Time Value of Money (ECON)

Capital

refers to wealth in the form of money or property that can be used to produce more wealth.

1. Equity Capital

2. Borrowed Capital

3. Human Capital

4. Social Capital

5. Natural Capital

Types of Capital

Equity Capital

owned by individuals who have invested their money or property in a business project or venture in the hope of receiving a profit.

Borrowed Capital

obtained from lenders for investment, with a promise to repay the principal amount and interest on a specific date.

Cash Flow Diagram

a graphical representation of cash flows drawn on a time scale.

1. Horizontal Line

2. Arrows

3. Depends on the person’s viewpoint

What are the three elements in cash flow diagram?

Horizontal Line

Represents the time with progression of time moving from left to right (i.e. month, year).

Arrows

Represents cash flows.

Arrow up

receipts (positive cash flow or cash inflow i.e income)

Arrow down

disbursements (negative cash flow or cash outflow i.e expenses)

Depends on the person’s viewpoint

Borrower’s viewpoint

Lender’s viewpoint

1. Single Cash Flows

2. Equal Uniform Series

3. Linear Gradient Series

4. Geometric Gradient Series

5. Irregular Series

Types of Cash Flows

Single Cash Flows

simplest case involves the equivalence of a single present amount (P)and its future worth (F).

Equal Uniform Series

transactions arranged as a series of equal cash flows at regular intervals.

Linear Gradient Series

cash flow that increase or decrease by uniform amount each periods.

Geometric Gradient Series

cash flows that increase or decrease by a fixed percentage.

Irregular Series

consists of cash flow that change with no pattern.

Interest

the amount of money paid for the use of borrowed capital or income produced by money which has been loaned.

Simple Interest

the interest on a loan that is based only on the principal. Usually used for short-term loans where the period is measured in days rather than years.

1. Ordinary Simple Interest

2. Exact Simple Interest

Types of Simple Interest

Ordinary Simple Interest

interest is computed on the basis of 12 months of 30 days each which is equivalent to 360 days a year. In this case, the value of n that is used in the preceding formulas may be computed as: n= d/360; where d is the number of days the principal was invested

Exact Simple Interest

interest is computed based on the exact number of days in a given year which is 365 days for a normal year and 366 days during a leap year (which occurs every 4 years, or if it is a century year, it must be divided by 400).

Discount

in simple terms is the interest deducted in advance. It is the difference between the amount a borrower receives in cash (present worth) and the amount he pays in the future (future worth).

Compound Interest

-interest which is based on the principal plus the previous accumulated interest.

-It may also be defined as ‘interest on top of interest.”

-This is usually used in commercial practice especially for longer periods.

Rate of Interest

The cost of borrowing money or the amount earned by a unit principal per unit time.

1. Nominal Rates of Interest

2. Effective Rates of Interest

Types of Rates of Interest

Nominal Rates of Interest

is the basic annual rate of interest. It specifies the rate of interest and the number of interest periods in one year.

Effective Rates of Interest

is the actual or the exact rate of interest earned on the principal during a one-year period.

Continuous Compounding

based on the assumption that cash payments occur once per year but compounding is continuous throughout the year.

Annuities

a series of equal payments occurring at equal interval of time.

1. Ordinary Annuity

2. Deferred Annuity

Types of Annuities

Ordinary Annuity

this type of annuity is one where the payments are made at the end of each period beginning from the first period.

Deferred Annuity

this type of annuity is one where the first payment is made several periods after the beginning of the annuity.

Annuity Due

The annuity due is when payments are made at the beginning of the payment period.

Perpetuity

is an annuity where the payment period extends forever, which means that the periodic payments continue indefinitely.

Arithmetic Gradient Series

-An arithmetic gradient cash flow is one wherein the cash flow changes (increase or decreases) by the same amount in each cash flow period. The amount of increase or decrease is called gradient.

Geometric Gradient Series

is when the periodic payment increases or decreases by a

constant percentage.

Capitalized Cost (CC) - Present Worth

this is one of the most important applications of perpetuity. The capitalized cost of any property is the sum of its first cost and the present worth of all costs for replacement, operation, and maintenance for a long period or forever.

Amortization

is any mode of paying debt, the principal and the interest included, usually by a series of uniform amount every period.

Amortization schedule

a table showing the payments throughout the total

interest period.