+
Rate of return
+
Sensitivity analysis
coated membrane template

Level 2 analysis

Raw material costs = $100,000

Purchased equipment costs = $250,000

Lang factors at lowest value of the range
Snapshot of TPC
Case I tab
P4 - membrane coating
Basis: per year
Materials
direct costs (DC)
fixed capital invest. (FCI)
total capital invest. (TCI)
land + buildings =
Basis:
Total product costs
$100,000
$512,500
$729,737
$729,737
$35,000
1
from bill of materials tab
from TCI tab
from TCI tab
from TCI tab
from TCI tab
year of operation
+
What is the sensitivity of TPC to
raw material cost variations?

± 10%, one standard deviation of raw material costs (bulk
chemicals);

Standard deviation levels

± 1 standard deviation = 50% of the range

± 2 standard deviations = ~95% of the range

For this case, ± 2 standard deviations of raw material costs
would give $80,000 and $120,000 as the raw materials cost
range

Change raw materials costs on bill of materials Tab; read TPC
result on TPC Case I Tab
TPC vs. raw material costs
± 2 standard deviations; 10% = one standard deviation;
notice the TPC sensitivity to raw materials costs
total product cost
460,000
total product costs, $/year
+
450,000
y = 1.3606x + 288775
R² = 1
440,000
430,000
420,000
410,000
400,000
390,000
0
25,000
50,000 75,000 100,000 125,000 150,000
raw material cost, $/year
+
What is the sensitivity of TPC to
PEC cost variations?

Capital cost estimates are within 35% of actual (we take this
to be 2 standard deviations)

Change PEC costs on PEC Tab; read TCI result on TCI Tab or
read TCI, TPC results on TPC Case I Tab
TCI, TPC vs PEC
effect of PEC on TCI, TPC
otal capital investment or total product
cost
+
$1,400,000
y = 2.2438x + 387860
R² = 1
$1,200,000
$1,000,000
TCI
$800,000
TPC
$600,000
Linear (TCI)
Linear (TPC)
$400,000
y = 0.893x + 309063
R² = 1
$200,000
$0
$0
$200,000
Purchase equipment costs, $
$400,000
+
How can you use sensitivity plots
during design?

Evaluate high-cost elements for the process, focus on
reducing these

Rapidly eliminate alternatives that exceed cost quality
accuracy

Refine cost estimates to evaluate alternatives that have costs
within the expected accuracy of the costing methods
+
Costs due to interest
on investment

Money has a time value

A business expects to receive a return
on money invested

The amount of the return is related to
the degree of risk that the entire
investment may be lost
+
Various investment cost elements

Borrowed capital vs. owned capital


Interest on owned capital cannot be charged as a true cost
Interest effects in a small business

$20,000 invested in a start-up – FCI + WC

Profit = $8,000

Owned capital: profit = $8,000

Borrowed capital (10% interest): profit = $8,000 – 0.1*$20,000 =
$6,000
+

Interest effects in a large business

New capital can come from issued stocks and bonds, borrowing
from banks or insurance companies, depreciation funds set aside,
profits not distributed to shareholders,…
Source of capital Interest,
Actual interest,
dividend %/year dividend before
taxes, %/yr
Actual interest,
dividend after
taxes, %/yr
Bonds
6
6
4
Bank loans
7
7
4.6
Preferred stock
7
10.6
7
Common stock
0
13.6
9
+
Including cost of capital in
economic analysis

Capital is charged at a low interest rate – it could be used for
alternative investments, i.e., it could pays off funded debts or
be invested in risk-free loans

Interest is paid on owned capital at a rate equal to the
presetn return on all the company’s capital

Design practice for interest and investment costs-alternatives

No interest costs are included – all necessary capital comes from
owned capital

Interest is charged on the total capital investment at a set interest
rate
+

Property taxes


Taxes

Local government jurisdiction –
county or city
Excise taxes

Charges for import customs, transfer
of stocks and bonds

Gasoline, alcoholic beverages

Indirect, as they are passed to the
consumer

There may be local excise taxes
Income taxes

Based on gross earnings = total
income – total product cost

Federal and state governments (0 –
5% of gross income)
+
Corporate taxes

Normal tax – federal government

Surtax – 2nd federal income tax based on gross earnings
above a certain limit

> $100,000: 34% tax rate

Capital gains tax – tax on profits made for the sale of capital
assets (land, buildings, equipment); long-term if held more
than a year, short-term if held more than a year

Contributions – tax deductible up to 10% of taxable income

Carry-back, carry-forward of losses – 3 year window
+

Investment credit – deduction for new investments in
machinery, equipment

Taxes and depreciation – discussion to follow

Excess-profits tax – (national emergencies)

Tax returns

Cash basis – only money received or paid out during the period

Accrual basis – income and expenses included when they occur
even if money is not yet received or sent
+


Depreciation
methods

Arbitrary, does not include interest
costs

Straight-line

Declining balance

Sum-of-the-years digits
Accounts for interest on the investment

Sinking fund

Present worth methods
Case study: Harsh’s car

V = $20,000

Vs = $500

A = 15 years
+
deprecia on methods
$20,000
Asset value (Harsh' car)
Va, str line
Va, declining
Va, reciprocal
Va, double declining
$10,000
$0
0
5
10
Usage period, years
15
+
Profitability
standard

Quantifiable standards only operate as
guides to decisions

Profit evaluation is based on prediction
of future results [“…it is hard to make
predictions, especially about the
future.” – Yogi Berra]

A primary factor in evaluations is the
consideration of alternatives

Typical choices

Capital investment in a project with
high risk

Capital investment in a safe venture
+
Five common methods
for profitability
evaluations
1.
Rate of return on investment
2.
Discounted cash flow on full-life
performance
3.
Net present worth
4.
Capitalized costs
5.
Payout period
+
1. Rate of return (RoR)

Annual RoR on TCI, before taxes = annual profit/(TCI + WC)

Annual RoR on TCI, after taxes.


Modify annual profit by taxes
Annual RoR, capital recovery with minimal profit

Generate fictitious expenses at min profit, divide by (TCI+WC)
+
Example: Rate of return on investment
+
RoR
advantages

TCI, WC, income, expenses
disadvantages

No time value of money

Assumes constant costs for
projects

Depreciation may vary

Maintenance costs increase
with time

Sales volume may increase
or decrease
+
2. Discounted cash flow rate of
return

We determine an index (i), or interest rate, that discounts the
annual flows to a zero present value at the end of the project
life, when properly compared to the initial investment

What does i represent?

The after-tax interest rate at which the investment is repaid by
proceeds from the project, or

The maximum after-tax interest rate at which funds could be
borrowed for the investment and just break even at the end of the
service life.
+
Discounted cash flow rate of return
What is the interest at which this project will pay principal +
interest at end of life?

Addresses time value of money

Computes amount of investment unreturned @ each year
over the project life

Trial-and-error solution: vary RoR so that the initial
investment goes to zero at the end of the project ife

It gives the maximum interest rate at which capital can be
borrowed when net cash flow just pays all the principle and
interest
+
Estimated cash flow to project
year
Cash flow to project
0
(110,000) = -(TCI+WC)
1
30,000
2
31,000
3
36,000
4
40,000
5
43,000
+
3. Net present worth

Complementary to DCC RoR

Substitutes the cost of capital at an interest rate, i, for the
discounted cash flow rate of return

For the data provided in the DCC ROR problem, we set the
interest rate, say 15%, and compute the difference between the
present value of the annual cash flows and the initial required
investment
+
+
Spreadsheet structure
for DCF of present
value and net present
worth

Source: Peters, Timmerhaus, West
+
4. Capitalized costs

This method is useful for comparing alternatives within a
single overall project.

Capitalized costs related to investment:


Money for initial purchase of equipment, and

Generating sufficient funds via interest accumulation to permit
perpetual replacement (i.e., sustainability)
Example: one process section has alternatives + low or no
differences in operating costs, then the alternative giving the
least capitalized cost would be the desirable economic
choice.
+
Capitalized costs
K=
capitalized cost
V=
initial equipment cost
Vreplace = equipment replacement cost
n=
estimate useful life, years
i=
interest rate
Capitalized
cost factor
+
Capitalized costs
inclusion of operating costs

Operating costs can be included by adding an additional
capitalized cost to cover operating costs during the project
life

Each annual operating cost is considered as equivalent to a
piece of equipment that lasts one year

Procedure:

Find present (discounted) value of each year’s costs by the prior
method (discount factor is applied, d=1/(1+i)n)

S Pvi is capitalized by multiplying by the capitalization factor for
the initial investment. The total capitalized costs is the sum of this
value + operating costs + working capital.
+
5. Payout period

Minimum length of time necessary to recover the original
capital investment via cash flow to the project, based on total
income minus all costs except depreciation

Interest effects are neglected
+
Comparison of
alternative
investments:
5 profitability methods
3 investments with:
•
different TCI, WC
•
different service lives
•
different cash flow and expenses
1.
Rate of return on investment
2.
Discounted cash flow on full-life
performance
3.
Net present worth
4.
Capitalized costs
5.
Payout period
+
3 investments
investment characteristics
investment
FCI, $
1 $ 100,000
2 $ 170,000
3 $ 210,000
WC, $
$
$
$
10,000
10,000
15,000
Vs, $
$
$
$
10,000
15,000
20,000
n
cash flow annual cash
after taxes, expenses, $
$
5 tabulated
$ 44,000
7 $ 52,000 $ 28,000
8 $ 59,000 $ 21,000
cash flow after taxes = total annual income/revenue minus all costs save depreciation and investment interest
annual cash expenses = operation, maintenance, taxes, insurance = total annual income - annual cash flow
For investment 1: year 1 = $30,000; year 2 = $31,000; year 3 = $36,000; year 4 = $40,000; year 5 = $43,000
investment characteristics
investment
FCI, $
1 $ 100,000
2 $ 170,000
3 $ 210,000
WC, $
$
$
$
10,000
10,000
15,000
Vs, $
$
$
$
10,000
15,000
20,000
n
cash flow annual cash
after taxes, expenses, $
$
5 tabulated
$ 44,000
7 $ 52,000 $ 28,000
8 $ 59,000 $ 21,000
cash flow after taxes = total annual income/revenue minus all costs save depreciation and investment interest
annual cash expenses = operation, maintenance, taxes, insurance = total annual income - annual cash flow
For investment 1: year 1 = $30,000; year 2 = $31,000; year 3 = $36,000; year 4 = $40,000; year 5 = $43,000
+
1. Rate of return on initial
investment
+
Investment 1
Investment 1
TCI
$100,000
depreciation
cash flow to
project
year
0
1
2
3
4
5
salvage
-$100,000
$30,000
$31,000
$36,000
$40,000
$43,000
$10,000
average profit
total initial $
WC
Vs
$10,000
$18,000
N
$10,000
average
profit
annual CF
5
average
annual RoR
16.4%
$12,000
$13,000
$18,000
$22,000
$25,000
$18,000 per year
$110,000
annual expenses
$44,000
avg profit/(FCI+Vs)
+
Investment 2
Investment 2
TCI
$170,000
depreciation
cash flow to
project
year
0
1
2
3
4
5
6
7
salvage
-$170,000
$52,000
$52,000
$52,000
$52,000
$52,000
$52,000
$52,000
$10,000
average profit
total initial $
WC
Vs
$10,000
$22,143
N
$15,000
average
profit
annual CF annual expenses
7
52000
$28,000
average
annual RoR
16.6%
$29,857
$29,857
$29,857
$29,857
$29,857
$29,857
$29,857
$29,857 per year
$180,000
avg profit/(FCI+Vs)
+
Investment 3
Investment 3
TCI
$210,000
depreciation
cash flow to
project
year
0
1
2
3
4
5
6
7
8
salvage
-$210,000
$59,000
$59,000
$59,000
$59,000
$59,000
$59,000
$59,000
$59,000
$10,000
average profit
total initial $
N
Vs
WC
$15,000
$23,750
$20,000
average
profit
annual CF annual expenses
$21,000
$59,000
8
average
annual RoR
15.7%
$35,250
$35,250
$35,250
$35,250
$35,250
$35,250
$35,250
$35,250
$35,250 per year
$225,000
avg profit/(FCI+Vs)
+
Summary table
investment initial $
profit (avg) avg RoR
1
$110,000
$18,000
16.4%
2
$180,000
$29,857
16.6%
3
$225,000
$35,250
15.7%
Which do we choose? All have similar average rates of
return? All are above the ‘minimum’ 15% return.
+
Average RoR, incremental
investment

We can also compare these investments to each other as
follows:

The project investment follows the order, 1,2, and 3

Pairwise, find the ratio of the profit difference to the initial
investment difference

The investment with the highest value is preferred
+
Differential rate of return
D
differential
comparison D profit
investment RoR
2 to 1
$11,857
$70,000
16.9%
3 to 2
$5,393
$45,000
12.0%
Project 2 is better than project 1;
Project 2 is better than project 3
(less efficient use of capital for 3)
investment characteristics
investment
FCI, $
1 $ 100,000
2 $ 170,000
3 $ 210,000
WC, $
$
$
$
10,000
10,000
15,000
Vs, $
$
$
$
10,000
15,000
20,000
n
cash flow annual cash
after taxes, expenses, $
$
5 tabulated
$ 44,000
7 $ 52,000 $ 28,000
8 $ 59,000 $ 21,000
cash flow after taxes = total annual income/revenue minus all costs save depreciation and investment interest
annual cash expenses = operation, maintenance, taxes, insurance = total annual income - annual cash flow
For investment 1: year 1 = $30,000; year 2 = $31,000; year 3 = $36,000; year 4 = $40,000; year 5 = $43,000
+
Minimum payout period
No interest charge
+
Minimum payout period
no interest charge
investment depr. FCI
avg profit/yr avg depr./yr payout period
1
$90,000
$18,000
$18,000
2.50
2
$155,000
$29,857
$22,143
2.98
3
$190,000
$35,250
$23,750
3.22
Investment 1 has the lowest payout period, and is
recommended
investment characteristics
investment
FCI, $
1 $ 100,000
2 $ 170,000
3 $ 210,000
WC, $
$
$
$
10,000
10,000
15,000
Vs, $
$
$
$
10,000
15,000
20,000
n
cash flow annual cash
after taxes, expenses, $
$
5 tabulated
$ 44,000
7 $ 52,000 $ 28,000
8 $ 59,000 $ 21,000
cash flow after taxes = total annual income/revenue minus all costs save depreciation and investment interest
annual cash expenses = operation, maintenance, taxes, insurance = total annual income - annual cash flow
For investment 1: year 1 = $30,000; year 2 = $31,000; year 3 = $36,000; year 4 = $40,000; year 5 = $43,000
+
Discounted cash flow RoR
Investment 1
FCI
$100,000
WC
$10,000
n=
5 years
salvage
$10,000
interest rate when investment is just repaid by the cash flow at end of service life
RoR estimate of i
20.7% use Solver, Goal Seek to find i for residual = 0
cash flow to project
discount present
year
cash flow factor
value
0 $110,000
1
$30,000
0.8284
$24,852
2
$31,000
0.6862
$21,273
3
$36,000
0.5685
$20,464
4
$40,000
0.4709
$18,836
5
$43,000
0.3901
$16,774
WC+salvage $20,000
$7,802
sum CF
$200,000
net present
value
$110,000
TCI + WC
$110,000
when residual = 0, net cash flow just pays for principal + interest
residual =
$0 target value
Investment 2
FCI
$170,000
WC
$10,000
n=
7 years
salvage
$15,000
interest rate when investment is just repaid by the cash flow at end of service life
RoR estimate of i
22.8% use Solver, Goal Seek to find i for residual = 0
cash flow to project
discount present
year
cash flow factor
value
0 $170,000
1
$52,000
0.8145
$42,356
2
$52,000
0.6635
$34,501
3
$52,000
0.5404
$28,102
4
$52,000
0.4402
$22,890
5
$52,000
0.3586
$18,645
6
$52,000
0.2921
$15,187
7
$52,000
0.2379
$12,371
WC+salvage $25,000
$5,947
sum CF
$389,000
net present
value
$180,000
TCI + WC
$180,000
when residual = 0, net cash flow just pays for principal + interest
residual =
$0 target value
Investment 3
FCI
$210,000
WC
$15,000
n=
8 years
salvage
$20,000
interest rate when investment is just repaid by the cash flow at end of service life
RoR estimate of i
21.4% use Solver, Goal Seek to find i for residual = 0
cash flow to project
discount present
year
cash flow factor
value
0 $210,000
1
$59,000
0.8240
$48,618
2
$59,000
0.6790
$40,064
3
$59,000
0.5596
$33,014
4
$59,000
0.4611
$27,205
5
$59,000
0.3800
$22,418
6
$59,000
0.3131
$18,473
7
$59,000
0.2580
$15,223
8
$59,000
0.2126
$12,544
WC+salvage $35,000
$7,441
sum CF
$507,000
net present
value
$225,000
TCI + WC
$225,000
when residual = 0, net cash flow just pays for principal + interest
residual =
$0 target value
+
DCF RoR

DCD RoR’s are similar: 20.7%, 22.8%, and 21.4%

This method works well when the service lives of the projects
are the same; with different service lives, the net present
worth method is better

Approximate method, narrow range of service lives

Pair-wise comparison: base time is the longer service life
investment characteristics
investment
FCI, $
1 $ 100,000
2 $ 170,000
3 $ 210,000
WC, $
$
$
$
10,000
10,000
15,000
Vs, $
$
$
$
10,000
15,000
20,000
n
cash flow annual cash
after taxes, expenses, $
$
5 tabulated
$ 44,000
7 $ 52,000 $ 28,000
8 $ 59,000 $ 21,000
cash flow after taxes = total annual income/revenue minus all costs save depreciation and investment interest
annual cash expenses = operation, maintenance, taxes, insurance = total annual income - annual cash flow
For investment 1: year 1 = $30,000; year 2 = $31,000; year 3 = $36,000; year 4 = $40,000; year 5 = $43,000
+
Net present worth
Investment 1
FCI
$100,000
WC
$10,000
n=
5 years
salvage
$10,000
RoR estimate of i
15.0% set minimum interest target
cash flow to project
discount present
year
cash flow factor
value
0 $110,000
1
$30,000
0.8696
$26,087
2
$31,000
0.7561
$23,440
3
$36,000
0.6575
$23,671
4
$40,000
0.5718
$22,870
5
$43,000
0.4972
$21,379
WC+salvage $20,000
$9,944
sum CF
$200,000
net present
value
TCI + WC
net present worth =
$127,390
$110,000
$17,390
Investment 2
FCI
$170,000
WC
$10,000
n=
7 years
salvage
$15,000
RoR estimate of i
15.0% set minimum interest target
cash flow to project
discount present
year
cash flow factor
value
0 $170,000
1
$52,000
0.8696
$45,217
2
$52,000
0.7561
$39,319
3
$52,000
0.6575
$34,191
4
$52,000
0.5718
$29,731
5
$52,000
0.4972
$25,853
6
$52,000
0.4323
$22,481
7
$52,000
0.3759
$19,549
WC+salvage $25,000
$9,398
sum CF
$389,000
net present
value
TCI + WC
net present worth =
$225,740
$180,000
$45,740
Investment 3
FCI
$210,000
WC
$15,000
n=
8 years
salvage
$20,000
RoR estimate of i
15.0% set minimum interest target
cash flow to project
discount present
year
cash flow factor
value
0 $210,000
1
$59,000
0.8696
$51,304
2
$59,000
0.7561
$44,612
3
$59,000
0.6575
$38,793
4
$59,000
0.5718
$33,733
5
$59,000
0.4972
$29,333
6
$59,000
0.4323
$25,507
7
$59,000
0.3759
$22,180
8
$59,000
0.3269
$19,287
WC+salvage $35,000
$11,442
sum CF
$507,000
net present
value
TCI + WC
net present worth =
$276,194
$225,000
$51,194
+
Net present worth

Investment 1 = $17,400

Investment 2 = $45,700

Investment 3 = $51,200
Project 3 is preferred
investment characteristics
investment
FCI, $
1 $ 100,000
2 $ 170,000
3 $ 210,000
WC, $
$
$
$
10,000
10,000
15,000
Vs, $
$
$
$
10,000
15,000
20,000
n
cash flow annual cash
after taxes, expenses, $
$
5 tabulated
$ 44,000
7 $ 52,000 $ 28,000
8 $ 59,000 $ 21,000
cash flow after taxes = total annual income/revenue minus all costs save depreciation and investment interest
annual cash expenses = operation, maintenance, taxes, insurance = total annual income - annual cash flow
For investment 1: year 1 = $30,000; year 2 = $31,000; year 3 = $36,000; year 4 = $40,000; year 5 = $43,000
+
Capitalized costs
+
Capitalized cost method

Determine the capitalized cost for the original investment
such that we could achieve an indefinite number of
replacements + the capitalized present value of the cash
expenses + working capital

Method

Get the present value of the annual cash expenses

Determine the capitalized present value

These are computed at the target interest rate, 15%
capitalized costs
investment FCI, $
WC, $
Vs, $
n
1 $100,000
$10,000
$10,000
2 $170,000
$10,000
$15,000
3 $210,000
$15,000
$20,000
target interest =
Investment
1
2
3
annual
cash flow
cash
after taxes, expenses,
$
$
5 tabulated
$44,000
7
$52,000
$28,000
8
$59,000
$21,000
15%
Cr
Vs
Cn
$90,000
$10,000
$44,000
$155,000
$15,000
$28,000
$190,000
$20,000
$21,000
we want the minimum capitalized cost
capitalized capitalized
Wc
cost
cost factor
$10,000
$492,323
1.99
$10,000
$460,039
1.60
$15,000
$457,277
1.49
n
5
7
8
+
ANALYSIS:
5 METHODS
1.
Rate of return on investment: project 2
preferred
2.
Discounted cash flow on full-life:
project 3 preferred
3.
Net present worth: project 3 preferred
4.
Capitalized costs: project 3 preferred
5.
Payout period: project 1 preferred
+
CRITIQUE

RoR, initial investment: does not include the time value of money

Minimum payout period: does not include the time value of
money

DCF RoR, net present worth, capitalized costs:

All include the time value of money

While project 3 is preferred over project 2, the choice is narrow

A more accurate evaluation is needed

Go from straight line to a more realistic depreciation method

Go from end-of-year costs to continuous interest compounding

Variations in prestart-up costs between alternatives may be a factor
to consider
+
Some heuristics for
profitability

Select smallest investment for needed
service that gives the required return
for the company

Challenge the accuracy of your
estimates: service life for example

Consider process risk, particularly if
you select a project with a larger-thannecessary investment

Turbulent times = usually invest
minimum capital

Perceived value: green processes can
have significant marketing advantages

Other factors: gut feel, beat your
competition, expand an existing
plant,…
+
Rate of return
GOOD LUCK!!!