Chapter 13A – Lecture Notes
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I. Appendix 13A: the concept of present value (Slide #1 is the
title slide for this appendix)
Learning Objective 7: Understand present value concepts
and the use of present value tables.
A. The mathematics of interest
i. A dollar received today is worth more than a dollar
received a year from now because you can put it in
the bank today and have more than a dollar a year
from now.
ii. An example
1. Assume a bank pays 8% interest on a $100
deposit made today.
2. How much will the $100 be worth in one year?
3. The equation needed to answer this question is as
shown, where:
a. F = the ending balance.
b. P = the amount invested now.
c. r = the rate of interest per period.
d. n = the number of periods.
4. Solving this equation, the answer is $108.
5. The $100 outlay is called the present value of the
$108 amount to be received in one year. It is also
known as the discounted value of the future $108
receipt.
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iii. Compound interest – the example continued
1. What if the $108 was left in the bank for a
second year? How much would the original $100
be worth at the end of the second year?
2. The equation needed to answer this question is as
shown, where:
a. F = the ending balance.
b. P = the amount invested now.
c. r = the rate of interest per period.
d. n = the number of periods.
3. Solving this equation, the answer is $116.64.
a. The interest that is paid in the second year
on the interest earned in the first year is
known as compound interest.
B. Computation of present value
i. An investment can be viewed in two ways – its
future value or its present value. In the example
just completed, the present value was known and
the future value was the unknown that we
computed. Let’s look at the opposite situation –
the future value is known and the present value is
the unknown that we must compute.
ii. Present value – an example
1. Assume a bond will pay $100 in two years. If an
investor can earn 12% on their investments, what
is the present value of the bond?
2. The equation needed to answer this question is as
shown, where:
a. F = the ending balance.
b. P = the amount invested now.
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Chapter 13A – Lecture Notes
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c. r = the rate of interest per period.
d. n = the number of periods.
3. Solving this equation, P = $79.72.
a. This process is called discounting. We have
discounted the $100 to its present value of
$79.72. The interest rate used to find the
present value is called the discount rate.
4. We can verify, as shown on the slide, that if we
put $79.72 in the bank today at 12% interest, it
would grow to $100 at the end of two years.
5. We can also use the present value of $1 table
from Appendix 13B-1 to verify the accuracy of
the $79.72 figure.
a. An excerpt of the appropriate table is as
shown.
b. The appropriate present value factor is 0.797
and the present value is $79.72.
Quick Check – present value calculations
C. Present value of a series of cash flows
i. Although some investments involve a single sum to
be received (or paid) at a single point in the future,
other investments involve a series of identical cash
flows known as an annuity.
ii. Lacey Inc. – an example
1. Assume Lacey Inc. purchased a tract of land on
which a $60,000 payment will be due each of the
next five years.
2. What is the present value of this stream of cash
payments when the discount rate is 12%?
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3. Appendix 13B-2 contains a present value of an
annuity of $1 table. An excerpt from this table is
as shown.
4. The appropriate present value factor is 3.605. The
present value is $216,300.
Quic Concept Check – present value of an annuity calculations
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