Engineering Economics Lecture 3.pptx

ENGINEERING ECONOMICS Lecture # 3

Faizan Shafique

The concept of Equivalence

The Concept of Equivalence • Alternatives should be compared as far as possible when they produce similar results, serve the same purpose, or accomplish the same function. • The question arises that how can these alternatives be compared when interest is involved over extended period of time?

The Concept of Equivalence • The solution is to reduce these alternatives to an equivalent basis that is dependent on: 1. The Interest rate 2. The amount of money involved 3. The timing of the monetary receipts and/or expenses 4. The manner in which the interest is paid and the invested capital is recovered.

The Concept of Equivalence • Consider a situation in which we borrow $5000 and agree to repay it in 5 years at an interest rate of 8% per year. • There are many ways by which principal of this loan ($5000) and the interest on it can be repaid. • Two of these involving simple interest are shown.

As the ratio is constant at 0.08 for both plans, we can deduce that both repayment methods considered are equivalent, even though each involves a different total end of year payment and different total interest.

Cash Flow Diagrams

Cash Flow Diagrams • Following notations are used in cash flow diagrams: • I

total interest earned or paid

• P

present sum of money or principal amount lent or

•

borrowed

• F

future sum of money

• n

number of interest periods (e.g., years)

• i

interest rate per interest period

• A

end of period cash flows

Cash Flow Diagrams From Lender’s Point Of View

Plan 1: Pay principal ‘P’ in four equal End-of-year payments ‘A’ at an interest rate of ‘i%’ A Cash inflows

Cash outflows

0

1

2

3

Interest rate = i% per year

P

4 = n

Cash Flow Diagrams From Lender’s Point Of View Plan 2: Pay principal ‘P’ and interest ‘I‘ in one payment at the end of four years F Cash inflows

Cash outflows

0

1

2

3

Interest rate = i% per year

P

4 = n

Cash Flow Diagrams From Borrower’s Point Of View

Plan 1: Pay principal ‘P’ in four equal End-of-year payments ‘A’ at an interest rate of ‘i%’ P Interest rate = i% per year

Cash inflows 0

1

2

3

Cash outflows

A

4 = n

Cash Flow Diagrams From Borrower’s Point Of View

Plan 2: Pay principal ‘P’ and interest ‘I‘ in one payment at the end of four years P Interest rate = i% per year

Cash inflows 0

1

2

3

4 = n

Cash outflows

F

Cash Flow Diagrams Practice Problem

An investment of Rs. 100,000 can be made by a construction company that will produce uniform annual revenue of Rs. 50,000 for four years and then have a market (recovery) value of Rs. 25,000 at the end of year four. Annual expenses will be Rs. 30,000 at the end of each year for operating and maintaining the project. Draw a cash flow diagram for the five year life of the project. Use construction company’s viewpoint.

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