Description
Introduction
How do business leaders plan for the long-term future of their businesses? After the long-term decisions are made, how do business leaders track, monitor, and assess day-to-day, week-to-week, and month-to-month progress? Chapters Eight: How is Capital Budgeting Used to Make Decisions and Chapter Nine: How are Operating Budgets Created address these questions.
Reading Assignment
Chapter Eight, How is Capital Budgeting Used to Make Decisions provides a description of one of the most used models in managerial accounting and in finance: Net present values. This chapter begins by discussing how to compute the time value of money. It then presents how this is used to analyze long-term projects. Two major models used to assess long-term projects are: (1) Net present values (NPV) and (2) Internal rate of return (IRR).
Chapter Nine, How are Operating Budgets Created, describes a major model: The master budget, which is used by business managers and leaders to monitor the operation of their business (which is why it’s called an operating budget). The master budget is consists of an array of other, smaller budgets which report on specific segments of the business.
Chapters 8 & 9 End-Of-Chapter Questions
*Please scroll down to the bottom section of this page to see last week’s end-of-chapter answers.
Discussion Assignment
SportsMax sells sporting goods equipment at 100 stores throughout North America. Robert Manning is the manager of one SportsMax retail store in Chicago. The company is in the planning phase of establishing its operating budget for this coming year and has asked that all store managers submit their estimates of sales revenue, costs, and resulting profit. During the control phase, each store manager is evaluated by comparing budgeted profit with actual profit. Store managers who exceed budgeted profit are given a bonus equal to 10 percent of actual profit in excess of budgeted profit.
Required:
a. Describe the ethical conflict that Robert Manning is facing.
b. As the president and CEO of SportsMax, how might you motivate Robert Manning to provide an accurate operating budget?
Accounting Assignment
Net Present Value Analysis. Architect Services, Inc., would like to purchase a blueprint machine for $50,000. The machine is expected to have a life of 4 years, and a salvage value of $10,000. Annual maintenance costs will total $14,000. Annual savings are predicted to be $30,000. The company’s required rate of return is 11 percent.
Required:
a. Ignoring the time value of money, calculate the net cash inflow or outflow resulting from this investment opportunity.
b. Find the net present value of this investment using the format presented in Figure 8.2.
c. Should the company purchase the blueprint machine? Explain.
Learning Journal
The Learning Journal is a space where you should reflect upon what was learned during the week. How it applies to your daily life and will help you with your life (career) goals. For this week’s reflection, please describe the components of an operating budget and how the different components contribute to the overall budget.
Required Textbook and Materials: UoPeople courses use open educational resources (OER) and other materials specifically donated to the University with free permissions for educational use. Therefore, students are not required to purchase any textbooks or sign up for any websites that have a cost associated with them. The main required textbooks for this course are listed below, and can be readily accessed using the provided links. There may be additional required/recommended readings, supplemental materials, or other resources and websites necessary for lessons; these will be provided for you in the course’s General Information and Forums area, and throughout the term via the weekly course Unit areas and the Learning Guides.
Heisinger, K., & Hoyle, J. B. (2012). Managerial Accounting. Creative Commons by-nc-sa 3.0. https://open.umn.edu/opentextbooks/textbooks/managerial-accounting
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Chapter 8
How Is Capital Budgeting Used to Make Decisions?
© Thinkstock
Julie Jackson is the president and owner of Jackson’s Quality Copies, a store that
makes photocopies for its customers and that has several copy machines. Julie has
the following discussion with Mike Haley, the company’s accountant:
Mike, I think it’s time to buy a new copy machine. Our volume of copies has
Julie: increased dramatically over the last year, and we need a copier that does a
better job of handling the big jobs.
Mike: Do you have any idea how much the new machine will cost?
Julie:
We can purchase a new copier for $50,000, maintenance costs will total $1,000
a year, and the copier is expected to last 7 years. Since the new machine is
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quicker and will require less attention by our employees, we should save
about $11,000 a year in labor costs.
Mike: Will it have any salvage value at the end of seven years?
Julie: Yes. The salvage value should be about $5,000.
Mike: How soon do you want to do this?
As soon as possible. From what I can tell, this is a winning proposition. The
cash inflows of $82,000 that we will get from the labor cost savings and the
Julie:
salvage value exceed the cash outflows of $57,000 that we expect to spend on
the machine and annual maintenance costs. What do you think?
Let me take a look at the numbers before we jump into this. We have to
Mike: consider more than just total cash inflows and outflows. I’ll get back to you
by the end of the week.
Julie: Okay, thanks for your help!
Jackson’s Quality Copies is facing a decision common to many organizations:
whether to invest in equipment that will last for many years or to continue with
existing equipment. This type of decision differs from the decisions covered in the
previous chapter because long-term investment decisions affect organizations for
several years. We will return to Julie’s plan to purchase a new copier after we
provide background information on long-term investment decisions.
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8.1 Capital Budgeting and Decision Making
LEARNING OBJECTIVE
1. Apply the concept of the time value of money to capital budgeting
decisions.
Question: What is the difference between management decisions made in Chapter 7 “How Are
Relevant Revenues and Costs Used to Make Decisions?” and management decisions made in
this chapter?
Answer: The types of decisions covered in this chapter and Chapter 7 “How Are
Relevant Revenues and Costs Used to Make Decisions?” are similar in that they
require an analysis of differential revenues and costs. However, Chapter 7 “How Are
Relevant Revenues and Costs Used to Make Decisions?” involves short-run
operating decisions (e.g., special orders from customers), while this chapter focuses
on long-run capacity decisions (e.g., purchasing long-lived assets to increase
capacity for many years).
Organizations make a variety of long-run investment decisions. The San Francisco
Symphony invests in stage risers for its orchestra members. McDonald’s invests in
new restaurants. Honda Motor Co. invests in new manufacturing facilities. Bank of
America invests in new branches. These examples have one common feature: all of
these companies are investing in assets that will affect the organization for several
years.
1. The process of analyzing and
deciding which long-term
investments (or capital
expenditure decision) to make.
Question: The process of analyzing and deciding which long-term investments to make is
called a capital budgeting decision1, also known as a capital expenditure decision.
Capital budgeting decisions involve using company funds (capital) to invest in long-term
assets. How does the evaluation of these types of capital budgeting decisions differ from
short-term operating decisions discussed in Chapter 7 “How Are Relevant Revenues and
Costs Used to Make Decisions?”?
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Answer: When looking at capital budgeting decisions that affect future years, we
must consider the time value of money. The time value of money concept is the
premise that a dollar received today is worth more than a dollar received in the
future. To clarify this point, suppose a friend owes you $100. Would you prefer to
receive $100 today or 3 years from today? The money is worth more to you if you
receive it today because you can invest the $100 for 3 years.
For capital budgeting decisions, the issue is how to value future cash flows in
today’s dollars. The term cash flow2 refers to the amount of cash received or paid at
a specific point in time. The term present value3 describes the value of future cash
flows (both in and out) in today’s dollars.
2. The amount of cash received or
paid at a specific point in time.
3. The term used to describe
future cash flows (both in and
out) in today’s dollars.
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Business in Action 8.1
© Thinkstock
Capital Budgeting Decisions at JCPenney and Kohl’s
JCPenney Company has over 1,000 department stores in the United States, and
Kohl’s Corporation has over 800. Both companies cater to a “middle market.”
In October 2006, Kohl’s announced plans to open 65 new stores. At about the
same time, JCPenney announced plans to open 20 new stores, 17 of which would
be stand-alone stores. This was a departure from JCPenney’s typical approach
of serving as an anchor store for regional shopping malls.
The decision to open new stores is an example of a capital budgeting decision
because management must analyze the cash flows associated with the new
stores over the long term.
Source: James Covert, “Chasing Mr. and Mrs. Middle Market: J.C. Penney, Kohl’s
Open 85 New Stores,” The Wall Street Journal, October 6, 2006.
When managers evaluate investments in long-term assets, they want to know how
much cash would be spent on the investment and how much cash would be received
as a result of the investment. The investment proposal is likely rejected if cash
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inflows do not exceed cash outflows. (Think about a personal investment. If you
would receive only $700 in the future from an investment of $1,000 today, you
undoubtedly would not make the investment because you would lose $300!) If cash
inflows are expected to exceed cash outflows, managers must consider when the
cash inflows and outflows occur before taking on the investment. (Again, consider
an investment of $1,000 today. If you expect to receive $1,050 in 20 years rather
than at the end of 1 year, you would probably think twice before investing because
it would take 20 years to make $50!)
Question: We use two methods to evaluate long-term investments, both of which consider the
time value of money. What are these two methods?
Answer: The first is called the net present value (NPV) method, and the second is called
the internal rate of return method. Before presenting these two methods, let’s discuss
the time value of money (present value) concepts.
The Present Value Formula
Question: Suppose you invest $1,000 for 1 year at an interest rate of 5 percent per year, as
shown in the following timeline. How much will you have at the end of 1 year (or what is the
future value of the investment)?
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Answer: You will have $1,050:
$1,050 = $1,000 × (1 + .05)
Question: Let’s change course and find the present value of the same future cash flow. If
you receive $1,050 in 1 year, how much is that worth in today’s dollars assuming an annual
interest rate of 5 percent?
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Answer: The present value is $1,000, calculated as follows:
$1,000 =
$1,050
(1 + .05)
Question: Let’s go back to finding a future value. Assume you invest $1,000 today at an
annual rate of 5 percent for 2 years. How much will you have at the end of 2 years?
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Answer: At the end of 1 year, you will have $1,050 (= $1,000 × [1 + .05]). At the end of
the second year, you will have $1,102.50, which is $1,050 × (1 + .05). The equation is
$1,102.50 = $1,000 × (1 + .05) × (1 + .05)
or
$1,102.50 = $1,000 × (1 + .05)2
Question: Again, let’s change course and find the present value of the same future cash
flow. If you receive $1,102.50 in 2 years, how much is that worth in today’s dollars assuming
an annual interest rate of 5 percent?
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Answer: The present value is $1,000, calculated as follows:
$1,000 =
$1,102. 50
(1 + .05)
2
These examples show that one equation can be used to find the present value of a
future cash flow. The equation is
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Key Equation
P=
Fn
(1 + r)n
where
P = Present value of an amount
Fn = Amount received n years in the future
r = Annual interest rate
n = Number of years
Question: Let’s use this formula to solve for the following: Assume $500 will be received 4
years from today, and the annual interest rate is 10 percent. What is the present value of this
cash flow?
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Answer: The present value is $341.51, calculated as follows:
P =
=
Fn
(1 + r)n
$500
(1+. 10)4
$500
=
1. 4641
= $341. 51
Present Value Tables
Question: Although most managers use spreadsheets, such as Excel, to perform present value
calculations (discussed later in this chapter), you can also use the present value tables in the
appendix to this chapter, labeled Figure 8.9 “Present Value of $1 Received at the End of ” and
Figure 8.10 “Present Value of a $1 Annuity Received at the End of Each Period for “, for these
calculations. Figure 8.9 “Present Value of $1 Received at the End of ” simply provides the
present value of $1 (i.e., F = $1) given the number of years (n) and the interest rate (r). How
are these tables used to calculate present value amounts?
Answer: Let’s look at an example to see how these tables work. Assume $1 will be
received 4 years from today (n = 4), and the interest rate is 10 percent (r = 10
percent). What is the present value of this cash flow? Look at Figure 8.9 “Present
Value of $1 Received at the End of ” in the appendix. Find the column labeled 10
percent and the row labeled 4. The present value is $0.6830, or $0.68 rounded. The
table amount given is often called a factor. The factor in this example is 0.6830 (note
that the formula to find this factor is shown at the top of Figure 8.9 “Present Value
of $1 Received at the End of “).
Now assume all the same facts, except that $500 rather than $1 will be received in 4
years. To find the present value, simply multiply the factor found in Figure 8.9
“Present Value of $1 Received at the End of ” by $500, as follows:
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Present value = Amount received in the future × Present value factor
= $500 × 0.6830
= $341. 50
Notice that this present value is the same as the one we calculated using the
formula P = Fn ÷ (1 + r)n, with the exception of a small difference due to rounding the
factor in Figure 8.9 “Present Value of $1 Received at the End of “. Next, we use
present value concepts to evaluate projects with the NPV method.
KEY TAKEAWAY
• Present value calculations tell us the value of future cash flows in
today’s dollars. The present value of a cash flow can be calculated
by using the formula P = Fn ÷ (1 + r)n. It can also be calculated by
using the tables in the appendix of this chapter. Simply find the
factor in Figure 8.9 “Present Value of $1 Received at the End of ”
given the number of years (n) and annual interest rate (r). Then
multiply the factor by the future cash flow, as follows:
Present value = Amount received in the future × Present value factor
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REVIEW PROBLEM 8.1
For each of the following independent scenarios, calculate the present value
of the cash flow described. Round to the nearest dollar.
1. You will receive $5,000, 5 years from today, and the interest rate is 8
percent.
2. You will receive $80,000, 9 years from today, and the interest rate is 10
percent.
3. You will receive $400,000, 20 years from today, and the interest rate is 20
percent.
4. You will receive $250,000, 10 years from today, and the interest rate is 15
percent.
Solution to Review Problem 8.1
Two approaches can be used to find the present value of a cash flow. The
first requires using the formula P = Fn ÷ (1 + r)n. The second requires using
Figure 8.9 “Present Value of $1 Received at the End of ” in the appendix to
find the present value factor and inserting it in the following formula:
Present value = Amount received in the future × Present value factor (from Figure
8.9 “Present Value of $1 Received at the End of “)
We show both approaches in the following solutions.
1. Using the formula P = Fn ÷ (1 + r)n, we get
$3,403 = $5,000 ÷ (1 + .08) 5
Using Figure 8.9 “Present Value of $1 Received at the End of “, we
get
Present value = Future value × Present value factor
$3,403 = $5,000 × 0.6806
2. Using the formula P = Fn ÷ (1 + r)n, we get
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$33,928 = $80,000 ÷ (1+. 10) 9
Using Figure 8.9 “Present Value of $1 Received at the End of “, we
get
Present value = Future value × Present value factor
$33,928 = $80,000 × 0.4241
3. The small difference between the two approaches is due to
rounding the factor in Figure 8.9 “Present Value of $1 Received at
the End of “.
Using the formula P = Fn ÷ (1 + r)n, we get
10,434 = $400,000 ÷ (1+. 20) 20
Using Figure 8.9 “Present Value of $1 Received at the End of “, we
get
Present value = Future value × Present value factor
$10,440 = $400,000 × 0.0261
4. The small difference between the two approaches is due to
rounding the factor Figure 8.9 “Present Value of $1 Received at
the End of “.
Using the formula P = Fn ÷ (1 + r)n, we get
$61,796 = $250,000 ÷ (1+. 15)
10
Using Figure 8.9 “Present Value of $1 Received at the End of “, we
get
Present value = Future value × Present value factor
$61,800 = $250,000 × 0.2472
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8.2 Net Present Value
LEARNING OBJECTIVE
1. Evaluate investments using the net present value (NPV) approach.
Question: Now that we have the tools to calculate the present value of future cash flows, we
can use this information to make decisions about long-term investment opportunities. How
does this information help companies to evaluate long-term investments?
Answer: The net present value (NPV)4 method of evaluating investments adds the
present value of all cash inflows and subtracts the present value of all cash
outflows. The term discounted cash flows is also used to describe the NPV method. In
the previous section, we described how to find the present value of a cash flow. The
term net in net present value means to combine the present value of all cash flows
related to an investment (both positive and negative).
Recall the problem facing Jackson’s Quality Copies at the beginning of the chapter.
The company’s president and owner, Julie Jackson, would like to purchase a new
copy machine. Julie feels the investment is worthwhile because the cash inflows
over the copier’s life total $82,000, and the cash outflows total $57,000, resulting in
net cash inflows of $25,000 (= $82,000 – $57,000). However, this approach ignores
the timing of the cash flows. We know from the previous section that the further
into the future the cash flows occur, the lower the value in today’s dollars.
Question: How do managers adjust for the timing differences related to future cash flows?
4. A method used to evaluate
long-term investments. It is
calculated by adding the
present value of all cash
inflows and subtracting the
present value of all cash
outflows.
Answer: Most managers use the NPV approach. This approach requires three steps
to evaluate an investment:
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Step 1. Identify the amount and timing of the cash flows required over the life
of the investment.
Step 2. Establish an appropriate interest rate to be used for evaluating the
investment, typically called the required rate of return5. (This rate is also called
the discount rate or hurdle rate.)
Step 3. Calculate and evaluate the NPV of the investment.
Let’s use Jackson’s Quality Copies as an example to see how this process works.
Step 1. Identify the amount and timing of the cash flows required over the life
of the investment.
Question: What are the cash flows associated with the copy machine that Jackson’s Quality
Copies would like to buy?
Answer: Jackson’s Quality Copies will pay $50,000 for the new copier, which is
expected to last 7 years. Annual maintenance costs will total $1,000 a year, labor
cost savings will total $11,000 a year, and the company will sell the copier for $5,000
at the end of 7 years. Figure 8.1 “Cash Flows for Copy Machine Investment by
Jackson’s Quality Copies” summarizes the cash flows related to this investment.
Amounts in parentheses are cash outflows. All other amounts are cash inflows.
Figure 8.1 Cash Flows for Copy Machine Investment by Jackson’s Quality Copies
5. The interest rate used for
evaluating long-term
investments; it represents the
company’s minimum
acceptable return (or discount
rate; also called hurdle rate).
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Step 2. Establish an appropriate interest rate to be used for evaluating the
investment.
Question: How do managers establish the interest rate to be used for evaluating an
investment?
Answer: Although managers often estimate the interest rate, this estimate is
typically based on the organization’s cost of capital. The cost of capital6 is the
weighted average costs associated with debt and equity used to fund long-term
investments. The cost of debt is simply the interest rate associated with the debt
(e.g., interest for bank loans or bonds issued). The cost of equity is more difficult to
determine and represents the return required by owners of the organization. The
weighted average of these two sources of capital represents the cost of capital
(finance textbooks address the complexities of this calculation in more detail).
The general rule is the higher the risk of the investment, the higher the required
rate of return (assume required rate of return is synonymous with interest rate for the
purpose of calculating the NPV). A firm evaluating a long-term investment with risk
similar to the firm’s average risk will typically use the cost of capital. However, if a
long-term investment carries higher than average risk for the firm, the firm will
use a required rate of return higher than the cost of capital.
The accountant at Jackson’s Quality Copies, Mike Haley, has established the cost of
capital for the firm at 10 percent. Since the proposed purchase of a copy machine is
of average risk to the company, Mike will use 10 percent as the required rate of
return.
Step 3. Calculate and evaluate the NPV of the investment.
6. The weighted average costs
associated with debt and equity
used to fund long-term
investments.
8.2 Net Present Value
Question: How do managers calculate the NPV of an investment?
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Answer: Figure 8.2 “NPV Calculation for Copy Machine Investment by Jackson’s
Quality Copies” shows the NPV calculation for Jackson’s Quality Copies. Examine
this table carefully. The cash flows come from Figure 8.1 “Cash Flows for Copy
Machine Investment by Jackson’s Quality Copies”. The present value factors come
from Figure 8.9 “Present Value of $1 Received at the End of ” in the appendix (r = 10
percent; n = year). The bottom row, labeled present value is calculated by multiplying
the total cash in (out) × present value factor, and it represents total cash flows for
each time period in today’s dollars. The bottom right of Figure 8.2 “NPV Calculation
for Copy Machine Investment by Jackson’s Quality Copies” shows the NPV for the
investment, which is the sum of the bottom row labeled present value.
Figure 8.2 NPV Calculation for Copy Machine Investment by Jackson’s Quality Copies
The NPV is $1,250. Because NPV is > 0, accept the investment. (The investment provides a return greater than 10
percent.)
The NPV Rule
Question: Once the NPV is calculated, how do managers use this information to evaluate a
long-term investment?
Answer: Managers apply the following rule to decide whether to proceed with the
investment:
NPV Rule: If the NPV is greater than or equal to zero, accept the investment; otherwise,
reject the investment.
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As summarized in Figure 8.3 “The NPV Rule”, if the NPV is greater than zero, the
rate of return from the investment is higher than the required rate of return. If the
NPV is zero, the rate of return from the investment equals the required rate of
return. If the NPV is less than zero, the rate of return from the investment is less
than the required rate of return. Since the NPV is greater than zero for Jackson’s
Quality Copies, the investment is generating a return greater than the company’s
required rate of return of 10 percent.
Figure 8.3 The NPV Rule
Note that the present value calculations in Figure 8.3 “The NPV Rule” assume that
the cash flows for years 1 through 7 occur at the end of each year. In reality, these
cash flows occur throughout each year. The impact of this assumption on the NPV
calculation is typically negligible.
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Business in Action 8.2
Cost of Capital by Industry
Cost of capital can be estimated for a single company or for entire industries.
New York University’s Stern School of Business maintains cost of capital
figures by industry. Almost 7,000 firms were included in accumulating this
information. The following sampling of industries compares the cost of capital
across industries. Notice that high-risk industries (e.g., computer, e-commerce,
Internet, and semiconductor) have relatively high costs of capital.
Air transportation
11.48 percent
Auto and truck
11.04 percent
Auto parts
9.56 percent
Beverage (soft drinks)
8.16 percent
Computer
14.49 percent
E-commerce
15.65 percent
Grocery
9.79 percent
Internet
15.98 percent
Retail store
9.30 percent
Semiconductor
19.03 percent
Source: New York University’s Stern Business School, “Home Page,”
http://pages.stern.nyu.edu.
Annuity Tables
Question: Notice in Figure 8.1 “Cash Flows for Copy Machine Investment by Jackson’s Quality
Copies” that the rows labeled maintenance cost and labor savings have identical cash flows
from one year to the next. Identical cash flows that occur in regular intervals, such as these
at Jackson’s Quality Copies, are called an annuity7. How can we use annuities in an
alternate format to calculate the NPV?
7. A term used to describe
identical cash flows that occur
in regular intervals.
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Answer: In Figure 8.4 “Alternative NPV Calculation for Jackson’s Quality Copies”, we
demonstrate an alternative approach to calculating the NPV.
Figure 8.4 Alternative NPV Calculation for Jackson’s Quality Copies
*Because this is not an annuity, use Figure 8.9 “Present Value of $1 Received at the End of ” in the appendix.
**Because this is an annuity, use Figure 8.10 “Present Value of a $1 Annuity Received at the End of Each Period for ”
in the appendix. The number of years (n) equals seven since identical cash flows occur each year for seven years.
Note: the NPV of $1,250 is the same as the NPV in Figure 8.2 “NPV Calculation for Copy Machine Investment by
Jackson’s Quality Copies”.
The purchase price and salvage value rows in Figure 8.4 “Alternative NPV Calculation
for Jackson’s Quality Copies” represent one-time cash flows, and thus we use Figure
8.9 “Present Value of $1 Received at the End of ” in the appendix to find the present
value factor for these items (these are not annuities). The annual maintenance costs
and annual labor savings rows represent cash flows that occur each year for seven
years (these are annuities). We use Figure 8.10 “Present Value of a $1 Annuity
Received at the End of Each Period for ” in the appendix to find the present value
factor for these items (note that the number of years, n, equals seven since the cash
flows occur each year for seven years). Simply multiply the cash flow shown in
column (A) by the present value factor shown in column (B) to find the present
value for each line item. Then sum the present value column to find the NPV. This
alternative approach results in the same NPV shown in Figure 8.2 “NPV Calculation
for Copy Machine Investment by Jackson’s Quality Copies”.
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Business in Action 8.3
© Thinkstock
Winning the Lottery
Like many other states, California pays out lottery winnings in installments
over several years. For example, a $1,000,000 lottery winner in California will
receive $50,000 each year for 20 years.
Does this mean that the State of California must have $1,000,000 on the day the
winner claims the prize? No. In fact, California has approximately $550,000 in
cash to pay $1,000,000 over 20 years. This $550,000 in cash represents the
present value of a $50,000 annuity lasting 20 years, and the state invests it so
that it can provide $1,000,000 to the winner over 20 years.
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Source: California State Lottery, “California State Lottery Home Page,”
http://www.calottery.com.
KEY TAKEAWAY
• Present value calculations tell us the value of cash flows in today’s
dollars. The NPV method adds the present value of all cash inflows and
subtracts the present value of all cash outflows related to a long-term
investment. If the NPV is greater than or equal to zero, accept the
investment; otherwise, reject the investment.
8.2 Net Present Value
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REVIEW PROBLEM 8.2
The management of Chip Manufacturing, Inc., would like to purchase a
specialized production machine for $700,000. The machine is expected to
have a life of 4 years, and a salvage value of $100,000. Annual maintenance
costs will total $30,000. Annual labor and material savings are predicted to
be $250,000. The company’s required rate of return is 15 percent.
1. Ignoring the time value of money, calculate the net cash inflow or
outflow resulting from this investment opportunity.
2. Find the NPV of this investment using the format presented in Figure 8.2
“NPV Calculation for Copy Machine Investment by Jackson’s Quality
Copies”.
3. Find the NPV of this investment using the format presented in Figure 8.4
“Alternative NPV Calculation for Jackson’s Quality Copies”.
4. Should Chip Manufacturing, Inc., purchase the specialized production
machine? Explain.
Solution to Review Problem 8.2
1. The net cash inflow, ignoring the time value of money, is
$280,000, calculated as follows:
2. The NPV is $(14,720), calculated as follows:
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3. The alternative format used for calculating the NPV is shown as
follows. Note that the NPV here is identical to the NPV calculated
previously in part 2.
*Because this is not an annuity, use Figure 8.9 “Present Value of $1 Received at the End of
” in the appendix.
**Because this is an annuity, use Figure 8.10 “Present Value of a $1 Annuity Received at
the End of Each Period for ” in the appendix. The number of years (n) equals four since
identical cash flows occur each year for four years.
4. Because the NPV is less than 0, the return generated by this investment
is less than the company’s required rate of return of 15 percent. Thus
Chip Manufacturing, Inc., should not purchase the specialized
production machine.
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8.3 The Internal Rate of Return
LEARNING OBJECTIVE
1. Evaluate investments using the internal rate of return (IRR) approach.
Question: Using the internal rate of return (IRR) to evaluate investments is similar to using
the net present value (NPV) in that both methods consider the time value of money.
However, the IRR provides additional information that helps companies evaluate long-term
investments. What is the IRR, and how does it help managers make decisions related to longterm investments?
Answer: The internal rate of return (IRR)8 is the rate required (r) to get an NPV of
zero for a series of cash flows. The IRR represents the time-adjusted rate of return
for the investment being considered. The IRR decision rule states that if the IRR is
greater than or equal to the company’s required rate of return (recall that this is
often called the hurdle rate), the investment is accepted; otherwise, the investment
is rejected.
Most managers use a spreadsheet, such as Excel, to calculate the IRR for an
investment (we discuss this later in the chapter). However, we can also use trial and
error to approximate the IRR. The goal is simply to find the rate that generates an NPV of
zero. Let’s go back to the Jackson’s Quality Copies example. Figure 8.4 “Alternative
NPV Calculation for Jackson’s Quality Copies” provides the projected cash flows for
a new copy machine and the NPV calculation using a rate of 10 percent. Recall that
the NPV was $1,250, indicating the investment generates a return greater than the
company’s required rate of return of 10 percent.
8. A method used to evaluate
long-term investments. It is
defined as the rate required to
get a net present value of zero
for a series of cash flows.
Although it is useful to know that the investment’s return is greater than the
company’s required rate of return, managers often want to know the exact return
generated by the investment. (It is often not enough to state that the exact return is
something higher than 10 percent!) Managers also like to rank investment
opportunities by the return each investment is expected to generate. Our goal now
is to determine the exact return—that is, to determine the IRR. We know from
Figure 8.4 “Alternative NPV Calculation for Jackson’s Quality Copies” that the copy
machine investment generates a return greater than 10 percent. Figure 8.5 “Finding
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Chapter 8 How Is Capital Budgeting Used to Make Decisions?
the IRR for Jackson’s Quality Copies” summarizes this calculation with the 2
columns under the 10 percent heading.
The far right side of Figure 8.5 “Finding the IRR for Jackson’s Quality Copies” shows
that the NPV is $(2,100) if the rate is increased to 12 percent (recall our goal is to
find the rate that yields an NPV of 0). Thus the IRR is between 10 and 12 percent.
Next, we try 11 percent. As shown in the middle of Figure 8.5 “Finding the IRR for
Jackson’s Quality Copies”, 11 percent provides an NPV of $(469). Thus the IRR is
between 10 and 11 percent; it is closer to 11 percent because $(469) is closer to 0
than $1,250. (Note that as the rate increases, the NPV decreases, and as the rate
decreases, the NPV increases.)
Figure 8.5 Finding the IRR for Jackson’s Quality Copies
*Because this is not an annuity, use Figure 8.9 “Present Value of $1 Received at the End of ” in the appendix.
**Because this is an annuity, use Figure 8.10 “Present Value of a $1 Annuity Received at the End of Each Period for ”
in the appendix. The number of years (n) equals seven since identical cash flows occur each year for seven years.
Note: the NPV of $(469) is closest to 0. Thus the IRR is close to 11 percent.
This trial and error approach allows us to approximate the IRR. As stated earlier, if
the IRR is greater than or equal to the company’s required rate of return, the
investment is accepted; otherwise, the investment is rejected. For Jackson’s Quality
Copies, the IRR of approximately 11 percent is greater than
