ERT461 BIOSYSTEMS ENGINEERING DESIGN 1
ERT424 BIOPROCESS PLANT DESIGN 1
1





The Interest Rate
Simple Interest
Compound Interest
Amortizing a Loan
Compounding More Than Once per
Year
Which would you prefer -$10,000 today or $10,000 in 5
years?
Why is TIME such an important
element in your decision?
TIME allows you the opportunity to
postpone consumption and earn
INTEREST.
 Simple
Interest
Interest paid (earned) on only the original
amount, or principal, borrowed (lent).

Compound Interest
Interest paid (earned) on any previous
interest earned, as well as on the
principal borrowed (lent).
Formula
SI = P0(i)(n)
SI: Simple Interest
P0: Deposit today (t=0)
i: Interest Rate per Period
n:Number of Time Periods

Assume that you deposit $1,000 in an
account earning 7% simple interest for
2 years. What is the accumulated
interest at the end of the 2nd year?
 SI
= P0(i)(n)
= $1,000(.07)(2)
= $140

What is the Future Value (FV) of the
deposit?
FV

= P0 + SI
= $1,000 + $140
= $1,140
Future Value is the value at some future
time of a present amount of money, or a
series of payments, evaluated at a given
interest rate.

What is the Present Value (PV) of the
previous problem?
The Present Value is simply the
$1,000 you originally deposited.
That is the value today!

Present Value is the current value of a
future amount of money, or a series of
payments, evaluated at a given interest
rate.
Future Value (U.S. Dollars)
Future Value of a Single $1,000 Deposit
20000
10% Simple
Interest
7% Compound
Interest
10% Compound
Interest
15000
10000
5000
0
1st Year 10th
Year
20th
Year
30th
Year
Assume that you deposit $1,000
at a compound interest rate of 7%
for 2 years.
0
1
7%
2
$1,000
FV2
FV1 = P0 (1+i)1
= $1,000 (1.07)
= $1,070
Compound Interest
You earned $70 interest on your
$1,000 deposit over the first year.
This is the same amount of interest
you would earn under simple interest.
Future Value
Single Deposit (Formula)
FV1 = P0 (1+i)1
= $1,000 (1.07)
= $1,070
FV2 = FV1 (1+i)1
= P0 (1+i)(1+i) =
$1,000(1.07)(1.07)
= P0 (1+i)2
= $1,000(1.07)2
= $1,144.90
You earned an EXTRA $4.90 in Year 2 with
compound over simple interest.
FV1
FV2
= P0(1+i)1
= P0(1+i)2
General Future Value Formula:
FVn = P0 (1+i)n
or FVn = P0 (FVIFi,n) -- See Table I
FVIFi,n is found on Table I
at the end of the book.
Period
1
2
3
4
5
6%
1.060
1.124
1.191
1.262
1.338
7%
1.070
1.145
1.225
1.311
1.403
8%
1.080
1.166
1.260
1.360
1.469
FV2
= $1,000 (FVIF7%,2)
= $1,000 (1.145)
= $1,145 [Due to Rounding]
Period
6%
7%
1
1.060
1.070
2
1.124
1.145
3
1.191
1.225
4
1.262
1.311
5
1.338
1.403
8%
1.080
1.166
1.260
1.360
1.469
Julie Miller wants to know how large her deposit
of $10,000 today will become at a compound
annual interest rate of 10% for 5 years.
0
1
2
3
4
5
10%
$10,000
FV5

Calculation based on general formula:
FVn = P0 (1+i)n
FV5 = $10,000 (1+ 0.10)
= $16,105.10
5

Calculation based on Table I:
FV5 = $10,000 (FVIF10%, 5)
= $10,000 (1.611)
= $16,110
[Due to
Rounding]
Quick! How long does it take to
double $5,000 at a compound
rate of 12% per year (approx.)?
We will use the “Rule-of-72”.
Quick! How long does it take to
double $5,000 at a compound
rate of 12% per year (approx.)?
Approx. Years to Double = 72 / i%
72 / 12% = 6 Years
[Actual Time is 6.12 Years]




Estimating
Cost/Benefit for
Engineering
Projects
Incremental Cash
Flows
Developing Cash
Flow Statements
Generalized Cash
Flow Approach
21
Elements of Investment Decision
•
•
•
•
•
•
Identification of Investment Opportunities
Generation of Cash Flows
Measures of Investment Worth
Our focus in this
Project Selection
chapter is to
develop the format
Project Implementation
of after-tax cash
flow statements.
Project-Control/Post-Audit
22
Classification of Investment Projects
Expansion project
Profit-adding
project
Product Improvement
project
Cost Improvement
project
Project
Profit-maintaining
project
Replacement Project
Necessity project
23
Types of Cash Flow Elements in Project
Analysis
24
Cash Flows from Operating Activities
Income Statement Approach
Operating revenues
Cost of goods sold
Depreciation
Operating expenses
Interest expenses
Taxable income
Income taxes
Net income
+ Depreciation
Direct Cash Flow Approach
Operating revenues
- Cost of goods sold
- Operating expenses
- Interest expenses
- Income taxes
Cash flow from operation
25
Cash Flow Element
Operating activities:
Other Terms Used in Business
Gross income
Gross revenue, Sales revenue, Gross Profit, Operating revenue
Cost savings
Cost reduction
Manufacturing expenses
Cost of goods sold, Cost of revenue
O&M cost
Operating expenses
Operating income
Operating profit, Gross margin
Interest expenses
Interest payments, Debt cost
Income taxes
Income taxes owed
Investing activities
Capital investment
Purchase of new equipment, Capital expenditure
Salvage value
Net selling price, Disposal value, Resale value
Investment in working capital
Working capital requirement
Working capital release
Working capital recovery
Gains taxes
Capital gains taxes, Ordinary gains taxes
Financing activities:
Borrowed funds
Borrowed amounts, Loan amount
Principal repayments
Loan repayment
26
A Typical Format used for Presenting Cash
Flow Statement
Cash flow statement
+ Net income
+Depreciation
Income statement
Revenues
Expenses
Cost of goods sold
Depreciation
Debt interest
Operating expenses
Taxable income
Income taxes
Net income
-Capital investment
+ Proceeds from sales of
depreciable assets
- Gains tax
- Investments in working
capital
+ Working capital recovery
+ Borrowed funds
-Repayment of principal
Operating
activities
+
Investing
activities
+
Financing
activities
Net cash flow
27

defines depreciation as the ‘allocation of the
depreciable amount of an asset over its
estimated life’.


According to the matching concept, revenues
should be matched with expenses in order to
determine the accounting profit.
The cost of the asset purchased should be
spread over the periods in which the asset
will benefit a company.


The assets are acquired or constructed with
the intention of being used and not with the
intention for resale.
regards assets as depreciable when they
◦ Are expected to be used in more than one
accounting period.
◦ Have a finite useful life, and
◦ Are held for use in the production or supply of
goods and services, for rental to others, or for
administrative purposes.

Freehold Land

Leasehold Land (Long Lease)
◦ It has an indefinite useful life, and it retains its
value indefinitely.
◦ It has an unexpired lease period not less than 50
years

Investment Property
◦ Which construction work and development have
been completed
◦ Which is held for its investment potential, any
rental income being negotiated at arm’s length.

Freehold Land

Leasehold Land (Long Lease)
◦ It has an indefinite useful life, and it retains its
value indefinitely.
◦ It has an unexpired lease period not less than 50
years

Investment Property
◦ Which construction work and development have
been completed
◦ Which is held for its investment potential, any
rental income being negotiated at arm’s length.

Depreciation is computed by dividing the
depreciable amount of the asset by the
expected number of accounting periods of its
useful life.
Depreciation = Cost of Asset – Estimated Residual Value
Estimated Useful Economic Life


Useful economic life is not equal to physical
life
It is the period over which the present owner
intends to use the asset

It is the amount received after disposal of the
asset
Cost of asset - Residual value = Total amount to be depreciated
Cost of asset
$1200
Residual/scrap/salvage value $200
Estimated useful life
4 years
Annual charge for depreciation
= $1200-$200
4
= $1000
4
=$250
When Projects Require only Operating and Investing
Activities
• Project Nature: Installation of a new computer control system
• Financial Data:
– Investment: $125,000
– Project life: 5 years
– Salvage value: $50,000
– Annual labor savings: $100,000
– Annual additional expenses:
• Labor: $20,000
• Material: $12,000
• Overhead: $8,000
– Depreciation Method: 5-yr Straight Line Method
– Income tax rate: 40%
– MARR: 15%
38
Questions
• (a) Develop the project’s cash flows over its
project life.
• (b) Is this project justifiable at a MARR of
15%?
• (c) What is the internal rate of return of this
project?
39
Income Statement
Revenues
0
1
2
3
4
5
$100,000 $100,000 $100,000 $100,000 $100,000
Expenses:
Labor
20,000
20,000
20,000
20,000
20,000
Material
12,000
12,000
12,000
12,000
12,000
Overhead
8,000
8,000
8,000
8,000
8,000
17,863
30,613
21,863
15,613
5,581
$42,137
$29,387
$38,137
$44,387
$54,419
16,855
11,755
15,255
17,755
21,768
$25,282
$17,632
$22,882
$26,632
$32,651
Depreciation
Taxable Income
Income Taxes (40%)
Net Income
40
Cash Flow Statement
Cash Flow Statement
0
1
2
3
4
5
Operating Activities:
Net Income
$25,282 $17,632 $22,882 $26,632 $32,651
Depreciation
17,863
30,613
21,863
15,613
5,581
Investment Activities:
Investment
(125,000)
Salvage
50,000
Gains Tax
(6,613)
Net Cash Flow
($125,000) $43,145 $48,245 $44,745 $42,245 $81,619
41
Net Cash Flow Table Generated by Traditional
Method
A
B
C
D
E
F
G
H
I
J
Year
End
Investment &
Salvage Value
Revenue
Labor
Expenses
Materials
Overhead
Depreciation
Taxable
Income
Income
Taxes
Net Cash
Flow
0
-$125,000
-$125,000
1
$100,000
20,000
12,000
8,000
$17,863
42,137
16,855
$43,145
2
100,000
20,000
12,000
8,000
30,613
29,387
11,755
$48,245
3
100,000
20,000
12,000
8,000
21,863
38,137
15,255
$44,745
4
100,000
20,000
12,000
8,000
15,613
44,387
17,755
$42,245
5
100,000
20,000
12,000
8,000
5,581
54,419
21,678
$38,232
16,525
6,613
$43,387
50,000*
*Salvage value
Note that
H = C-D-E-F-G
I = 0.4 * H
J= B+C-D-E-F-I
Information required to
calculate the income taxes
42
Question (b):

Is this investment
justifiable at a MARR of
15%?
$81,619
$48,245
$43,145

PW(15%) = -$125,000
+ +$43,145(P/F, 15%,
1) + . . . . + $81,620
(P/F, 15%, 5)
= $43,151 > 0
◦ Yes, Accept the
Project !
$44,745 $42,245
0
1
2
3
4
5
Years
$125,000
43
Question (C):
• Determine the IRR for this investment
project.
• At i = 25%
PW(25%) = $7,351
• At i = 30%
PW (30%) = -$6,124
IRR = 27.61% > 15%, accept the project.
44
Rate of Return Analysis (IRR = 27.61%)
n=0
n =1
n=2
n=3
n=4
n=5
Beginning
Balance
-$125,000 -$116,376 -$100,271 -$83,218 -$63,955
Return on
Investment
(interest)
-$34,521
-$32,140
-$27,692
-$22,982 -$17,665
Payment
-$125,000 +$43,145 +$48,245 +$44,745 +$42,245 +$81,620
Project
Balance
-$125,000 -$116,376 -$100,271 -$83,218
-$63,955
0
45


Working capital means
the amount carried in
cash, accounts
receivable, and
inventory that is
available to meet dayto-day operating
needs.
How to treat working
capital investments:
just like a capital
expenditure except that
no depreciation is
allowed.
46
Working Capital Requirements
(Example 12.2)
Price (revenue) per unit
Unit variable manufacturing costs
Labor
Material
Overhead
$10
Monthly volume
Finished goods inventory to maintain
833 units
2 – month supply
Raw materials inventory to maintain
Accounts payable
Accounts receivable
1 – month supply
30 days
60 days
$2
$1.20
$0.80
47
Required Working Capital Investments
During year 1
Sales
Expenses
Income taxes
Net amount
Income
Actual cash
/Expense
Received/paid
Reported
$100,000
$83,333
(10,000 units)
$40,000
$46,665
(10,000 units) (11,667 units)
$16,855
$16,855
$43,145
$19,814
Difference
-$16,666
+$6665
0
-$23,333
This differential amount must be invested
at the beginning of the year
48
Table 12.4
Item
related to
working
capital
investment
49
Cash Flow Diagram including Working Capital
$23,331
$43,145
0
1
$48,245 $44,745
2
3
$125,000 Investment in
physical assets
$23,331 Investment in
working capital
Working capital
recovery
$81,619
$42,245
4
5
$23,331
0
$23,331
1
2
3
4
5
Years
Working capital recovery cycles
50


Key issue: Interest
payment is a taxdeductible expense.
What Needs to Be
Done: Once loan
repayment schedule
is known, separate
interest payment
from the annual
installment.

What about
Principal Payment?
As the amount of
borrowing is NOT
viewed as income
to the borrower, the
repayment of
principal is NOT
viewed as expenses
either– NO tax
effect.
51
Loan Repayment Schedule (Example 12.4)
Amount financed: $62,500, or 50% of total capital expenditure
Financing rate: 10% per year
Annual installment: $16,487 or, A = $62,500(A/P, 10%, 5)
End of
Year
Beginning
Balance
Interest
Payment
Principal
Payment
Ending
Balance
1
$62,500
$6,250
$10,237
$52,263
2
52,263
5,226
11,261
41,002
3
41,002
4,100
12,387
28,615
4
28,615
2,861
13,626
14,989
5
14,989
1,499
14,988
0
$16,487
52
Table 12.5
Items related
to financing
activities
53


Negative taxable
income (project
loss) means you
can reduce your
taxable income
from regular
business
operation by the
amount of loss,
which results in a
tax savings.
Taxable
income
Income
taxes
(35%)
Handling Project Loss
Regular
Business
Project
Combined
Operation
$100M
(10M)
$90M
$35M
?
$31.5M
Tax savings
Tax Savings = $35M - $31.5M
= $3.5M
Or (10M)(0.35) = -$3.5M
54



When to Use: When
undertaking a project
does not change a
company’s marginal
tax rate.
Pros: The cash flows
can be generated
more quickly.
Cons: The process is
less intuitive and not
commonly
understood by
business people.
55
Table 12.8
Investing
activities
Operating
activities
Financing
activities
56
Summary
• Identifying and estimating relevant project cash flows is
perhaps the most challenging aspect of engineering
economic analysis. All cash flows can be organized into
one of the following three categories:
1. Operating activities.
2. Investing activities
3. Financing activities.
57
•Cash Items
1. New investment and disposal of existing assets
2. Salvage value (or net selling price)
3. Working capital
4. Working capital release
5. Cash revenues/savings
6. Manufacturing, operating, and maintenance costs.
7. Interest and loan payments
8. Taxes and tax credits
58
• Non-cash items
1. Depreciation expenses
2. Amortization expenses
• The income statement approach is typically used in
organizing project cash flows. This approach groups cash
flows according to whether they are operating, investing,
or financing functions.
• The generalized cash flow approach to organizing cash
flows can be used when a project does not change a
company’s marginal tax rate. The cash flows can be
generated more quickly and the formatting of the results is
less elaborate than with the income statement approach.
However, the generalized approach is less intuitive and not
commonly understood by business people.
59