Reading 6 - The Time Value of Money Theory

Question 1

Summarize interest rate r

Answer 1

The interest rate, r, is the required rate of return; r is also called the discount rate or opportunity cost.

Question 2

How can an interest rate be viewed?

Answer 2

An interest rate can be viewed as the sum of the real risk-free interest rate and a set of premiums that compensate lenders for risk: an inflation premium, a default risk premium, a liquidity premium, and a maturity premium.

Question 3

How are FV and PV related?

Answer 3

The future value, FV, is the present value, PV, times the future value factor, (1 + r)^N.

Question 4

Note on the interest rate and equivalency

Answer 4

The interest rate, r, makes current and future currency amounts equivalent based on their time value.

Question 5

Limitations of the stated annual interest rate

Answer 5

The stated annual interest rate is a quoted interest rate that does not account for compounding within the year.

Question 6

Periodic rate

Answer 6

The periodic rate is the quoted interest rate per period; it equals the stated annual interest rate divided by the number of compounding periods per year.

Question 7

Effective annual rate

Answer 7

The effective annual rate is the amount by which a unit of currency will grow in a year with interest on interest included.

Question 8

Annuity

Answer 8

An annuity is a finite set of level sequential cash flows.

Question 9

Types of annuities

Answer 9

There are two types of annuities, the annuity due and the ordinary annuity. The annuity due has a first cash flow that occurs immediately; the ordinary annuity has a first cash flow that occurs one period from the present (indexed at t = 1).

Question 10

Time lines Method

Answer 10

On a time line, we can index the present as 0 and then display equally spaced hash marks to represent a number of periods into the future. This representation allows us to index how many periods away each cash flow will be paid.

Question 11

Annuity factors

Answer 11

Annuities may be handled in a similar fashion as single payments if we use annuity factors instead of single-payment factors.

Question 12

PV to FV relationship

Answer 12

The present value, PV, is the future value, FV, times the present value factor, (1 + r)^{−<em>N</em>}.

Question 13

Present value of a perpetuity

Answer 13

The present value of a perpetuity is A/r, where A is the periodic payment to be received forever.

Question 14

Key note about cash flow additivity principle

Answer 14

The cash flow additivity principle can be used to solve problems with uneven cash flows by combining single payments and annuities.