Walden University Time Value of Money Paper Unit 8 Payback period example https://www.youtube.com/watch?v=NwSmUDvWTPA Unit 8 Complete assignment questions

Walden University Time Value of Money Paper Unit 8 Payback period example https://www.youtube.com/watch?v=NwSmUDvWTPA Unit 8 Complete assignment questions Complete the information requested in parts (a) and (b) of the Self-Study Review Problem on page 467. Then answer the following questions related to capital investment proposals. (1) What is meant by the expression, time value of money? (2) Why should all capital investment proposals include time value of money (present value) calculations of future cash flows that are to be received from the alternative investments?Some nonfinancial factors included in capital investment decisions are more important now than they were 20-25 years ago. Give some examples of the types of nonfinancial factors that managers would consider more important in today’s capital investment decisions than they were in the past.What level of management would be involved in making capital investment decisions? Why? Why are these decisions more critical than day-to-day decisions made by individuals and companies? CHAPTER 10
Planning for
Capital Investments
C
A
After you have mastered the material in this chapter, you will be able to:
L
LO 10-1
Explain the time value of money concept.
V
LO 10-2
Determine and interpret the net present
value of an investment opportunity.
E
LO 10-3
Determine and interpret the internal
R rate of return of an investment opportunity.
LO 10-4
Evaluate investment opportunities
Tusing the payback method and the unadjusted rate
of return.
,
LEARNING OBJECTIVES
Video lectures and accompanying self-assessment quizzes are available in Connect®
for all learning objectives.
T
CHAPTER
E
R
R
E
OPENING
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C
The president of EZ Rentals (EZ) is considering expanding the company’s rental service busiE
ness to include LCD projectors that can be used with notebook computers. A marketing
study forecasts that renting
1 projectors could generate revenue of $200,000 per year. The
8
possibility of increasing revenue
is alluring, but EZ’s president has a number of unanswered
5
9
have a salvage value? Does
T EZ have the money to buy them? Does EZ have the technical
expertise to support theSproduct? How much will training cost? How long will customer
questions. How much do the projectors cost? What is their expected useful life? Will they
­demand last? What if EZ buys the projectors and they become technologically obsolete?
How quickly will EZ be able to recover the investment? Are there more profitable ways to
invest EZ’s funds?
Spending large sums of money that will have long-term effects on company profits makes
most managers anxious. What if a cell phone manufacturer spends millions of dollars to build a
­factory in the United States and its competitors locate their manufacturing facilities in countries
that provide cheap labor? The manufacturer’s cell phones will be overpriced, but it cannot move
overseas because it cannot find a buyer for the factory. What if a pharmaceutical company
spends millions of dollars to develop a drug that then fails to receive FDA approval? What if a
C
communications company installs underground cable
A but satellite transmission steals its
L that rapidly becomes technologically
­market? What if a company buys computer equipment
V
obsolete? Although these possibilities may be remote, they can be expensive when they do
E
­occur. For example, Wachovia Bank’s 1997 annual report discloses a $70 million write-off of
R
computer equipment. This chapter discusses some of
T the analytical techniques companies use
,
to evaluate major investment opportunities.
T
E
R
R
The August 8, 2013, drawing for the PowerballEmultiN This
state lottery had an advertised value of $448 million.
C the
amount, however, was based on the assumption that
winner would take his or her prize as 30 equalE
annual
The Curious Accountant
payments of $14.9 million. If the winnings were taken in
1
this manner, the first payment would be made immediately, and the others would be paid annually over
8 the
next 29 years. The winner also had the option of5taking
an immediate, lump-sum payment of $258.2 million.
9
Assume that you work as a personal financial
T planner and that one of your clients held the winningSlottery
ticket. If you think you could invest your client’s winnings and earn an annual return of 7 percent, would
you advise your client to take the lump-sum payment or
the annual payments? Why? (Answer on page 461.)
© McGraw-Hill Education
448
Chapter 10
CAPITAL INVESTMENT DECISIONS
LO 10-1
Explain the time value of
money concept.
Purchases of long-term operational assets are capital investments. Capital investments
differ from stock and bond investments in an important respect. Investments in stocks and
bonds can be sold in organized markets such as the New York Stock Exchange. In contrast, investments in capital assets normally can be recovered only by using those assets.
Once a company purchases a capital asset, it is committed to that investment for an extended period of time. If the market turns sour, the company is stuck with the consequences. It may also be unable to seize new opportunities because its capital is committed.
Business profitability ultimately hinges, to a large extent, on the quality of a few key
capital investment decisions.
A capital investment decision is essentially a decision to exchange current cash outflows
for the expectation of receiving future cash inflows. For EZ Rentals, purchasing LCD projectors, cash outflows today, provides the opportunity to collect $200,000 per year in rental
revenue, cash inflows in the future. Assuming the projectors have useful lives of four years
and no salvage value, how much should EZ be willing to pay for the future cash inflows? If
you were EZ’s president, would you spend $700,000 today to receive $200,000 each year for
C would give up $700,000 today for the opportunity to receive
the next four years? You
$800,000 (4 × $200,000)Ain the future. What if you collect less than $200,000 per year? If
revenue is only $160,000 per year, you would lose $60,000 [$700,000 − (4 × $160,000)]. Is
L
$700,000 too much to pay for the opportunity to receive $200,000 per year for four years?
If $700,000 is too much,Vwould you spend $600,000? If not, how about $500,000? There is
no one right answer to these
E questions. However, understanding the time value of money
concept can help you develop a rational response.
R
T
Time Value of Money
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© C. Zachariasen/PhotoAlto
The time value of money concept recognizes that the present value of a dollar received
in the future is less than a dollar. For example, you may be willing to pay only $0.90
­today for a promise toTreceive $1.00 one year from today. The further into the future the
receipt is expected toE
occur, the smaller is its present value. In other words, $1.00 to be
received two years from today is worth less than $1.00 to be received one year from
­today. Likewise, $1.00Rto be received three years from today is less valuable than $1.00 to
be received two yearsR
from today, and so on.
The present value of cash inflows decreases as the time until expected receipt
­increases for severalEreasons. First, you could deposit today’s dollar in a savings
­account to earn interest
N that increases its total value. If you wait for your money,
you lose the opportunity to earn interest. Second, the expectation of receiving a
­future dollar carriesCan element of risk. Changed conditions may result in the
­failure to collect. Finally,
inflation diminishes the buying power of the dollar. In
E
other words, the longer you must wait to receive a dollar, the less you will be able to
buy with it.
When a company
1 invests in capital assets, it sacrifices present dollars in
­exchange for the opportunity to receive future dollars. Since trading current dollars for
8
future dollars is risky, companies expect compensation before they invest in capital
5 a company expects is called return on investment (ROI). As
­assets. The compensation
discussed in Chapter 9,9ROI is expressed as a percentage of the investment. For example, the ROI for a $1,000 investment that earns annual income of $100 is 10 percent
($100 ÷ $1,000 = 10%).T
S
Determining the Minimum Rate of Return
To establish the minimum expected return on investment before accepting an investment
­opportunity, most companies consider their cost of capital. To attract capital, companies
must provide benefits to their creditors and owners. Creditors expect interest payments;
Planning for Capital Investments
owners expect dividends and increased stock value. Companies that earn lower returns than
their cost of capital eventually go bankrupt; they cannot continually pay out more than they
­collect. The cost of capital represents the minimum rate of return on investments. Calculating the cost of capital is a complex exercise which is beyond the scope of this text. It is
addressed in finance courses. We discuss how management accountants use the cost of capital to evaluate investment opportunities. Companies describe the cost of capital in a variety
of ways: the minimum rate of return, the desired rate of return, the required rate of return,
the hurdle rate, the cutoff rate, or the discount rate. These terms are used interchangeably
throughout this chapter.
CHECK YOURSELF 10.1
Study the following cash inflow streams expected from two different potential investments:
Year 1
Year 2
C Year 3 Total
Alternative 1
$2,000
$3,000
$4,000
$9,000
Alternative 2
4,000
3,000A 2,000   9,000
L
Based on visual observation alone, which alternative hasV
the higher present value? Why?
E
Answer Alternative 2 has the higher present value. The size of the discount increases as the length of
R in year 3 has a lower present value than a
the time period increases. In other words, a dollar received
dollar received in year 1. Since most of the expected cash inflows from Alternative 2 are received earlier
T
than those from Alternative 1, Alternative 2 has a higher present value even though the total expected
,
cash inflows are the same.
T
E
Converting Future Cash Inflows to Their
R
Equivalent Present Values
Ra future cash flow, present value can
Given a desired rate of return and the amount of
be determined using algebra. To illustrate, refer
E to the $200,000 EZ expects to earn
the first year it leases LCD projectors.1 Assuming EZ desires a 12 percent rate of reN
turn, what amount of cash would EZ be willing to invest today (present value outflow)
Cthe year (future value)? The answer
to obtain a $200,000 cash inflow at the end of
­follows:2
E
Investment + (0.12 × Investment) = Future cash inflow
1 = $200,000
1.12 × Investment
8 = $200,000 ÷ 1.12
Investment
5 = $178,571
Investment
9
If EZ invests $178,571 cash on January 1 and earns a 12 percent return on the investT investor who is able to earn a 12 perment, EZ will have $200,000 on December 31. An
cent return on investment is indifferent between
S having $178,571 now or receiving
The following computations assume the $200,000 cash inflow is received on the last day of each year. In actual
practice, the timing of cash inflows is less precise and present value computations are recognized to be approximate,
not exact.
2
All computations in this chapter are rounded to the nearest whole dollar.
1
449
450
Chapter 10
$200,000 one year from now. The two options are equal, as shown in the following mathematical proof:
Investment + (0.12 × Investment) = $200,000
$178,571 + (0.12 × $178,571) = $200,000
$178,571 + $21,429 = $200,000
$200,000 = $200,000
Present Value Table for Single-Amount Cash Inflows
The algebra illustrated above is used to convert a one-time future receipt of cash to its present value. One-time receipts of cash are frequently called single-payment, or lump-sum,
cash flows. Because EZ desires a 12 percent rate of return, the present value of the first
cash inflow is $178,571. We can also determine the present value of a $200,000 single
amount (lump sum) at the end of the second, third, and fourth years. Instead of using cumbersome algebraic computations to convert these future values to their present value equivalents, f­inancial analysts frequently use a table of conversion factors to convert future
C
values to their present value equivalents. The table of conversion factors used to convert
future values into present
A values is commonly called a present value table.3 A typical
present value table presents columns with different return rates and rows with different
L
periods of time, like ­Appendix Table 1 located at the end of this chapter.
V present value table, locate the conversion factor in Table 1 at
To illustrate using the
the intersection of the E
12% column and the one-period row. The conversion factor is
0.892857. Multiplying this factor by the $200,000 expected cash inflow yields $178,571
($200,000 × 0.892857).RThis is the same value determined algebraically in the previous
­section of this chapter. The
T conversion factors in the present value tables simplify converting
future values to present values.
, for the second, third, and fourth periods are 0.797194, 0.711780,
The conversion factors
and 0.635518, respectively. These factors are in the 12% column at rows 2, 3, and 4, respectively. Locate these factors in Appendix Table 1. Multiplying the conversion factors by the
future cash inflow for T
each period produces their present value equivalents, shown in
­Exhibit 10.1. Exhibit 10.1
E indicates that investing $607,470 today at a 12 percent rate of
return is equivalent to receiving $200,000 per year for four years. Because EZ Rentals
­desires to earn (at least) aR12 percent rate of return, the company should be willing to pay up
to $607,470 to purchase R
the LCD projectors.
E
Present Value Table for Annuities
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The algebra described previously
for converting equal lump-sum cash inflows to present
value equivalents can be C
further simplified by adding the present value table factors together
E
EXHIBIT 10.1
1
Present Value of a $200,000
Cash Inflow to Be Received for Four Years
8
5 FV
PV
=
×
Present Value
Table Factor
=
Present Value
Equivalent
9$200,000
Period 1
=
×
0.892857
=
$178,571
Period 2
=
200,000
×
0.797194
=
159,439
T 200,000
Period 3
=
×
0.711780
=
142,356
S 200,000
Period 4
=
×
0.635518
=
127,104
Total
$607,470
3
The present value table is based on the formula [1 ÷ (1 + r)n] where r equals the rate of return and n equals the number
of periods.
Planning for Capital Investments
before multiplying them by the cash inflows. The total of the present value table factors in
Exhibit 10.1 is 3.037349 (0.892857 + 0.797194 + 0.711780 + 0.635518). Multiplying this
accumulated conversion factor by the expected annual cash inflow results in the same
present value equivalent of $607,470 ($200,000 × 3.037349). As with lump-sum conversion
factors, accumulated conversion factors can be calculated and organized in a table with columns for different rates of return and rows for different periods of time. Appendix Table 2 is
a present value table of accumulated conversion factors. Locate the conversion factor at the
intersection of the 12% column and the fourth time-period row. The factor at this intersection is 3.037349, confirming that the accumulated conversion factors represent the sum of
the single-payment conversion factors.
The conversion factors in Appendix Table 2 apply to annuities. An annuity is a series of
cash flows that meets three criteria: (1) equal payment amounts, (2) equal time intervals
between payments, and (3) a constant rate of return. For EZ Rentals, the expected cash inflows from renting LCD projectors are all for equivalent amounts ($200,000); the expected
intervals between cash inflows are equal lengths of time (one year); and the rate of return for
each inflow is constant at 12 percent. The series of expected cash inflows from renting the
projectors is therefore an annuity. The present value of an annuity table can be used only if
C
all of these conditions are satisfied.
The present value of an annuity table (Appendix
A Table 2) simplifies converting future
cash inflows to their present value equivalents. EZ Rentals can convert the cash inflows as
L multiplying each conversion factor by
shown in Exhibit 10.1, using four conversion factors,
the annual cash inflow (four multiplications), and adding
the resulting products. In contrast,
V
EZ can recognize that the series of payments is an annuity, which requires multiplying a
single conversion factor from Appendix Table 2E
by the amount of the annuity payment.
­Regardless of the conversion method, the result isRthe same (a present value of $607,470).
Recall that EZ can also make the conversion using algebra. The table values are derived
from algebraic formulas. The present value tablesTreduce the computations needed to convert future values to present values.
,
Software Programs That Calculate Present Values
Software programs offer an even more efficient means
T of converting future values into present value equivalents. These programs are frequently built into handheld financial calculaE
tors and computer spreadsheet programs. As an example, we demonstrate the procedures
used in a Microsoft Excel spreadsheet.
R
An Excel spreadsheet offers a variety of financial functions, one of which converts a
R
future value annuity into its present value equivalent. This present value function uses the
E rate of return, nper is the number of
syntax PV(rate,nper,pmt) in which rate is the desired
periods, and pmt is the amount of the payment (periodic
cash inflow). To convert a future
N
value annuity into its present value equivalent, provide the function with the appropriate
C of the annuity (cash inflows) into a
amounts for the rate, number of periods, and amount
spreadsheet cell. Press the Enter key and the present
E value equivalent appears in the spreadsheet cell.
The power of the spreadsheet to perform computations instantly is extremely useful for
answering what-if questions. Exhibit 10.2 demonstrates
1 this power by providing spreadsheet
conversions for three different scenarios. The first scenario demonstrates the annuity as8 equivalent ($607,470) of a four-year
sumptions for EZ Rentals, providing the present value
cash inflow of $200,000 per year at a 12 percent rate
5 of interest. The present value is a negative number. This format indicates that an initial $607,470 cash outflow is required to obtain
9 equivalent in Scenario 2 shows the
the four-year series of cash inflows. The present value
present value if the annuity assumptions reflect a 14
T percent, rather than 12 percent, desired
rate of return. The present value equivalent in Scenario 3 shows the present value if the anS
nuity assumptions under Scenario 1 are changed to reflect annual cash inflows of $300,000,
rather than $200,000. A wide range of scenarios could be readily considered by changing
any or all of the variables in the spreadsheet function. In each case, the computer does the
calculations, giving the manager more time to analyze the data rather than compute them.
Although software is widely used in business practice, the diversity of interfaces
used by different calculators and spreadsheet programs makes it unsuitable for textbook
451
452
Chapter 10
EXHIBIT 10.2
Microsoft Excel Spreadsheet Present Value Function
C
A
L
V
E
R
T
,
presentations. This text T
uses the present value tables in the Appendix in the text illustrations and the end-of-chapter
E exercises and problems. If you use software to solve these
problems, your answers will be the same. All of these tools—formulas, conversion
R based on the same mathematical principles and will produce
­t ables, and software—are
the same results.
R
E
Ordinary Annuity Assumption
All of the conversion methods
described previously assume the cash inflows occur at the
N
end of each accounting period. This distribution pattern is called an ordinary annuity.4 In
C
practice, cash inflows are likely to be received throughout the period, not just at the end. For
example, EZ Rentals is E
likely to collect cash revenue from renting projectors each month
rather than in a single lump-sum receipt at the end of each of the four years. Companies
frequently use the ordinary annuity assumption in practice because it simplifies time value
of money computations.1Because capital investment decisions are necessarily based on uncertain projections about8future cash inflows, the lives of investment opportunities, and the
appropriate rates of return, achieving pinpoint accuracy is impossible. Sacrificing precision
for simplicity by using 5
the ordinary annuity assumption is a reasonable trade-off in the
­decision-making process.9
T
Reinvestment Assumption
The present value computations
in the previous sections show that investing $607,470 today
S
at a 12 percent rate of return is equivalent to receiving four individual $200,000 payments at
When equal cash inflows occur at the beginn…
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