133.5
Equity
133.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Total Cash Flow & Capital -445.0 -48.5
43.0 124.8 199.8 197.5 191.3 188.4 181.9 180.8 225.8 1,039.6
NPV Total Cash Flow 15% -387.0 -423.6 -395.4 -324.0 -224.7 -139.3 -67.4
-5.8
45.9
90.6 139.1
IRR Total Cash Flow
0.0% 0.0% 0.0% 0.0% 3.6% 10.4% 14.7% 17.4% 19.3% 21.0%
NPV and IRR of Net Cash Flow
998.7
Net Cash Flow
-6.2 -85.9 -46.3
41.7 122.9 126.9 126.9 130.3 181.9 180.8 225.8
133.5
Equity
133.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Net Cash Flow & Equity -139.7 -85.9 -46.3
41.7 122.9 126.9 126.9 130.3 181.9 180.8 225.8
865.2
NPV Net Cash Flow 15% -121.5 -186.4 -216.9 -193.1 -131.9 -77.1 -29.4
13.2
64.9 109.6 158.1
IRR Net Cash Flow
0.0% 0.0% 0.0% 0.0% 1.9% 11.0% 16.5% 21.2% 24.0% 26.3%
Accumulated Net Present Value
200.0
100.0
0.0
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
-100.0
-200.0
-300.0
NPV Total Cash Flow 15%
-400.0
NPV Net Cash Flow 15%
-500.0
Fig. 6: Net Present Value accumulation over the planning horizon
Internal Rate of Return
30.0%
25.0%
IRR Total Cash Flow
IRR Net Cash Flow
20.0%
15.0%
10.0%
5.0%
0.0%
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
-5.0%
Fig. 7: Internal Rate of Return over the planning horizon
12
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August 21 2006
8. Sensitivity Analysis
Sensitivity analysis for exploring and better understanding the effects of uncertainties can be
done in many different ways. Here we will use three methods:
1. Impact Analysis
2. Scenario Analysis
3. Monte Carlo Simulation
Impact Analysis deals with only one uncertain item at the time, for example sales price, sales
quantity or cost of equipment. To facilitate this we insert so-called impact factors as shown on
Assumptions and Results sheet on page 4, all with the default value 100%. These are
multiplied with the uncertain items (in cells next to the right). Next step is to apply Data
Tables in Excel in order to calculate results like Internal Rate of Equity for a range of impact
factors, say from 50% to 150%. This is done for each of the uncertain items. The result is a
table as shown below. Finally this is presented in a graphical way in Fig 8.
Impact Analysis on IRR of Equity:
Price
Sales
26.3%
26.3%
0.0%
2.9%
-50%
50%
50%
2.4%
8.4%
-40%
60%
60%
9.3%
13.4%
-30%
70%
70%
15.5%
18.0%
-20%
80%
80%
21.1%
22.3%
-10%
90%
90%
26.3%
26.3%
0%
100%
100%
31.3%
30.2%
10%
110%
110%
36.0%
33.8%
20%
120%
120%
40.4%
37.3%
30%
130%
130%
44.7%
40.6%
40%
140%
140%
48.8%
43.9%
50%
150%
150%
50%
60%
70%
80%
90%
100%
110%
120%
130%
140%
150%
Equipment
26.3%
34.1%
32.4%
30.7%
29.2%
27.7%
26.3%
25.0%
23.8%
22.6%
21.5%
20.4%
Impact Analysis
60.0%
50.0%
IRR of Equity
40.0%
30.0%
20.0%
Price
10.0%
Sales
Equipment
-50%
-40%
-30%
-20%
0.0%
-10%
0%
10%
20%
30%
Deviation
Fig. 8: Impact Analysis on IRR of Equity
13
40%
50%
PJ
August 21 2006
Scenario Analysis deals with simultaneous changes in more than one uncertain item. Excel
Scenario Manager is used for this purpose. The changing cells are selected and their values
for each scenario, for example that the cost of equipment is in the best case only 90% of the
base estimate but 120% in the worst case. The scenarios are named, for example Pessimistic
Scenario and Optimistic Scenario. Result cells are selected, in our case the IRR of Equity. The
result of this is:
Scenario Summary
Changing Cells:
Equipment
Sales Quantity
Sales Price
Result Cells:
IRR_Total
IRR_Equity
100%
100%
100%
90%
120%
130%
120%
90%
80%
19.2%
23.7%
33.4%
48.1%
9.5%
7.4%
Monte Carlo Simulation is the most advanced of the sensitivity analysis methods. To do this
we need an add-in to Excel like for example @Risk or Crystal Ball. These simulation tools
allow the user to specify a probability distribution for each of the uncertain items. In our case
we use the Three Point Method assuming a Triangular or Beta distribution for each item. This
means that the user gives an optimistic estimate a, a most likely estimate m and finally a
pessimistic estimate b, see further Supplement 1.
The tools then use built-in random number generators to make as many observations of these
items as the user finds necessary. The result will be a histogram of a selected output item, in
our case the IRR of Equity. Next page shows is an example of such a histogram. Let us
assume that the user has decided that IRR = 20% is critical, i.e. values under this threshold are
not sufficient. He will now be able to see what the probability of this is.
Histogram
160
140
100
80
60
40
20
5%
10
%
15
%
20
%
25
%
30
%
35
%
40
%
45
%
M
or
e
0
0%
Frequency
120
IRR of Equity
Fig. 9: An example of a histogram of IRR of Equity
14
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August 21 2006
9. Final Comments
In this text a computer model of profitability analysis has been described. Models of this type
have proved very useful for evaluating investment projects. In some cases using a model like
this has saved companies and individuals from investing in bad projects. In other cases these
models have helped building up a convincing feasibility study for promising projects.
It should of course be kept in mind that everything depends on good data. Here the slogan
“garbage in – garbage out” certainly is valid. However it should also be mentioned that it is
very useful to set up a profitability analysis model early in the project work and use the
sensitivity information as a guide to allocate resources to data gathering and other project
work.
Use of models like this has other benefits that may not be so obvious. It stimulates insight and
understanding when the user is able to ask various kinds of “what-if” questions and analyse
sensitivity and break-even points (for example with the Goal Seeking feature of Excel). It is
the experience of the author after 30 years of teaching in this field that it is first when students
build a model like this that they really understand the financial aspects of a company. By
experimenting with the model hey are for example able to see how operating statement, cash
flow and balance sheet are interrelated.
As mentioned in the introduction the model described here forms the basis for a course on
profitability assessment. In that course the participants actually develop the model themselves
during the course. At the end of the course they apply the model to a real world case usually
selected by them. The experience of this course has been very good.
15
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August 21 2006
Supplement 1: The Three Point Cost Estimation Method
In the Three Point Method it is assumed that a Triangular or Beta distribution can be used to
describe each item. This means that the user gives an optimistic estimate a, a most likely
estimate m and finally a pessimistic estimate b. A Triangular distribution might look like this:
Triangular distribution:
Probability
Values
a
m
b
Fig. 10: An example of a Triangular distribution
However, in the following we will assume the Beta distribution. The expected value is
calculated as t = ( a + 4*m + b) / 6 and the standard deviation is found by s = ( b – a ) / 6. The
variance will then be v = s^2. When adding together the cost of many items we sum the
expected values on one hand and the variances on the other hand. The standard deviation of
the total is then found as the square root of the total variance.
The central limit theory of statistics states that the more items are added, the closer will the
distribution of the total be to the Normal distribution. This applies even though the items to be
added are not normally distributed, as here. This is why the Normal distribution is chosen
here as an approximation for the total. In order to be able to give lower and upper bounds on
the total cost we use confidence limits, i.e.:
Lower bound on Total Cost = Expected Total Cost – Z * Standard Deviation
Upper bound on Total Cost = Expected Total Cost + Z * Standard Deviation
where Z is determined by the confidence level using the standardized Normal distribution.
The following table gives examples of this:
Confidence Level
90%
95%
98%
99.9%
Value of Z:
1.28
1.65
2.05
3.09
In section 2 of this text we used the traditional contingency method to deal with uncertainties,
i.e. ca 10% was added to each cost category (buildings, equipment and other initial cost). In
the following it is shown how we drop the contingencies and apply the Three Point Method:
16
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August 21 2006
Three Point Estimation Method:
Optimistic Pessimistic
Estimate Estimate
25
15
8
4
30
15
Expected
Value
20
5
21
Confidence Level:
2.05
98%
Standard Variance
Deviation
3
2
0
1
6
3
34
40
63
52
46
3
9
110
8
12
20
160
14
20
30
132
10
15
25
8
1
1
2
69
1
2
3
150
165
224
200
182
9
75
8
25
15
50
11
36
1
4
1
17
33
37
217
242
254
65
55
352
308
296
46
4
19
275
10
103
Here we use 98% confidence level so Z = 2.05. The Total expected cost is 275 MUSD. The
variance of the Total cost is 103 so the standard deviation is sqrt(103) = 10. To obtain an
upper limit we add 2.05 * 10 to the expected cost which gives 296 MUSD which in this case
is very close to the 300 MUSD found by the traditional contingency method.
17
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August 21 2006
Supplement 2: Source and Allocation of Funds
An alternative approach to the Cash Flow Analysis in section 6 of this text is the “Source and
Allocation of Funds” approach. This contains three sections:
1. Source of funds (Profit before Tax + Depreciation + Drawdown of Loans and Equity)
2. Allocation of Funds (Investment + Repayment + Paid Tax & Dividend)
3. Changes in Net Current Assets (Cash, Debtors, Stocks, Creditors)
The first section describes where cash is generated, i.e. from operations and drawdown of
loans and equity from shareholders.The second section describes how the cash flow is used,
i.e. to pay capital expenditure in the beginning, repayments of loans, taxes and dividend to the
shareholders. The final section analyses the difference which can among other things be
because the cash account of the company is increasing.
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
Total
Source of Funds
Profit before Tax
Depreciation
Funds from Operations
Loan Drawdown
Equity Drawdown
Funds for allocation
-6.2
0.0
-6.2
311.5
133.5
438.8
-84.4
42.0
-42.4
0
0
-42.4
-9.4
42.0
32.6
0
0
32.6
71.9
42.0
113.9
0
0
113.9
153.1
42.0
195.1
0
0
195.1
159.3
42.0
201.3
0
0
201.3
175.5
32.0
207.5
0
0
207.5
211.8
2.0
213.8
0
0
213.8
218.0
2.0
220.0
0
0
220.0
218.0
2.0
220.0
0
0
220.0
218.0
2.0
220.0
0
0
220.0
1325.6
250.0
1575.6
311.5
133.5
2020.6
Alloction of Funds
Investment
Repayment
Paid Taxes
Paid Dividend
Total allocation
300.0
0.0
0.0
0.0
300.0
0.0
0.0
0.0
0.0
0.0
0.0
51.9
0.0
0.0
51.9
0.0
51.9
0.0
0.0
51.9
0.0
51.9
0.0
21.6
73.5
0.0
51.9
22.5
39.2
113.6
0.0
51.9
28.7
39.2
119.8
0.0
51.9
31.6
43.2
126.7
0.0
0.0
38.1
52.1
90.2
0.0
0.0
39.2
53.6
92.9
0.0
0.0
39.2
53.6
92.9
300.0
311.5
199.4
302.5
1113.3
Changes Net Curr. Assets
138.8
-42.4
-19.3
61.9
121.6
87.7
87.8
87.1
129.8
127.1
127.1
907.2
0.0
138.8
138.8
0.0
0
138.8
138.8
52.9
-85.9
7.5
45
-33.4
52.9
6.6
-46.3
22.5
0
-23.8
6.6
48.3
41.7
22.5
0
64.2
48.3
149.6
101.4
22.5
0
123.9
149.6
237.4
87.7
0.0
0
87.7
237.4
325.1
87.8
0.0
0
87.8
325.1
412.2
87.1
0.0
0
87.1
412.2
542.0
129.8
0.0
0
129.8
542.0
669.1
127.1
0.0
0
127.1
669.1
796.2
127.1
0.0
0
127.1
2581.9
3378.2
796.2
75.0
45.0
916.2
0.0
138.8
9.0
-42.4
-4.5
-19.3
2.3
61.9
2.3
121.6
0.0
87.7
0.0
87.8
0.0
87.1
0.0
129.8
0.0
127.1
0.0
127.1
9.0
907.2
Analysis of Changes
Current Assets
Cash at start of year
Cash at end of year
Changes in Cash
Debtor changes
Stock Movements
Changes in Current Assets
Liabilities
Creditor changes
Changes Net Curr. Assets
18