Chapter 5.
EVALUATION OF
SINGLE PROJECT
©2017 Batangas State University
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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.
Net Annual Profit
ROR =
Capital Invested
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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
ROR =
Capital Invested
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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 = P81,000
Taxes and Insurance Cost
= P270,000(0.04) = P10,800
Depreciation Cost
= P29,609 (used Sinking Fund Method
where i = 25%)
Total Cost
= P121,409
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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
63,991
ROR =
x100
270,000
RoR = 23.70%
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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
Annual costs:
P185,400
Depreciation
P29,609
Operation and maintenance P81000
Taxes and insurance
P10800
Total Annual Cost
Net annual profit
RoR
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P121,409
P63,991
P63,991
P270,000
X100
23.70%
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
Note: Annual Cash Inflows includes Annual Revenue
Annual Cash Outflows includes Total Cost including depreciation and interest on capital
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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
Taxes and Insurance Cost
= P270,000(0.04) = P10,800
Depreciation Cost
= P29,609 (used Sinking Fund Method
where i = 25%)
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
Operation and maintenance
Taxes and insurance
Interest on capital
Total Annual Cost
Excess
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P29,609
P81000
P10800
P67,500
P188,909
- P3,509
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
Present worth Method = PW inflows – PW outflows
Note: Inflows includes the annual revenue and salvage value
Outflows includes the investment and overhead cost excluding depreciation
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Present Worth Method
Solution:
PW of cash inflows = P185,400 (P/A, 25%, 5) + P27,000 (P/F, 25%, 5)
= P185,400 (2.6893) + P27,000 (0.3277)
= P506,370
Annual Cost (excluding depreciation )= 91,800
PW of cash outflows = P270,000+ P91,800 (P/A, 25%, 5)
= P516,880
PW=PW of cash inflows – PW of cash outflows
=P506,370 - P516,880
PW=-P10,510
Decision.
*Since the PW of the net cash flows is less than zero (-P10,510) the investment is not
justified or not ideal.
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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 in future time using also the formula in
money-time relationships.
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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
Future worth Method = FW inflows – FW outflows
Note: Inflows includes the annual revenue and salvage value
Outflows
includes the investment and overhead cost excluding depreciation
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Future Worth Method
Solution.
FW of cash inflows = P27,000 + P185,400 (F/A, 25%, 5)
= P27,000 + P185,400 (8.2070)
= P1,548,580
Annual Cost (excluding depreciation )= 91,800
PW of cash outflows = P91,800 (F/A, 25%, 5) + P270,000 (F/P,25%,5)
= P1,577,390
FW=FW of cash inflows – FW of cash outflows
=P1,548,580 – P1,577,390
FW=-P28,810
Decision
*Since the FW of the net cash flows is less than zero (-P28,810) 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
The shorter the payback period the better investment.
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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)
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