Chapter 5.
EVALUATION OF
SINGLE
PROJECT
©2028017 Batangas State
University
Introduction
All engineering economy studies of capital projects should consider
the return that a given project will or should produce. A basic question this
book addresses is whether a proposed capital investment and its associated
expenditures can be recovered by revenue (or savings) over time in addition
to a return on the capital that is sufficiently attractive in view of the risks
involved and the potential alternative uses.
In this chapter, we concentrate on the correct use of five methods for
evaluatingthe economic profitability of a single proposed problem solution.
The five methods are Present Worth (PW), Future Worth (FW), Annual
Worth (AW), Internal Rate of Return (IRR), Payback Period
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Learning Objectives
Discuss methods of evaluation.
Critique contemporary methods of
evaluation.
Evaluate single project in determining
project profitability.
Make a decision based on the
evaluation.
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Rate of Return
Rate of return is a measure of the effectiveness of an investment of
capital. It is a financial efficiency. When this method is used, it is necessary
to decide whether the computed rate of return is sufficient to justify the
investment. The advantage of this method is that it is easily understood by
management and investors. The applications of the rate of return method is
controlled by the following conditions. A single investment of capital at the
beginning of the first year of the project life and identical revenue and cost
data for each year. The capital invested is the total investment required to
finance the project, whether equity or borrowed.
ROR 
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Net Annual Profit
Capital Invested
Rate of Return
Example. An investment of P270,000 can be made in a project that will
produce a uniform annual revenue of P185,400 for 5 years and then have a
salvage value of 10% of the investment. Out-of-pocket cost for operation
and maintenance will be P81,000 per year. Taxes and insurance will be 4%
of the first cost per year. The company expects capital to earn not less than
25% before income taxes. Is this a desirable investment? Use ROR Method
Given:
Investment = P270,000
Annual Revenue = P185,400 for 5 years
Salvage Value = 10% of investment
Operation and Maintenance Cost = P81,000 per year
Taxes and Insurance Cost = 4% of Investment
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Rate of Return
Solution:
Step 1: Identify the Given
Given:
Investment = P270,000
Annual Revenue = P185,400 for 5 years
Salvage Value = 10% of investment
Operation and Maintenance Cost = P81,000 per year
Taxes and Insurance Cost = 4% of Investment
Step 2: Analyze what method will be used
Net
Annual
Profit
Capital
Invested
ROR 
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Note: Annual Proft = Annual Revenue - Annual Cost
Capital Invested = First Cost or Investment
Cost
Rate of Return
Solution:
Step 3: Determine the Total Annual Cost and Total Annual Revenue
Based from the problem, annual revenue = P185,000, then we need to
determine what is the total cost to determine the Net Annual Profit
Remember: In ROR Method, Depreciation Cost is included in the Total Cost
Operation and Maintenance Cost =
= P270,000(0.04)
P81,000
= P10,800
Taxes and Insurance Cost
= P29,609 (used Sinking Fund Methodwhere i = 25%)
Depreciation Cost
= P121,409
Total Cost
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Rate of Return
Solution:
Step 4: Determine the Net Annual Profit
Net Annual Profit = Total Annual Revenue - Total Annual Cost
= P185,000 - P121,409
= P63,991
Step 5: Use the formula to determine the rate of return
Net Annual Profit
ROR  Capital Invested
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63,991
ROR  270,000
x100
RoR = 23.70%
Rate of Return
Solution:
Step 6: Make a Decision
*Since the computed rate of return is less than the
minimum required rate of return of 25%, the investment
is not desirable or not accepted.
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Rate of Return
Solution using tabulated form:
Determine the inflows such as income and outflows such
as expenses.
Annual revenue
An n u a l c o s t s :
P185,400
Depre ci at ion
O p e r a t i o n a n d m a i nt e na nc e
Ta x e s a n d i nsura nc e
P29,609
P81000
P10800
To t a l A n n u a l C o s t
N e t a n n u a l profi t
RoR
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P121,409
P63,991
P63,991
P270,000
X100
23.70%
Rate of Return
Example. A company estimates that insulation of steam pipes in the factory
will reduce the fuel bill by as much as 25%. The cost of the insulation is
P100,000 installed and the annual cost of taxes and insurance is 6% of the
first cost. Without the insulation, the annual fuel bill is P200,000. If the
insulation is worthless after 5 years of use, and a minimum return on
investment of 10% is desired, would it be worthwhile to invest in the
insulation? Solve using the ROR method.
Given:
Investment = P100,000
Annual fuel bill = P200,000
Salvage Value = 0
Taxes and Insurance Cost = 6% of Investment
Return on investment = 10%
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Rate of Return
Solution: Net Annual Profit = Revenue – Total Cost
Computing Annual Savings:
Annual Savings: P200,000(0.25) = P50,000
Computing Annual Cost:
Depreciation: (P100,000-0)(0.10)/1.10^5-1 = P16,379.75
T&I = 0.06(P100,000) = P6,000
TAC = P22,379.75
ROR:
ROR=Net Annual Profit/Capital Invested
ROR=(Savings-Cost)/Capital Invested
ROR=(P50,000-P22,379.75)/P100,000 x 100% = 27.62%, recommend to invest
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Annual Worth Method
In this method, interest on the original investment (sometimes
called minimum required profit) is included as a cost. If the
excess of the annual cash inflows over annual cash outflows is
not less than zero the proposed investment is justified-is valid.
This method is covered by the same limitations as the rate of
return pattern a single initial investment of capital and uniform
revenue and cost throughout the life of the investment.
Excess  Annual Cash Inflows - Annual Cash
Outflows
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Annual Worth Method
Example. An investment of P270,000 can be made in a project that will
produce a uniform annual revenue of P185,400 for 5 years and then have
a salvage value of 10% of the investment. Out-of-pocket cost for
operation and maintenance will be P81,000 per year. Taxes and
insurance will be 4% of the first cost per year. The company expects
capital to earn not less than 25% before income taxes. Is this a desirable
investment? Use Annual Worth Method
Given:
Investment = P270,000
Annual Revenue = P185,400 for 5 years
Salvage Value = 10% of investment
Operation and Maintenance Cost = P81,000 per year
Taxes and Insurance Cost = 4% of Investment
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Annual Worth Method
Solution:
Step 1: Identify the Given
Given:
Investment = P270,000
Annual Revenue = P185,400 for 5 years
Salvage Value = 10% of investment
Operation and Maintenance Cost = P81,000 per year
Taxes and Insurance Cost = 4% of Investment
Step 2: Analyze what method will be used
Excess  Annual Cash Inflows - Annual Cash Outflows
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Note: Annual Cash
Inflows includes
Annual Revenue
Annual Worth Method
Solution:
Step 3: Determine the Annual Cash Inflow and Annual Cash Outflow
Based from the problem, annual revenue = P185,000 which is the
cash inflow, we need to determine the total annual cash outflows
Operation and Maintenance Cost = P81,000
= P270,000(0.04) = P10,800
Taxes and Insurance Cost
= P29,609 (used Sinking Fund Method where i = 25%)
Depreciation Cost
Interest on Capital
= P270,000(0.25) = P67,500
Total Annual Cash Outflows = P188,909
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Annual Worth Method
Solution:
Step 4: Determine the Excess using Annual Worth Method
Excess  Annual Cash Inflows
- Annual Cash Outflows
= P185,400 - P188,909
Excess = (P3,509)
Step 5: Make a Decision
*Since the excess of annual cash inflows over annual cash outflows is less
than zero (-P3,509) the investment is not desirable or not ideal.
Note: If excess is positive value, then the investment is advisable, otherwise, do not invest.
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Annual Worth Method
Solution using tabulated form:
Annual revenue
Annual costs:
P185,400
Depreciation
P29,609
Operation and maintenance P81000
Taxes and insurance
P10800
Interest on capital
P67,500
Total Annual Cost
Excess
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P188,909
-P3,509
Annual Worth Method
Example. An investment of P3M can be made in a business that will produce a
uniform annual revenue of P1.2M for five years and then have a salvage value of
10% of the investment. Operations and maintenance will be P100,000 per year.
Taxes and insurance will be 5% of the first cost per year. The investor expects to
earn not less than 20% before income taxes. Is this a good investment? Use the
annual cost method.
Given:
Investment = P3M
Annual Revenue = P1.2M for 5 years Salvage
Value = 10% of investment = P300,000
Operation and Maintenance Cost = P100,000 per year
Taxes and Insurance Cost = 5% of Investment = P150,000
Interest on Capital = 20% = P600,000
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Annual Worth Method
Example. An investment of P3M can be made in a business that will produce
a uniform annual revenue of P1.2M for five years and then have a salvage
value of 10% of the investment. Operations and maintenance will be
P100,000 per year. Taxes and insurance will be 5% of the first cost per year.
The investor expects to earn not less than 20% before income taxes. Is this a
good investment? Use the annual cost method.
Given:
Investment = P3M
Annual Revenue = P1.2M for 5 years
Salvage Value = 10% of investment
Operation and Maintenance Cost = P100,000 per year
Taxes and Insurance Cost = 5% of Investment
Interest on Capital = 20%
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Annual Worth Method
Solution using tabulated form: conclusion: not desirable
Annual revenue
Annual costs:
P1.2M
Depreciation
P362,825.20
Operation and maintenance
P100,000
Taxes and insurance(5%)
P150,000
Interest on capital (20%)
P600,000
Total Annual Cost
Excess
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P1,212,825.2
-P12,825.20
Present Worth Method
This pattern for economy studies is based on the concept of present worth.
If the present worth of the net cash flows is equal to, or greater than zero,
the project is justified economically. The present worth method is flexible
and can be used for any type of economy study. It is extensively in making
economy studies in the public works field, where long-lived structures are
involved.
Present worth Method = PW inflows – PW outflows
Here, we will just get the present value of money using the formula in money-time
relationship.
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Present Worth Method
Example. An investment of P270,000 can be made in a
project that will produce a uniform annual revenue of
P185,400 for 5 years and then have a salvage value of
10% of the investment. Out-of-pocket cost for operation
and maintenance will be P81,000 per year. Taxes and
insurance will be 4% of the first cost per year. The
company expects capital to earn not less than 25%
before income taxes. Is this a desirable investment? Use
Present Worth Method
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Present Worth Method
Solution:
Step 1: Identify the Given
Given:
Investment = P270,000
Annual Revenue = P185,400 for 5 years
Salvage Value = 10% of investment
Operation and Maintenance Cost =
P81,000 per year
Taxes and Insurance Cost = 4% of
Investment
Step 2: Analyze what method will be
used
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Present
worth Method = PW inflows
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Present Worth Method
Solution:
PW of cash inflows = P185,400 ((1-1.25^-5)/0.25) + P27,000 (1.25^-5)
= P185,400 (2.6893) + P27,000 (0.3277)
= P507,439.87
Annual Cost (excluding depreciation )= OM + T&I = 91,800
PW of cash outflows = P270,000+ P91,800 ((1-1.25^-5)/0.25)
= P516,875.90
PW=PW of cash inflows – PW of cash outflows
=P507,439.87 - P516,875.90
PW=-P9436.03
Decision.
*Since the PW of the net cash flows is less than zero (-P9436.03) the investment is not
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justified
or not ideal.
Future Worth Method
The future worth method for economy studies is exactly comparable to the
present worth method except that all cash inflows and outflows are
compounded forward to a reference point in time called the future. If the
future worth of the net cash flow is equal to, or greater then zero, the project
is justified economically.
Future worth Method = FW inflows – FW outflows
Here, we will forward the value
of money-time relationships.
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money in future time using also the formula in
Future Worth Method
Example. An investment of P270,000 can be made in a
project that will produce a uniform annual revenue of
P185,400 for 5 years and then have a salvage value of
10% of the investment. Out-of-pocket cost for operation
and maintenance will be P81,000 per year. Taxes and
insurance will be 4% of the first cost per year. The
company expects capital to earn not less than 25% before
income taxes. Is this a desirable investment? Use Future
Worth Method
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Future Worth Method
Solution.
Step 1: Identify the Given
Given:
Investment = P270,000
Annual Revenue = P185,400 for 5 years
Salvage Value = 10% of investment
Operation and Maintenance Cost =
P81,000 per year
Taxes and Insurance Cost = 4% of
Investment
Step 2: Analyze what method will be
used
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Future Worth Method
Solution.
FW of cash inflows = P27,000 + P185,400 ((1.25^5-1)/0.25)
= P27,000 + P185,400 (8.2070)
= P1,548,583.59
Annual Cost (excluding depreciation )= 91,800
FW of cash outflows = P91,800 ((1.25^5-1)/0.25) + P270,000 (1.25^5)
= P1,577,380.08
FW=FW of cash inflows – FW of cash outflows
=P1,548,583.59 – P1,577,380.08
FW=-P28,796.49
Decision
*Since the FW of the net cash flows is less than zero (-P28,796.49)the investment is
not justified or not ideal.
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Payback Period
The payback period is commonly defined as the length of time required
to recover the first cost of an investment from the net cash flow produced
by that investment for an interest rate of zero.
•Payback period (years) = investment –
salvage
net annual cash flow
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Payback Period
Example. An investment of P270,000 can be made in
a project that will produce a uniform annual revenue of
P185,400 for 5 years and then have a salvage value of
10% of the investment. Out-of-pocket cost for
operation and maintenance will be P81,000 per year.
Taxes and insurance will be 4% of the first cost per
year. The company expects capital to earn not less than
25% before income taxes. Is this a desirable
investment? What is the payback period?
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Payback Period
Total annual cost = P81,000 +P270,000(0.04)
= P91,800
Net annual cash flows = P185,400 – P91,800
= P93,600
Payback period:= investment-salvage value
Net annual cash flows
= P270,000-P27,000
P93,600
= 2.6 years or 2 years and 7 months and
6 days
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Months = (Payback periodyears)*12
Days = (Computed Monthsmonths)*30
Chapter Test
Direction. Read and understand the given situation. Solve the problem using the given
methods of evaluation.
A man is considering P500,000 to open a semi-automatic auto washing business in a city of
400,000 population. The equipment can wash on the average of 12 cars per hour., using two
men to operate it and to do small amount of hand work. The man plans to hire two men, in
addition to himself and operate the station on an 8 hour basis, 6 days/week, 50weeks/year. He
will pay his employees P25 per hour. He expects to charge P25.00 for a car wah out of
pocket miscellaneous cost would be P8500/month. He would pay his employees for 2 weeks
for vacation each year. Because of the length of his lease, he must write off his investment
with 5 years. His capital now is earning 15% and he is employed at a steady job that pays
P25,000/month. he desires a rate of return of at least 20% on his investment. Would you
recommend the investment? Use the following method (ROR, Annual worth, Present, Future
and Payback Period)
Cost = Labor, Vacation Leave, Miscellaneous Fee, Depreciation and Owners Salary
Interest = 0.15%
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Chapter Test
ROR:
Given:
Revenue = 12 car/hr(8hr/day)(6days/wk)(50wks/yr)(P25/car) = P720,000/yr
Cost:
Labor = 2employee(8hr/day)(6days/wk)(50wks/yr)(P25/employee) = P120,000
Vacay Leave = 2employee(8hr/day)(12)(P25/employee) = P4,800
Misc Fee = P8500(12) = P102,000
Owner’s Salary = P25,000(12) = P300,000
Dep. = (P500,000-0)(0.15)/1.15^5-1 = P74,157.78
TAC= P600,957.78
ROR = (Revenue – Cost)/Investment
ROR = (P720,000 – P600,957.78)/P500,000 X 100% = 23.81%, therefore since greater than 20%, should invest
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Chapter Test
Annual Worth:
Given:
Revenue = 12 car/hr(8hr/day)(6days/wk)(50wks/yr)(P25/car) = P720,000/yr
Cost:
Labor = 2employee(8hr/day)(6days/wk)(50wks/yr)(P25/employee) = P120,000
Vacay Leave = 2employee(8hr/day)(12)(P25/employee) = P4,800
Misc Fee = P8500(12) = P102,000
Owner’s Salary = P25,000(12) = P300,000
Dep. = (P500,000-0)(0.15)/1.15^5-1 = P74,157.78
Interest on Capital = P500,000(0.20) = P100,000
TAC= P600,957.78 + P100,000 = P700,957.78
AW = P720,000 – P700,957.78 = 19,042.22, since greater than zero, therefore should invest
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Chapter Test
Present Worth:
Given:
Investment = P500,000
Revenue = 12 car/hr(8hr/day)(6days/wk)(50wks/yr)(P25/car) = P720,000
Cost:
Labor = 2employee(8hr/day)(6days/wk)(50wks/yr)(P25/employee) = P120,000
Vacay Leave = 2employee(8hr/day)(12)(P25/employee) = P4,800
Misc Fee = P8500(12) = P102,000
Owner’s Salary = P25,000(12) = P300,000
TAC= P526,800
Inflows = P720,000((1-1.15^-5/0.15)) = P2,413,551.67
Outflows = P500,000 + P526,800 ((1-1.15^-5/0.15)) = P2,265,915.31
PW = P2,413,551.67 - P2,265,915.31 = P147,636.36, since greater than zero, therefore we should invest
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Chapter Test
Future Worth:
Given:
Investment = P500,000
Revenue = 12 car/hr(8hr/day)(6days/wk)(50wks/yr)(P25/car) = P720,000
Cost:
Labor = 2employee(8hr/day)(6days/wk)(50wks/yr)(P25/employee) = P120,000
Vacay Leave = 2employee(8hr/day)(12)(P25/employee) = P4,800
Misc Fee = P8500(12) = P102,000
Owner’s Salary = P25,000(12) = P300,000
TAC= P526,800
Inflows = P720,000((1.15^5-1/0.15)) = P4,854,514.50
Outflows = P500,000(1.15^5) + P526,800 ((1.15^5-1/0.15)) = P4,557,565.04
FW = P4,854,514.50 - P4,557,565.04 = P296,949.46, since greater than zero, therefore we should invest
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Chapter Test
Payback Period:
Given:
Investment = P500,000
Revenue = 12 car/hr(8hr/day)(6days/wk)(50wks/yr)(P25/car) = P720,000
Cost:
Labor = 2employee(8hr/day)(6days/wk)(50wks/yr)(P25/employee) = P120,000
Vacay Leave = 2employee(8hr/day)(12)(P25/employee) = P4,800
Misc Fee = P8500(12) = P102,000
Owner’s Salary = P25,000(12) = P300,000
TAC= P526,800
Payback Period = (inv-sv)/(revenue-cost) = (P500,000-0)/(P720,000-P526,800) = 2.59 years = 2 years and
7 months and 2 days
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