Appendix Time value of money

Time Value of Money
APPENDIXD
Study Objectives
After studying this appendix, you should be able to:
[1] Distinguish between simple and compound
interest.
[2] Identify the variables fundamental to solving
present value problems.
[3] Solve for present value of a single amount.
[4] Solve for present value of an annuity.
[5] Compute the present value of notes and
bonds.
Would you rather receive $1,000 today or a year from now? You should prefer
to receive the $1,000 today because you can invest the $1,000 and earn interest
on it. As a result, you will have more than $1,000 a year from now. What this
example illustrates is the concept of the time value of money. Everyone pre-
fers to receive money today rather than in the future because of the interest
factor.
Interest is payment for the use of another person’s money. It is the difference be-
tween the amount borrowed or invested (called the principal) and the amount re-
paid or collected. The amount of interest to be paid or collected is usually stated as
a rate over a specific period of time. The rate of interest is generally stated as an
annual rate.
The amount of interest involved in any financing transaction is based on three
elements:
1. Principal (p): The original amount borrowed or invested.
2. Interest Rate (i): An annual percentage of the principal.
3. Time (n): The number of years that the principal is borrowed or invested.
Simple Interest
Simple interest is computed on the principal amount only. It is the return on the
principal for one period.Simple interest is usually expressed as shown in Illustration
D-1 on the next page.
Nature of Interest
Study Objective [1]
Distinguish between
simple and compound
interest.
D1
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D2 Appendix D Time Value of Money
Compound Interest
Compound interest is computed on principal and on any interest earned that has
not been paid or withdrawn. It is the return on the principal for two or more time
periods. Compounding computes interest not only on the principal but also on the
interest earned to date on that principal, assuming the interest is left on deposit.
To illustrate the difference between simple and compound interest, assume
that you deposit $1,000 in Bank Two, where it will earn simple interest of 9% per
year, and you deposit another $1,000 in Citizens Bank, where it will earn com-
pound interest of 9% per year compounded annually. Also assume that in both
cases you will not withdraw any interest until three years from the date of deposit.
Illustration D-2 shows the computation of interest you will receive and the accu-
mulated year-end balances.
Interest 5 Principal 3 Rate 3 Time
p i n
For example, if you borrowed $5,000 for 2 years at a simple interest rate of 12% annually,
you would pay $1,200 in total interest computed as follows:
Interest 5 p 3 i 3 n
5 $5,000 3 .12 3 2
5 $1,200
Illustration D-1
Interest computation
Illustration D-2
Simple versus compound
interest
Simple Interest
Calculation
Year 1
Year 2
Year 3
$1,000.00 × 9%
$1,000.00 × 9%
$1,000.00 × 9%
$
$
90.00
90.00
90.00
270.00
$1,090.00
$1,180.00
$1,270.00
$25.03
Difference
Simple
Interest
Accumulated
Year-End
Balance
Bank Two
Compound Interest
Calculation
Year 1
Year 2
Year 3
$1,000.00 × 9%
$1,090.00 × 9%
$1,188.10 × 9%
$
$
90.00
98.10
106.93
295.03
$1,090.00
$1,188.10
$1,295.03
Compound
Interest
Accumulated
Year-End
Balance
Citizens Bank
Note in Illustration D-2 that simple interest uses the initial principal of $1,000
to compute the interest in all three years. Compound interest uses the accumulated
balance (principal plus interest to date) at each year-end to compute interest in the
succeeding year—which explains why your compound interest account is larger.
Obviously,if you had a choice between investing your money at simple interest or at
compound interest, you would choose compound interest, all other things—especially
risk—being equal.In the example,compounding provides $25.03 of additional interest
income. For practical purposes, compounding assumes that unpaid interest earned be-
comes a part of the principal, and the accumulated balance at the end of each year
becomes the new principal on which interest is earned during the next year.
Illustration D-2 indicates that you should invest your money at the bank that
compounds interest annually.Most business situations use compound interest.Simple
interest is generally applicable only to short-term situations of one year or less.

Present Value Variables
The present value is the value now of a given amount to be paid or received in the
future, assuming compound interest.The present value is based on three variables:
(1) the dollar amount to be received (future amount), (2) the length of time until
the amount is received (number of periods), and (3) the interest rate (the discount
rate).The process of determining the present value is referred to as discounting the
future amount.
In this textbook,we use present value computations in measuring several items.
For example, Chapter 15 computed the present value of the principal and interest
payments to determine the market price of a bond. In addition, determining the
amount to be reported for notes payable and lease liabilities involves present value
computations.
Present Value of a Single Amount
To illustrate present value, assume that you want to invest a sum of money that will
yield $1,000 at the end of one year. What amount would you need to invest today
to have $1,000 one year from now? Illustration D-3 shows the formula for calculat-
ing present value.
Present Value of a Single Amount D3
Study Objective [3]
Solve for present value
of a single amount.
Thus, if you want a 10% rate of return, you would compute the present value of
$1,000 for one year as follows:
PV 5 FV 4 (1 1 i)n
5 $1,000 4 (1 1 .10)1
5 $1,000 4 1.10
5 $909.09
We know the future amount ($1,000), the discount rate (10%), and the
number of periods (1). These variables are depicted in the time diagram in
Illustration D-4.
i = 10%
n = 1 year
Present
Value (?)
$909.09
Future
Value
$1,000
Illustration D-4
Finding present value if
discounted for one period
If you receive the single amount of $1,000 in two years, discounted at
10% [PV 5 $1,000 4 (1 1 .10)2
], the present value of your $1,000 is $826.45
[($1,000 4 1.21), depicted as shown in Illustration D-5 on the next page.
Study Objective [2]
Identify the variables
fundamental to solving
present value problems.
Present Value 5 Future Value 4 (1 1 i)n
Illustration D-3
Formula for present value

You also could find the present value of your amount through tables that show
the present value of 1 for n periods. In Table 1, below, n (represented in the table’s
rows) is the number of discounting periods involved.The percentages (represented
in the table’s columns) are the periodic interest rates or discount rates. The 5-digit
decimal numbers in the intersections of the rows and columns are called the present
value of 1 factors.
When using Table 1 to determine present value, you multiply the future value
by the present value factor specified at the intersection of the number of periods
and the discount rate.
Table 1
Present Value of 1
(n)
Periods 4% 5% 6% 8% 9% 10% 11% 12% 15%
1 .96154 .95238 .94340 .92593 .91743 .90909 .90090 .89286 .86957
2 .92456 .90703 .89000 .85734 .84168 .82645 .81162 .79719 .75614
3 .88900 .86384 .83962 .79383 .77218 .75132 .73119 .71178 .65752
4 .85480 .82270 .79209 .73503 .70843 .68301 .65873 .63552 .57175
5 .82193 .78353 .74726 .68058 .64993 .62092 .59345 .56743 .49718
6 .79031 .74622 .70496 .63017 .59627 .56447 .53464 .50663 .43233
7 .75992 .71068 .66506 .58349 .54703 .51316 .48166 .45235 .37594
8 .73069 .67684 .62741 .54027 .50187 .46651 .43393 .40388 .32690
9 .70259 .64461 .59190 .50025 .46043 .42410 .39092 .36061 .28426
10 .67556 .61391 .55839 .46319 .42241 .38554 .35218 .32197 .24719
11 .64958 .58468 .52679 .42888 .38753 .35049 .31728 .28748 .21494
12 .62460 .55684 .49697 .39711 .35554 .31863 .28584 .25668 .18691
13 .60057 .53032 .46884 .36770 .32618 .28966 .25751 .22917 .16253
14 .57748 .50507 .44230 .34046 .29925 .26333 .23199 .20462 .14133
15 .55526 .48102 .41727 .31524 .27454 .23939 .20900 .18270 .12289
16 .53391 .45811 .39365 .29189 .25187 .21763 .18829 .16312 .10687
17 .51337 .43630 .37136 .27027 .23107 .19785 .16963 .14564 .09293
18 .49363 .41552 .35034 .25025 .21199 .17986 .15282 .13004 .08081
19 .47464 .39573 .33051 .23171 .19449 .16351 .13768 .11611 .07027
20 .45639 .37689 .31180 .21455 .17843 .14864 .12403 .10367 .06110
For example, the present value factor for one period at a discount rate of 10%
is .90909, which equals the $909.09 ($1,000 3 .90909) computed in Illustration D-4.
For two periods at a discount rate of 10%, the present value factor is .82645, which
equals the $826.45 ($1,000 3 .82645) computed previously.
Note that a higher discount rate produces a smaller present value. For example,
using a 15% discount rate, the present value of $1,000 due one year from now is
$869.57, versus $909.09 at 10%. Also note that the further removed from the pres-
ent the future value is, the smaller the present value. For example, using the same
Illustration D-5
Finding present value if
discounted for two periods
i = 10%
1
Present
Value (?)
0
Future
Value
2
n = 2 years$826.45 $1,000

Present Value of an Annuity D5
discount rate of 10%, the present value of $1,000 due in five years is $620.92, versus
the present value of $1,000 due in one year, which is $909.09.
The following two demonstration problems (Illustrations D-6 and D-7) illustrate
how to use Table 1.
Present Value of an Annuity
The preceding discussion involved the discounting of only a single future amount.
Businesses and individuals frequently engage in transactions in which a series of equal
dollar amounts are to be received or paid at evenly spaced time intervals (periodically).
Examples of a series of periodic receipts or payments are loan agreements,installment
sales,mortgage notes,lease (rental) contracts,and pension obligations.As discussed in
Chapter 15, these periodic receipts or payments are annuities.
The present value of an annuity is the value now of a series of future receipts
or payments, discounted assuming compound interest. In computing the present
value of an annuity, you need to know: (1) the discount rate, (2) the number of dis-
count periods, and (3) the amount of the periodic receipts or payments.
Illustration D-6
Demonstration problem—
Using Table 1 for PV of 1
i = 8%
2
PV = ?
Now
$10,000
3 years1
Suppose you have a winning lottery ticket and the state gives you the
option of taking $10,000 three years from now or taking the present
value of $10,000 now. The state uses an 8% rate in discounting. How
much will you receive if you accept your winnings now?
Answer: The present value factor from Table 1 is .79383
(3 periods at 8%). The present value of $10,000 to be received in
3 years discounted at 8% is $7,938.30 ($10,000 × .79383).
n = 3
Illustration D-7
Using Table 1 for PV of 1
i = 9%
3
PV = ?
Now
$5,000
4 years1
Determine the amount you must deposit now in a bond investment,
paying 9% interest, in order to accumulate $5,000 for a down
payment 4 years from now on a new Toyota Prius.
Answer: The present value factor from Table 1 is .70843
(4 periods at 9%). The present value of $5,000 to be received in
4 years discounted at 9% is $3,542.15 ($5,000 × .70843).
2
n = 4
Study Objective [4]
Solve for present value
of an annuity.

To illustrate how to compute the present value of an annuity, assume that you
will receive $1,000 cash annually for three years at a time when the discount rate is
10%. Illustration D-8 depicts this situation, and Illustration D-9 shows the compu-
tation of its present value.
Illustration D-9
Present value of a series of
future amounts computation
Present Value of 1
Future Amount 3 Factor at 10% 5 Present Value
$1,000 (one year away) .90909 $ 909.09
1,000 (two years away) .82645 826.45
1,000 (three years away) .75132 751.32
2.48686 $2,486.86
This method of calculation is required when the periodic cash flows are not
uniform in each period. However, when the future receipts are the same in each
period, there are two other ways to compute present value. First, you can multiply
the annual cash flow by the sum of the three present value factors. In the previous
example, $1,000 3 2.48686 equals $2,486.86. The second method is to use annuity
tables.As illustrated in Table 2 below, these tables show the present value of 1 to be
received periodically for a given number of periods.
Table 2
Present Value of an Annuity of 1
(n)
Periods 4% 5% 6% 8% 9% 10% 11% 12% 15%
1 .96154 .95238 .94340 .92593 .91743 .90909 .90090 .89286 .86957
2 1.88609 1.85941 1.83339 1.78326 1.75911 1.73554 1.71252 1.69005 1.62571
3 2.77509 2.72325 2.67301 2.57710 2.53130 2.48685 2.44371 2.40183 2.28323
4 3.62990 3.54595 3.46511 3.31213 3.23972 3.16986 3.10245 3.03735 2.85498
5 4.45182 4.32948 4.21236 3.99271 3.88965 3.79079 3.69590 3.60478 3.35216
6 5.24214 5.07569 4.91732 4.62288 4.48592 4.35526 4.23054 4.11141 3.78448
7 6.00205 5.78637 5.58238 5.20637 5.03295 4.86842 4.71220 4.56376 4.16042
8 6.73274 6.46321 6.20979 5.74664 5.53482 5.33493 5.14612 4.96764 4.48732
9 7.43533 7.10782 6.80169 6.24689 5.99525 5.75902 5.53705 5.32825 4.77158
10 8.11090 7.72173 7.36009 6.71008 6.41766 6.14457 5.88923 5.65022 5.01877
11 8.76048 8.30641 7.88687 7.13896 6.80519 6.49506 6.20652 5.93770 5.23371
12 9.38507 8.86325 8.38384 7.53608 7.16073 6.81369 6.49236 6.19437 5.42062
13 9.98565 9.39357 8.85268 7.90378 7.48690 7.10336 6.74987 6.42355 5.58315
14 10.56312 9.89864 9.29498 8.24424 7.78615 7.36669 6.98187 6.62817 5.72448
15 11.11839 10.37966 9.71225 8.55948 8.06069 7.60608 7.19087 6.81086 5.84737
16 11.65230 10.83777 10.10590 8.85137 8.31256 7.82371 7.37916 6.97399 5.95424
17 12.16567 11.27407 10.47726 9.12164 8.54363 8.02155 7.54879 7.11963 6.04716
18 12.65930 11.68959 10.82760 9.37189 8.75563 8.20141 7.70162 7.24967 6.12797
19 13.13394 12.08532 11.15812 9.60360 8.95012 8.36492 7.83929 7.36578 6.19823
20 13.59033 12.46221 11.46992 9.81815 9.12855 8.51356 7.96333 7.46944 6.25933
Illustration D-8
Time diagram for a three-year
annuity
i = 10%
2Now 3 years
PV = ? $1,000 $1,000$1,000
1
n = 3

Table 2 shows that the present value of an annuity of 1 factor for three periods
at 10% is 2.48685.1
(This present value factor is the total of the three individual
present value factors, as shown in Illustration D-9.) Applying this amount to the
annual cash flow of $1,000 produces a present value of $2,486.85.
The following demonstration problem (Illustration D-10) illustrates how to use
Table 2.
Time Periods and Discounting
In the preceding calculations, the discounting was done on an annual basis using an
annual interest rate. Discounting may also be done over shorter periods of time
such as monthly, quarterly, or semiannually.
When the time frame is less than one year, you need to convert the annual
interest rate to the applicable time frame. Assume, for example, that the investor
in Illustration D-8 received $500 semiannually for three years instead of $1,000
annually. In this case, the number of periods becomes six (3 3 2), the discount
rate is 5% (10% 4 2), the present value factor from Table 2 is 5.07569, and the
present value of the future cash flows is $2,537.85 (5.07569 3 $500). This amount
is slightly higher than the $2,486.86 computed in Illustration D-9 because interest
is paid twice during the same year; therefore interest is earned on the first half
year’s interest.
Computing the Present Value
of a Long-Term Note or Bond
The present value (or market price) of a long-term note or bond is a function of
three variables: (1) the payment amounts, (2) the length of time until the amounts
are paid, and (3) the discount rate. Our illustration uses a five-year bond issue.
i = 12%
4
PV = ?
Now
$6,000
5 years1
Kildare Company has just signed a capitalizable lease contract for equip-
ment that requires rental payments of $6,000 each, to be paid at the end
of each of the next 5 years. The appropriate discount rate is 12%. What
is the present value of the rental payments—that is, the amount used to
capitalize the leased equipment?
Answer: The present value factor from Table 2 is 3.60478
(5 periods at 12%). The present value of 5 payments of $6,000 each
discounted at 12% is $21,628.68 ($6,000 × 3.60478).
$6,000 $6,000
2 3
$6,000 $6,000
n = 5
Illustration D-10
Using Table 2 for PV of an
annuity of 1
1
The difference of .00001 between 2.48686 and 2.48685 is due to rounding.
Study Objective [5]
Compute the present
value of notes and bonds.
Computing the Present Value of a Long-Term Note or Bond D7

The first variable—dollars to be paid—is made up of two elements: (1) a series
of interest payments (an annuity), and (2) the principal amount (a single sum). To
compute the present value of the bond, we must discount both the interest pay-
ments and the principal amount—two different computations. The time diagrams
for a bond due in five years are shown in Illustration D-11.
When the investor’s market interest rate is equal to the bond’s contractual
interest rate, the present value of the bonds will equal the face value of the
bonds. To illustrate, assume a bond issue of 10%, five-year bonds with a face
value of $100,000 with interest payable semiannually on January 1 and July 1. If
the discount rate is the same as the contractual rate, the bonds will sell at face
value. In this case, the investor will receive the following: (1) $100,000 at matu-
rity, and (2) a series of ten $5,000 interest payments [($100,000 3 10%) 4 2]
over the term of the bonds. The length of time is expressed in terms of interest
periods—in this case—10, and the discount rate per interest period, 5%. The
following time diagram (Illustration D-12) depicts the variables involved in this
discounting situation.
Interest Rate (i)
1 yr.
Present
Value (?)
Now
Principal
Amount
5 yr.
Diagram
for
Principal
2 yr. 3 yr. 4 yr.
Interest
1 yr.
Present
Value (?)
Now 5 yr.
Diagram
for
Interest
2 yr. 3 yr. 4 yr.
Interest Rate (i)
Interest Interest Interest Interest
n = 5
n = 5
Illustration D-11
Present value of a bond time
diagram
i = 5%
1
Present
Value
(?)
Now
Principal
Amount
$100,000
10
Diagram
for
Principal
5 6
1
Present
Value
(?)
Now 10
Diagram
for
Interest
5 6
i = 5%
$5,000
2
2
3
3
4
4
7
7
8
8
9
9
$5,000 $5,000 $5,000 $5,000$5,000 $5,000 $5,000 $5,000
n = 10
n = 10
$5,000
Interest
Payments
Illustration D-12
Time diagram for present value
of a 10%, five-year bond
paying interest semiannually

Illustration D-13 shows the computation of the present value of these bonds.
Now assume that the investor’s required rate of return is 12%, not 10%. The
future amounts are again $100,000 and $5,000, respectively, but now a discount
rate of 6% (12% 4 2) must be used. The present value of the bonds is $92,639, as
computed in Illustration D-14.
Conversely, if the discount rate is 8% and the contractual rate is 10%, the pres-
ent value of the bonds is $108,111, computed as shown in Illustration D-15.
The above discussion relies on present value tables in solving present value
problems. Many people use spreadsheets such as Excel or financial calculators
(some even on websites) to compute present values,without the use of tables.Many
calculators, especially “financial calculators,” have present value (PV) functions
that allow you to calculate present values by merely inputting the proper amount,
discount rate, and periods, and pressing the PV key. Appendix E illustrates how to
use a financial calculator in various business situations.
Illustration D-13
Present value of principal
and interest—face value
10% Contractual Rate—10% Discount Rate
Present value of principal to be received at maturity
$100,000 3 PV of 1 due in 10 periods at 5%
$100,000 3 .61391 (Table 1) $ 61,391
Present value of interest to be received periodically
over the term of the bonds
$5,000 3 PV of 1 due periodically for 10 periods at 5%
$5,000 3 7.72173 (Table 2) 38,609*
Present value of bonds $100,000
*Rounded
Illustration D-14
and interest—discount
$100,000 3 .55839 (Table 1) $55,839
$5,000 3 7.36009 (Table 2) 36,800
Illustration D-15
and interest—premium
$100,000 3 .67556 (Table 1) $ 67,556
$5,000 3 8.11090 (Table 2) 40,555
Computing the Present Value of a Long-Term Note or Bond D9

[1] Distinguish between simple and compound
interest. Simple interest is computed on the principal only,
while compound interest is computed on the principal and any
interest earned that has not been withdrawn.
[2] Identify the variables fundamental to solving
present value problems. The following three variables are
fundamental to solving present value problems: (1) the future
amount, (2) the number of periods, and (3) the interest rate
(the discount rate).
[3] Solve for present value of a single amount. Pre-
pare a time diagram of the problem. Identify the future
amount, the number of discounting periods, and the discount
(interest) rate. Using the present value of a single amount
table, multiply the future amount by the present value factor
specified at the intersection of the number of periods and the
discount rate.
[4] Solve for present value of an annuity. Prepare a
time diagram of the problem. Identify the future annuity pay-
ments, the number of discounting periods, and the discount
(interest) rate. Using the present value of an annuity of 1 table,
multiply the amount of the annuity payments by the present
value factor specified at the intersection of the number of pe-
riods and the interest rate.
[5] Compute the present value of notes and bonds. To
determine the present value of the principal amount: Multiply
the principal amount (a single future amount) by the present
value factor (from the present value of 1 table) intersecting at
the number of periods (number of interest payments) and the
discount rate.
To determine the present value of the series of interest
payments: Multiply the amount of the interest payment by the
present value factor (from the present value of an annuity of 1
table) intersecting at the number of periods (number of inter-
est payments) and the discount rate. Add the present value of
the principal amount to the present value of the interest pay-
ments to arrive at the present value of the note or bond.
Summary of Study Objectives
Annuity A series of equal dollar amounts to be paid or re-
ceived at evenly spaced time intervals (periodically). (p. D5).
Compound interest The interest computed on the principal
and any interest earned that has not been paid or withdrawn.
(p. D2).
Discounting the future amount(s) The process of
determining present value. (p. D3).
Interest Payment for the use of another’s money. (p. D1).
Present value The value now of a given amount to be paid or
received in the future assuming compound interest. (p. D3).
Present value of an annuity The value now of a series
of future receipts or payments, discounted assuming com-
pound interest. (p. D5).
Principal The amount borrowed or invested. (p. D1).
Simple interest The interest computed on the principal
only. (p. D1).
Glossary
Use present value tables.
Brief Exercises
Use tables to solve exercises.
BED-1 For each of the following cases, indicate (a) to what interest rate columns, and (b) to
what number of periods you would refer in looking up the discount rate.
1. In Table 1 (present value of 1):
Number of Compounding
Annual Rate Years Involved Per Year
(a) 12% 6 Annually
(b) 10% 15 Annually
(c) 8% 12 Semiannually
2. In Table 2 (present value of an annuity of 1):
Number of Number of Frequency of
Annual Rate Years Involved Payments Involved Payments
(a) 8% 20 20 Annually
(b) 10% 5 5 Annually
(c) 12% 4 8 Semiannually
BED-2 (a) What is the present value of $30,000 due 8 periods from now, discounted at
8%? (b) What is the present value of $30,000 to be received at the end of each of 6 periods,
discounted at 9%?
Determine present values.

BED-3 Ramirez Company is considering an investment that will return a lump sum of $600,000
5 years from now. What amount should Ramirez Company pay for this investment in order to
earn a 10% return?
BED-4 LaRussa Company earns 9% on an investment that will return $700,000 8 years from
now.What is the amount LaRussa should invest now in order to earn this rate of return?
BED-5 Polley Company sold a 5-year, zero-interest-bearing $36,000 note receivable to Valley
Inc.Valley wishes to earn 10% over the remaining 4 years of the note. How much cash will Polley
receive upon sale of the note?
BED-6 Marichal Company issues a 3-year, zero-interest-bearing $60,000 note.The interest rate
used to discount the zero-interest-bearing note is 8%.What are the cash proceeds that Marichal
Company should receive?
BED-7 Colaw Company is considering investing in an annuity contract that will return $40,000
annually at the end of each year for 15 years.What amount should Colaw Company pay for this
investment if it earns a 6% return?
BED-8 Sauder Enterprises earns 11% on an investment that pays back $100,000 at the end of
each of the next 4 years. What is the amount Sauder Enterprises invested to earn the 11% rate
of return?
BED-9 Chicago Railroad Co. is about to issue $200,000 of 10-year bonds paying a 10% interest
rate, with interest payable semiannually. The discount rate for such securities is 8%. How much
can Chicago expect to receive for the sale of these bonds?
BED-10 Assume the same information as in BED-9 except that the discount rate is 10% instead
of 8%. In this case, how much can Chicago expect to receive from the sale of these bonds?
BED-11 Berghaus Company receives a $75,000, 6-year note bearing interest of 8% (paid an-
nually) from a customer at a time when the discount rate is 9%.What is the present value of the
note received by Berghaus Company?
BED-12 Troutman Enterprises issued 8%, 8-year, $1,000,000 par value bonds that pay interest
semiannually on October 1 and April 1.The bonds are dated April 1, 2012, and are issued on that
date. The discount rate of interest for such bonds on April 1, 2012, is 10%. What cash proceeds
did Troutman receive from issuance of the bonds?
BED-13 Ricky Cleland owns a garage and is contemplating purchasing a tire retreading ma-
chine for $16,280. After estimating costs and revenues, Ricky projects a net cash flow from the
retreading machine of $2,800 annually for 8 years. Ricky hopes to earn a return of 11% on such
investments. What is the present value of the retreading operation? Should Ricky Cleland pur-
chase the retreading machine?
BED-14 Martinez Company issues a 10%, 6-year mortgage note on January 1, 2012, to obtain
financing for new equipment. Land is used as collateral for the note.The terms provide for semi-
annual installment payments of $78,978.What were the cash proceeds received from the issuance
of the note?
BED-15 Durler Company is considering purchasing equipment. The equipment will produce
the following cash flows:Year 1, $30,000;Year 2, $40,000;Year 3, $60,000. Durler requires a mini-
mum rate of return of 12%.What is the maximum price Durler should pay for this equipment?
BED-16 If Carla Garcia invests $2,745 now,she will receive $10,000 at the end of 15 years.What
annual rate of interest will Carla earn on her investment? (Hint: Use Table 1.)
BED-17 Sara Altom has been offered the opportunity of investing $51,316 now. The invest-
ment will earn 10% per year and at the end of that time will return Sara $100,000. How many
years must Sara wait to receive $100,000? (Hint: Use Table 1.)
BED-18 Stacy Dains purchased an investment for $11,469.92. From this investment, she will
receive $1,000 annually for the next 20 years, starting one year from now. What rate of interest
will Stacy’s investment be earning for her? (Hint: Use Table 2.)
BED-19 Diana Rossi invests $8,559.48 now for a series of $1,000 annual returns, beginning one
year from now. Diana will earn a return of 8% on the initial investment. How many annual pay-
ments of $1,000 will Diana receive? (Hint: Use Table 2.)
BED-20 Minitori Company needs $10,000 on January 1, 2015. It is starting a fund on January
1, 2012.
Compute the present value of a
single-sum investment.
Compute the present value of a
single-sum investment.
Compute the present value of
a single-sum zero-interest-
bearing note.
a single-sum zero-interest-
bearing note.
an annuity investment.
an annuity investment.
bonds.
bonds.
a note.
Compute the value of a
machine for purposes of
making a purchase decision.
bonds.
a note.
Compute the maximum price
to pay for a machine.
Compute the interest rate on a
single sum.
Compute the number of
periods of a single sum.
Compute the interest rate on
an annuity.
Compute the number of
periods of an annuity.
Compute the amount to be
invested.
Brief Exercises D11

Instructions
Compute the amount that must be invested in the fund on January 1, 2012, to produce a $10,000
balance on January 1, 2015, if:
(a) The fund earns 8% per year compounded annually.
(b) The fund earns 8% per year compounded semiannually.
(c) The fund earns 12% per year compounded annually.
(d) The fund earns 12% per year compounded semiannually.
BED-21 Venuchi Company needs $10,000 on January 1, 2017. It is starting a fund to produce
that amount.
Instructions
Compute the amount that must be invested in the fund to produce a $10,000 balance on January
1, 2017, if:
(a) The initial investment is made January 1, 2012, and the fund earns 6% per year.
(b) The initial investment is made January 1, 2014, and the fund earns 6% per year.
(c) The initial investment is made January 1, 2012, and the fund earns 10% per year.
(d) The initial investment is made January 1, 2014, and the fund earns 10% per year.
BED-22 Letterman Corporation is buying new equipment. It can pay $39,500 today (option 1),
or $10,000 today and 5 yearly payments of $8,000 each, starting in one year (option 2).
Instructions
Which option should Letterman select? (Assume a discount rate of 10%.)
BED-23 Carmen Corporation is considering several investments.
Instructions
(a) One investment returns $10,000 per year for 5 years and provides a return of 10%. What is
the cost of this investment?
(b) Another investment costs $50,000 and returns a certain amount per year for 10 years, provid-
ing an 8% return.What amount is received each year?
(c) A third investment costs $70,000 and returns $11,971 each year for 15 years.What is the rate
of return on this investment?
BED-24 You are the beneficiary of a trust fund. The fund gives you the option of receiving
$5,000 per year for 10 years, $9,000 per year for 5 years, or $30,000 today.
Instructions
If the desired rate of return is 8%, which option should you select?
BED-25 You are purchasing a car for $24,000,and you obtain financing as follows:$2,400 down
payment, 12% interest, semiannual payments over 5 years.
Instructions
Compute the payment you will make every 6 months
BED-26 Contreras Corporation is considering purchasing bonds of Jose Company as an in-
vestment.The bonds have a face value of $40,000 with a 10% interest rate.The bonds mature in
4 years and pay interest semiannually.
Instructions
(a) What is the most Contreras should pay for the bonds if it desires a 12% return?
(b) What is the most Contreras should pay for the bonds if it desires an 8% return?
BED-27 Garcia Corporation is considering purchasing bonds of Fred Company as an invest-
ment.The bonds have a face value of $90,000 with a 9% interest rate.The bonds mature in 6 years
and pay interest semiannually.
Instructions
(a) What is the most Garcia should pay for the bonds if it desires a 10% return?
(b) What is the most Garcia should pay for the bonds if it desires an 8% return?
Compute the amount to be
invested.
Select the better payment
option.
Compute the cost of an invest-
ment, amount received, and rate
of return.
Select the best payment option.
Compute the semiannual car
payment.
bonds.
bonds.
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Appendix Time value of money

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Appendix Time value of money