Chapter 5:
Time Value of Money
Learning Objectives
71
Chapter 5
Time Value of Money
Learning Objectives
After reading this chapter, students should be able to:
Explain how the time value of money works and discuss why it is such an important concept in finance.
Calculate the present value and future value of lump sums.
Identify the different types of annuities and calculate the present value and future value of both an
ordinary annuity and an annuity due, and be able to calculate relevant annuity payments.
Calculate the present value and future value of an uneven cash flow stream, which will be used in later
chapters that show how to value common stocks and corporate projects.
Explain the difference between nominal, periodic, and effective interest rates.
Discuss the basics of loan amortization.

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72
Integrated Case
Chapter 5:
Time Value of Money
Answers to End-of-Chapter Questions
5-1
The opportunity cost is the rate of interest one could earn on an alternative investment with a risk
equal to the risk of the investment in question.
This is the value of I in the TVM equations, and it is
shown on the top of a time line, between the first and second tick marks.
It is not
a single rate—
the opportunity cost rate varies depending on the riskiness and maturity of an investment, and it
also varies from year to year depending on inflationary expectations (see Chapter 6).
5-2
True.
The second series is an uneven cash flow stream, but it contains an annuity of $400 for 8
years.
The series could also be thought of as a $100 annuity for 10 years plus an additional
payment of $100 in Year 2, plus additional payments of $300 in Years 3 through 10.
5-3
True, because of compounding effects—growth on growth.
The following example demonstrates
the point.
The annual growth rate is I in the following equation:
$1(1 + I)
10
= $2.
We can find I in the equation above as follows:
Using a financial calculator input N = 10, PV = -1, PMT = 0, FV = 2, and I/YR = ?
Solving for I/YR
you obtain 7.18%.
Viewed another way, if earnings had grown at the rate of 10% per year for 10 years, then EPS
would have increased from $1.00 to $2.59, found as follows:
Using a financial calculator, input N =
10, I/YR = 10, PV = -1, PMT = 0, and FV = ?.
Solving for FV you obtain $2.59.
This formulation
recognizes the “interest on interest” phenomenon.
5-4
For the same stated rate, daily compounding is best.
You would earn more “interest on interest.”
5-5
False.
One can find the present value of an embedded annuity and add this PV to the PVs of the
other individual cash flows to determine the present value of the cash flow stream.
5-6
The concept of a perpetuity implies that payments will be received forever. FV (Perpetuity) = PV
(Perpetuity)(1 + I)
∞
=
∞
.
5-7
The annual percentage rate (APR) is the periodic rate times the number of periods per year.
It is
also called the nominal, or stated, rate.
With the “Truth in Lending” law, Congress required that
financial institutions disclose the APR so the rate charged would be more “transparent” to
consumers.
The APR is equal to the effective annual rate only when compounding occurs annually.

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