Basic Knowledge of Transportation Economy (1) & (2)

Basic Knowledge of Transportation Economy (1) & (2) Lectures 21 & 22 (Textbook: Chapter 12)

Outline • Money and its Time Value (1) • Interest and Discount (1) • Simple and Compound Interest (1) • Nominal and Effective Interest Rate (1) • Cash Flows (2) • Equal Series of Payment (2) • Superposition of cash flow (2)

Money and its Time Value • Value of money is defined as the reciprocal of the price of the goods and services for which it can be exchanged. • When the general price level is on an upswing, the economy is said to experience price inflation. • When the price are falling, the economy is in a deflationary period. • The value of money decreases with price inflation and increases with price deflation. • As a major factor of production, it carries the ability to earn profits, and this earning power of money is reflected in the time value of money. • In the future, the present dollar would be incremented by the return it would earn in the meantime.

Interest and Discount • Interest: The premium paid or received for the use of money • Interest rate: The rate i at which interest accumulates is quoted as the percentage gained over the interest period • Interest period: The period at which interest is accumulated

Interest and Discount F i % . . . . . . n n-1 4 2 3 1 P P = principal or present sum F = future worth

Interest and Discount • Interest rate relates a sum of money presently in hand to its equivalent sum at some future date. Example 12.1 A business firm borrows $10,000 and agree to pay back $10,200 at the end of one month. Calculate the interest rate involved in the transaction. Solution: Interest = $200, Interest period = 1 month or 2% per month Interest Rate

Interest and Discount • Discount rate relates a sum of money at some future date to its equivalent at present. Example 12.2 An investor purchases a zero coupon bond for $867.98. The bond has a face value of $1000and matures in 1 year. This means that the bond can be cashed after 1 year for $1000. Calculate the discount rate involved in transaction. Solution: The future sum ($1000) was discounted by 1000-867.98 = $132,02 The discount rate was: or 15.21% per year Discount Rate

Simple and Compound Interest • Simple Interest refers to the case where the percentage of original sum of money is added at the end of each interest period. • Compound interest refers to that the original sum (principals) and the interest earned are allowed to earn interest during subsequent periods.

Simple and Compound Interest

Nominal and Effective Interest Rates • Frequently, interest rates are specified on the basis of a period (usually a year) when compounding occurs more frequently than the specified period. • By convention, the magnitude of the quoted nominal interest rate is equal to the product of interest per interest period times the number of interest periods in the specified period. Example:a nominal annual rate of 12% compounded semiannually: Interest rate is 6% per 6-month interest period Example:a nominal annual rate of 12% compounded monthly: Interest rate is 1% per month

Example 12.5

Solution of Example 12.5

Cash Flow

Equal Series of Payment

Single-Sum Factors F = ? i % … n-1 n 1 2 3 4 P P = ? i % … n n-1 1 2 3 4 F

Equal-Series Factors F = ? i % … n-1 n 0 1 2 3 4 … S S S S S S S = ? … … n-1 n 0 1 2 3 4 i % F

Equal-Series Factors P = ? i % … n n-1 1 2 3 4 … S S S S S S S = ? … … n-1 n 1 2 3 4 i % P

Example 12.8 4

Superposition of Cash Flow • A cash flow may be described as the superposition of its individual single-payment components. • The same principle of superposition applies to the same case of complex cash flows that can be decomposed into several simpler cash flow. • In each case several alternative ways of decomposing and superposing the cash flow’s parts are possible. • Find the simplest way of solving the problem before undertaking any calculations.

Example 12.9

Solution of Example 12.9

Basic Knowledge of Transportation Economy (1) & (2)