Financie
THE TIME VALUE OF MONEY by Richard A. DeFusco, CFA, Dennis W. McLeavey, CFA, Jerald E. Pinto, CFA, and David E. Runkle, CFA
LEARNING OUTCOMES
INTRODUCTION 1
As individuals, we often face decisions that involve saving money for a future use, or borrowing money for current consumption. We then need to determine the amount we need to invest, if we are saving, or the cost of borrowing, if we are shopping for a loan. As investment analysts, much of our work also involves evaluating transactions with present and future cash flows. When we place a value on any security, for example, we are attempting to determine the worth of a stream of future cash flows. To carry out all the above tasks accurately, we must understand the mathematics of time value of money problems. Money has time value in that individuals value a given amount of money more highly the earlier it is received. Therefore, a smaller amount of money
READING
5
The candidate should be able to:
a. interpret interest rates as required rate of return, discount rate, or opportunity cost;
Mastery
b. explain an interest rate as the sum of a real risk-free rate, expected inflation, and premiums that compensate investors for distinct types of risk;
c. calculate and interpret the effective annual rate, given the stated annual interest rate and the frequency of compounding;
d. solve time value of money problems when compounding periods are other than annual;
e. calculate and interpret the future value (FV) and present value (PV) of a single sum of money, an ordinary annuity, an annuity due, a perpetuity (PV only), and a series of unequal cash flows;
f. draw a time line and solve time value of money applications (for example, mortgages and savings for college tuition or retirement).
2 now may be equivalent in value to a larger amount received at a future date. The time value of money as a topic in investment mathematics deals with equivalence relationships between cash flows with different
LEARNING OUTCOMES
INTRODUCTION 1
As individuals, we often face decisions that involve saving money for a future use, or borrowing money for current consumption. We then need to determine the amount we need to invest, if we are saving, or the cost of borrowing, if we are shopping for a loan. As investment analysts, much of our work also involves evaluating transactions with present and future cash flows. When we place a value on any security, for example, we are attempting to determine the worth of a stream of future cash flows. To carry out all the above tasks accurately, we must understand the mathematics of time value of money problems. Money has time value in that individuals value a given amount of money more highly the earlier it is received. Therefore, a smaller amount of money
READING
5
The candidate should be able to:
a. interpret interest rates as required rate of return, discount rate, or opportunity cost;
Mastery
b. explain an interest rate as the sum of a real risk-free rate, expected inflation, and premiums that compensate investors for distinct types of risk;
c. calculate and interpret the effective annual rate, given the stated annual interest rate and the frequency of compounding;
d. solve time value of money problems when compounding periods are other than annual;
e. calculate and interpret the future value (FV) and present value (PV) of a single sum of money, an ordinary annuity, an annuity due, a perpetuity (PV only), and a series of unequal cash flows;
f. draw a time line and solve time value of money applications (for example, mortgages and savings for college tuition or retirement).
2 now may be equivalent in value to a larger amount received at a future date. The time value of money as a topic in investment mathematics deals with equivalence relationships between cash flows with different