Reading 1: Time Value of Money

Question 1

Interpret interest rates as required rates of return, discount rates, or opportunity costs.

Answer 1

An interest rate can be interpreted as:

• The rate of return required in equilibrium for a particular investment,
• The discount rate for calculating the present value of future cash flows, or as
• The opportunity cost of consuming now, rather than saving and investing.

Question 2

Explain an interest rate as the sum of a real risk-free rate and premiums that compensate investors for bearing distinc types of risks.

Answer 2

The real risk-free rate is a theoretical rate on a single-period loan when there is no expectation of inflation.

Nominal risk-free rate = real risk-free rate + expected inflation rate.

Securities may have several risks, and each increases the required rate of return. These include (i) default risk, (ii) liquidity risk and (iii) maturity risk.

The required rate of return on a security = real risk-free rate + expected inflation + default risk premium + liquidity premium + maturity risk premium.

Question 3

Calculate and interpret the effective annual rate, given the stated annual interest rate and the frequency of compounding.

Answer 3

Question 4

Calculate the solution for time value of money problems with differente frequencies of compounding.

Answer 4

For non-annual time value of money problems, divide the stated annual interest rate by the number of compounding periods per year, m, and multiply the number of years by the number of compounding periods per year.

Question 5

Calculate and interpret the future value (FV) and present value (PV) of a single sum of money, an ordinary annuity due, a perpetuity (PV only) and a series of unequal cash flows.

Answer 5

Question 6

Demonstrate the use of a time line in modeling and solving time value of money problems.

Answer 6

Constructing a time line showing future cash flows will help in solving many types of TVM problems. Cash flows occur at the end of the period depicted on the time line. The end of one period is the same as the beginning of the next period. For example, a cash flow at the beginning of Year 3 appears at time t = 2 on the time line.