SUBJECT
Code:
Description:
No. of Units:
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Time:
ENS191_ME
ENGINEERING ECONOMY
3 Units
Tuesday and Friday
9AM-10:30AM
CHAPTER 8: BASIC METHODS IN MAKING ECONOMY STUDIES
Rate of Return:
- It is the measure of the effectiveness of an investment of capital.
𝑅𝑂𝑅 =
𝑅𝑂𝑅 =
𝑁𝑒𝑡 𝐴𝑛𝑛𝑢𝑎𝑙 𝑃𝑟𝑜𝑓𝑖𝑡
𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
where:
Investment = Capital Invested
Annual Profit = Annual Income – Annual Expenses
Annual Expenses Includes the Following:
 Annual depreciation using the Sinking Fund
Method
 Annual regular disbursements (operation,
labor, maintenance, taxes)
 Annual equivalent or irregular expenses
Note:
In ROR, interest in capital is excluded
𝑁𝑒𝑡 𝐴𝑛𝑛𝑢𝑎𝑙 𝑆𝑎𝑣𝑖𝑛𝑔𝑠
𝐴𝑑𝑑𝑖𝑡𝑖𝑜𝑛𝑎𝑙 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
𝑅𝑂𝑅 > 𝑖 𝑓𝑜𝑟 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑡𝑜 𝑏𝑒 𝑗𝑢𝑠𝑡𝑖𝑓𝑖𝑒𝑑
Annual Worth Pattern:
CASE 1: Only One Project
Given:
Revenue, Expenses (Maintenance, Operation, Labor, Taxes, Insurance and Investment which
includes minimum required profit )
𝐵𝑎𝑠𝑖𝑠: 𝑇𝑜𝑡𝑎𝑙 𝐴𝑛𝑛𝑢𝑎𝑙 𝐸𝑥𝑝𝑒𝑛𝑠𝑒𝑠 < 𝐴𝑛𝑛𝑢𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒
CHAPTER 8: BASIC METHODS IN MAKING ECONOMY STUDIES
Annual Worth Pattern:
CASE 2: Two or More Alternatives
Given:
Revenue, Expenses (Maintenance, Operation, Labor, Taxes, Insurance and Investment which
includes minimum required profit )
𝐵𝑎𝑠𝑖𝑠: 𝐶ℎ𝑜𝑜𝑠𝑒 𝑎𝑙𝑡𝑒𝑟𝑛𝑎𝑡𝑖𝑣𝑒 𝑤𝑖𝑡ℎ 𝑔𝑟𝑒𝑎𝑡𝑒𝑠𝑡 𝑣𝑎𝑙𝑢𝑒 𝑓𝑜𝑟 𝑅𝑒𝑣𝑒𝑛𝑢𝑒 − 𝐸𝑥𝑝𝑒𝑛𝑠𝑒𝑠
Given:
No revenue, only expenses (Maintenance, Operation, Labor, Taxes, Insurance and Investment
which includes minimum required profit )
𝐵𝑎𝑠𝑖𝑠: 𝐶ℎ𝑜𝑜𝑠𝑒 𝑎𝑙𝑡𝑒𝑟𝑛𝑎𝑡𝑖𝑣𝑒 𝑤𝑖𝑡ℎ 𝑡ℎ𝑒 𝑙𝑒𝑎𝑠𝑡 𝑎𝑛𝑛𝑢𝑎𝑙 𝑒𝑥𝑝𝑒𝑛𝑠𝑒𝑠
Note:
In AWP, depreciation (SFM) and
interest in capital (MRP) is included
Where:
I = MRP or the Minimum Required Profit
I = FC (i)
CHAPTER 8: BASIC METHODS IN MAKING ECONOMY STUDIES
Present Worth Pattern:
- Its concept is based on the present worth of net cash flows. The project is justified economical if net cash
flows is equal to or greater than zero.
𝐵𝑎𝑠𝑖𝑠: 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑊𝑜𝑟𝑡ℎ 𝑜𝑓 𝑁𝑒𝑡 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤𝑠 ≥ 0
Note:
In PWP, depreciation is excluded
Future Worth Pattern:
- The concept is based on the future worth of net cash flows. The project is justified economical if the future
worth of net cash flows is equal to or greater than zero.
𝐵𝑎𝑠𝑖𝑠: 𝐹𝑢𝑡𝑢𝑟𝑒 𝑊𝑜𝑟𝑡ℎ 𝑜𝑓 𝑁𝑒𝑡 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤𝑠 ≥ 0
CHAPTER 8: BASIC METHODS IN MAKING ECONOMY STUDIES
Payback (Payout) Period Method:
- Its concept is based on the length of time required to recover the first cost of an investment from the net cash
flow produced by the investment for an interest rate of zero.
𝐶𝑎𝑝𝑖𝑡𝑎𝑙 − 𝑆𝑎𝑙𝑣𝑎𝑔𝑒 𝑉𝑎𝑙𝑢𝑒
𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜𝑑 =
𝑁𝑒𝑡 𝐴𝑛𝑛𝑢𝑎𝑙 𝑃𝑟𝑜𝑓𝑖𝑡
where:
Annual Profit = Annual Income – Annual Expenses
Note: Annual Expenses Includes (Excluding Depreciation)
1. Annual regular disbursement (operation, maintenance, labor, taxes, etc.)
2. Annual uniform equivalent cost for irregular expenses
CHAPTER 8: BASIC METHODS IN MAKING ECONOMY STUDIES
Example No.1 :
From Engineering Economy 2nd Edition by Hipolito B. Sta. Maria, p107, Past ME Board Problem – April 13, 1984
A young mechanical engineer is considering establishing his own small company. An investment of P100,000
will be required, which will be recovered in 15 years. It is estimated that sales will be P150,000 per year and
that operating expenses will be as follows:
Material
Labor
Overhead
Selling expense
P40,000 per year
70,000 per year
10,000 + 10% of sales per year
5,000 per year
The man will give up his regular job paying P15,000 per year and devote full time to the operation of the
business; this will result in decreasing labor cost by P10,000 per year, material cost by P7,000 per year and
overhead cost by P8,000 per year. If the man expects to earn at least 20% of his capital, should he invest?
CHAPTER 8: BASIC METHODS IN MAKING ECONOMY STUDIES
Example No.2 :
From Engineering Economy 2nd Edition by Hipolito B. Sta. Maria, p108, Past ME Board Problem – April 13, 1988
A food processing plant consumed 600,000 kwh of electric energy annually and pays an average of P2.00 per
kwh. A study is being made to generate its own power to supply the plant the energy required, and that the
power plant installed would cost P2,000,000. Annual operation and maintenance, P800,000. Other expenses,
P100,000 per year. Life of power plant is 15 years; salvage value at the end of life is P200,000; annual taxes and
insurance, 6% of first cost; and rate of interest is 15%. Using the sinking fund method for depreciation,
determine if the power plant is justifiable.
CHAPTER 8: BASIC METHODS IN MAKING ECONOMY STUDIES
Example No.3 :
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. Determine the payback period of the investment
in years.
CHAPTER 8: BASIC METHODS IN MAKING ECONOMY STUDIES
Example No.4 :
An investment worth P100,000 has a scrap value of P20,000. If it has a net profit P800 per day, what is the
payback period in months?
THANK YOU!
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