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Unformatted text preview: R. 1. R. 2. R. 3. R. 4. R. 5. R. 6. R. 7. CHAPTER 7 REVIEW QUESTIONS The competitive nature of the market will determine whether positive net
present value (NPV) projects can be found. In general, the greater the
market’s competition, the less of an opportunity to find positive NPV
projects. Most, if not all financial assets trade in highly competitive
markets such that few positive NPV opportunities are available. In contrast, real asset markets are less competitive, providing more opportunities to
uncover positive NPV projects. Corporate investments usually require outlays in the current period (negative
cash ﬂows or costs) and promise inﬂows in the future (positive cash ﬂows or
benefits). The concept of the time value of money requires that all cash
ﬂows be evaluated in the same time period. Discounting future cash ﬂows
back to the present allows the investment decision to be made by comparing the
present value of costs with the present value of benefits. The net present value (NPV) method of evaluating projects compares the present
value of all relevant cash outﬂows with the present value of all relevant
cash inflows. Acceptable projects, called positive net present value projects, are those whose present value of inflows exceed the present value of
outflows. The profitability index is NPV in ratio form; the present value of all
relevant cash inﬂows divided by the present value of all relevant cash outﬂows. Acceptable projects are those whose profitability index is greater
than one. The internal rate of return (IRR) is the discount rate that equates the
present value of the initial cash outlay with the present value of the future
cash benefits of the project. The IRR is also the discount rate that makes
NPV equal to zero. Acceptable projects are those whose IRR is greater than
the project’s required rate of return. ‘ The NPV profile is a graph that depicts the project’s NPV (on the vertical
axis) against various discount rates (on the horizontal axis). The point
where the NPV profile crosses the horizontal axis defines the project’s IRR. A standard project is a project whose cash ﬂow stream begins with one cash
outﬂow and is followed only by cash inﬂows. There are two kinds of
non—standard projects; borrowing projects and multiple sign change projects. A
borrowing project begins with a cash inﬂow and are followed by cash outﬂows. For
borrowing projects, the IRR acceptance criterion changes; acceptable
projects are those whose IRR is less than the project’s required rate of return. A
multiple sign change project is a project whose cash ﬂows switch from inﬂows 39 R. 8. R. 9. to outﬂows or outﬂows to inﬂows more than once. A different IRR can exist for
every sign change switch such that two changes in sign can result in two
IRRs, three changes in sign can result in three IRRs, on so on. An accept or reject project is one that can be evaluated on its own merits,
while ranking projects must be evaluated in relation to other projects. There
are no conﬂicts between the NPV and IRR methods in the case of accept or
reject projects However, for ranking projects, shortcomings of the IRR
method are exposed that may cause the IRR method to rank projects incorrectly.
The IRR method correctly measures a rate of return, but is biased toward short
term, small investment projects. Capital rationing is a shortage of investment capital caused either by an
unwillingness of external entities to provide additional capital, or by an
internal decision that a firm must limit growth. Capital rationing will
likely lead to a ranking of projects. As described in question 8 above, we
can expect conﬂicts in rank between the NPV and the IRR methods if the time
patterns of cash ﬂows from the projects differ greatly or if the amounts of
the capital investments are significantly different. ’R. 10.The payback method does not incorporate the time value of money nor does the rule incorporate cash ﬂows that occur beyond the payback period. Also, the
payback acceptance criterion relies on an arbitrary cutoff period. The
principal advantage of the payback method is its simplicity. R. 11.The accounting rate of return method requires the use of an arbitrary decision rule, does not discount future cash ﬂows, and depends on accounting rules
such as depreciation that can distort accounting income. The advantage of
the accounting rate of return method over NPV or the IRR is the fact that the accounting rate of return may help a financial manager manipulate the firm’s
accounting profitability. R. 12.The weighted average cost of capital is a measure of the average cost of capital to the firm. It is a measure of project risk for one—project firms
and for firms whose projects have identical risk. Using the WACC as an
estimate of the required rate of project return is inappropriate when the
project under consideration has a different level of risk than the average
risk in the firm’s existing assets. 40 CHAPTER 7 PROBLEMS 1. Project NPV P1 IRR Payback Notes
$ 8.94 1.0894 13.19% 3 Years Do as lump sum. > B $ 4.55 1.0455 15.00% 1 Year Do as lump sum.
C $ 9.92 1.0992 +50%,—20% 1 Year See below D $ 4.74 1.1053 15.89% 3 Years Do as annuity. E $19.68 1.1968 18.90% 3 Years Do as bond w/FV=$60. Project C should be treated as an uneven cashflow problem with the IRR being
found by a trial and error search while mapping out an NPV profile. There are two
IRR’s: +50% and —20%. Project C (and project E) can be solved on many
financial calculators much as bond problems were solved in Chapter 5. For
Project E, set the payment amount to $30, the number of periods to 3 and the
future value to 60. Note that the future value of $60 sums with the payment of $30
in the third period to form the full $90 cashﬂow. For Project C, some calculators
can handle the problem with the payment set equal to $230 and the future value
set equal to —$350 so that the combined payment and future value will for the
correct final cashﬂow of —$120. 2. NPV=$22,727.27.
Initial investment is $500,000 and cashﬂow received is $575,000 in one year. The
$575,000 cash flow is found by multiplying 10,000 sets times $57.50 per set. The
NPV is found by formula or financial calculator by taking the one year present value
of the cashflow using the lump sum approach and a discount rate of 10%. NPV = ~$500,000 + $575,000/1.10 = —$500,000 + 522,727.27 = $22,727.27. 3. NPV=$66,689.54.
The initial investment is $50,000 and the cash ﬂows received are $30,000 each
year for five consecutive years in years one through five. The NPV can be found using either the annuity function of a financial calculator or the annuity formula
with n = 5, I: 9% and A: $30,000. The present value of the annuity is $1 16,689.54. The
NPV is found by netting out the $50,000 initial cost and is equal to $66,689.54. 4. NPV=$220,645; Accept
The cashﬂows of the project are shown below: Year Cashﬂow Present Value
0 ($500,000) ($500,000)
1 $150,000 $138,889
2 $165,000 $141,461 The NPV is the sum of the present values
3 $181,500 $144,081 $220,645
4 ‘ $199,650 $146,749
5 $219,615 $149,466 41 5. PI=0.95695.
The initial investment is $700,000 and the cash ﬂows received are $200,000
each year for four consecutive years in years one through four. The PI can be
found using either the annuity function of a financial calculator or the annuity
formula with n=4, r=7.5% and A=$200,000. The present value of the annuity is
$669,865.26. The PI is found by dividing this present value of future cash
inﬂows by the absolute value of the initial cost ($700,000) and is equal to 0.95695. 6. PI=1.02637. The initial investment is $600,000. The cash ﬂows received are $100,000
each year for five consecutive years in years one through five and an additional
$450,000 in year five.. The PI can be found using both the annuity
approach to present value the $100,000 annual cash ﬂow and the lump sum
approach to present value the $450,000 cash ﬂow in year 5. The results
are then summed together to form the present value of future cash
inﬂows. Some financial calculators will allow the user to perform both
present values simulataneously by placing $100,000 in as the payment and
$450,000 as the future value (as well as n and r) and computing PV. The present
value of the annuity is $360,477.62. The present value of the lump sum is
$255,342.09. Together, the present value of the cash inﬂows is $615,819.71. The
PI is found by dividing this present value of future cash inﬂows by the absolute
value of the initial cost ($600,000) and is equal to 1.02637. 7. Yes, because the IRR: 16%.
The initial investment is $1,399,100 and produces cash inﬂows of $500,000
per year in years one through four. Most financial calculators will find the IRR by
entering $1,399,100 as the present value, n=4 and A=$500,000, and then
computing r. The answer of 16% can also be found by a trial and error search. 8. No, because the IRR: 10% and the NPV is negative: —$318,928 The intial investment is $7,272,727. The first year cash inﬂow is $2,000,000
and is found by multiplying the first year sales of 100,000 units times the $20 per
unit cash ﬂow figure. Second year sales are expected to be ten percent higher
and therefore the second year cash inﬂow is also expected to be ten percent
higher , or $2,200,000. The third and fourth year cash inﬂows also grow by ten
percent and (with compounding assumed) grow to $2,420,000 and $2,662,000,
respectively. The NPV with r=0% is $2,009,000. The NPV with r=10% is 0. So,
the IRR is 10% (since the NPV is $0). Advanced students may wish to try a
shortcut: present value the first year cash inﬂow of $2,000,000 at ten percent for
one year to $1,818,181 and enter it as an annuity ($a). Enter n=4 and
$7,272,727.27 as the present value and compute r. Adding ten percent to the
result (0.00%) will generate the correct answer of 10.00%. The reason is that each
of the cash inﬂows can be expressed as $1,818,181 future valued at ten percent. 42 9. 11.005%. Yes, the IRR exceeds the required rate of return. The solution is found
using trial and error. The cash inﬂows are a three year annuity from years four
to 6 & must be discounted first as a 3 year annuity and then as a 3 year lump sum. 10. No, because the lRR=8%.
The initial investment is $257,710 which is the sum of the three initial costs. The machine produces cash inﬂows of $100,000 per year in years one through three. Most
financial calculators will find the IRR by entering $257,710 as the present value, n=3 and A=$100,000, and then computing r. The answer of 8% can also be found
by a trial and error search. 11. IRR=13%.
The initial investment is $215,330 which is the sum of the two initial costs. The
machine produces one cash inﬂow of $275,000 in year two. Most financial
calculators will find the IRR by entering $275,000 as the future value, n=2
and $215,330 as the present value and then computing r. The answer of 13%
can also be found directly using the lump sum formula of Chapter 4. 12.a. 2 years. The payback is found by counting the number of years that it
takes to receive back as cash inﬂows the amount of money spent on the initial
investment. In this problem, $1,500 would be spent in order to receive
incremental cash inﬂows of $750 per year. After one year, $750 would be
received and $750 of the initial investment would remain “unreimbursed”. After the
second year the full $1,500 would be "reimbursed". b. 4 years. Using the same concepts as in 12(a), the $3,000 wouldn’t be fully
reimbursed until the end of the fourth year. 13. The payback is the number of years required in order to receive back as cash
inﬂows the amount of money that was spent on the investment. Both types of trees require a $500,000 investment. Thus the payback is the number of years
that it will take to receive $500,000 of cash inﬂows. a. 4 years. The $250,000 per year cash inﬂow starts in year three.
b. 5 years. The $125,000 per year cash inﬂow starts in year two. 14. 26.56% or 25.5% The accounting rate of return is defined as average accounting profit divided by average accounting value. Thus, this problem is solved by computing
profit and asset value in each year, averaging each value accross the
years, and then forming the desired ratio. Although precise definitions can vary, a
reasonable computation of the accounting rate of return follows: 43 15. 16. Year 1 Year 2 Year 3 Year 4 Year 5
Revenues $600,000 $800,000 $800,000 $800,000 $800,000
Cash expenses $150,000 $300,000 $300,000 $300,000 $300,000
Cash Profit $450,000 $500,000 $500,000 $500,000 $500,000
Depreciation $400,000 $400,000 $400,000 $400,000 $0
Accounting Profit $ 50,000 $100,000 $100,000 $100,000 $500,000 Average Profit = ($50,000 + $ 100,000+$ 100,000+ $ 100,000+ $500,000)/ 5 = $ 170,000 Year 1 Year 2 Year 3 Year 4 Year 5
Starting Book Value $1,600,000 $1,200,000 $800,000 $400,000 $0
Depreciation $ 400,000 $ 400,000 $400,000 $400,000 $0
Ending Book Value $1,200,000 33 800,000 $400,000 $ 0 $0
Mid—Year Book Value $1,400,000 $1,000,000 $600,000 $200,000 $0 The above table lists three definitions to book value: starting year, mid—year and
ending year. There is no definitive answer as to which is best. Note that the Year 0
Ending Book Value is $1,600 and that the Year 6 Starting Book Value would be
$0. The average book value is found by summing the figures from each of the
appropriate years and dividing by the number of years. Average starting book value = $666,667
Average mid—year book value = $640,000 Average ending book value = $666,667 Uses years one through six.
Uses years one through five.
Uses years zero through five. Dividing the $170,000 average profit by the $640,000 average book value produces
26.56% average accounting rate of return. By selecting the appropriate years, the starting and ending year book values approaches produce the same accounting rates
of return of 25.5%. The IRR of the project is 15.8%. Functionally speaking, projects can be ranked using either method. However, NPV usually gives the best ranking. In this problem, all three
projects add value to the firm. NPV correctly recognizes that Poject C has the
largest scale and therefore adds the most value to the firm even though it has the
lowest IRR. Project NPV IRR Rank w/NPV Rank w/IRR A $1.065 mil 18.03% middle middle
B $0.843 mil 25.41% worst best
C $1.320 mil 14.59% best worst
Proposal NPV IRR
(better) #1 $3,021,147 12.5%
#2 $ 623,835 21.7% 44 Proposal #1 has an initial investment of $15,000,000 and produces a five year
annuity as the inﬂow which does not begin until year four. Using the annuity
formula or the anuity function of a financial calculator, the five year $6 mil. stream
can be discounted to year four as (using 9% as r) $23,337,908. This value is then
discounted for three years using lump sum techniques to produce the present
value of $18,021,147. Netting out the initial cost produces the NPV of $3,021,147. The IRR of Proposal #1 must be found using a trial and error process. By simply
summing the cash ﬂows we can determine that the NPV using a discount rate of
0% is $15,000,000. A discount rate of 9% was found above to produce an NPV of
$3,021,147. Thus, a logical next guess might be 11%. The NPV using 11% is
$1,214,448. A next logical guess of 12.5% produces an NPV of approximately
zero and is therefore the IRR. Proposal #2 has an initial investment of $1,000,000 and produces a four year
annuity and a final receipt of $2,000,000 in year 5 as the inﬂow2. Using the
annuity formula or the anuity function of a financial calculator, the four year
$100,000 stream can be discounted to a present value of (using 9% as r)
$323,972. This value is then added to the present value of the $2,000,000 cash
ﬂow in year 5 of $1,299,863 for a total present value of cash inﬂows of
$1,623,835. Netting out the initial cost produces the NPV of $623,835. A shortcut method is to view the proposal as a five year bond with a payment of
$100,000 and a future value of $1,900,000. Note that the $1,900,000 is equal to
the fifth year cash flow less the $100,000 of the cash ﬂow that is already included
as the fifth payment. This shortcut especially assists the computation of the IRR. The IRR of Proposal #2 can also be found using a trial and error process. By
simply summing the cash ﬂows we can determine that the NPV using a discount
rate of 0% is $1,400,000. A discount rate of 9% was found above to produce an
NPV of $623,835. Thus, a logical next guess might be 18%. The NPV using 18% is $143,225. The process continue until the final answer of that produces an
NPV of approximately zero is found: 21.7%. Proposal 1 is better since it has the higher NPV. Even though Proposal 2 has a
higher IRR, its smaller scale adds less value to the foundation. 17. NPV=$3,239.22, IRR=7.93%; Accept
Note that this nonstandard project starts with a positive cash ﬂow and is
followed by negative cash ﬂows. The initial cash flow is a cash inﬂow of $20,000. The
remaining cash ﬂows are five annual outflows of $5,000 each. The NPV is found by discounting the annuity to —$16,760.78 and adding the initial proceeds
of $20,000 to compute NPV=$3,239.22. 45 The IRR can be found using annuity shortcuts as 7.93%. However, it is essential
to realize that this is a cost of borrowing, not a return on investing. Therefore, it
signals a favorable opportunity since the required rate of return is 15% 18. NPV= —$70,931;IRR=0% and IRR= —63.65%; Reject
The cashﬂows of the project are shown below: Year Cashﬂow
0 — $500,000
1 $200,000
2 $200,000
3 $200,000
4 — $ 100,000 The NPV is found as usual by discounting and summing all cash flows, being sure
to carry negative signs since the last cashﬂow is negative. The NPV is —$70,931. A
shortcut is to View the problem with n=4, A=$200,000, and FV= —$300,000
since the final cashﬂow of —$100,000 is the sum of the FV and A. The problem has up to two IRR’s since there are two sign changes. Trial and error
will reveal 0% and —63.65%. as the IRR’s since they set the NPV=0. 19. WACC: 11.19%
WACC = [% in Equity x Cost of Equity] + [% in Debt x Cost of Debt] WACC = [.58X 13.5%] + [42% x8%] = 7.83% + 3.36% = 11.19% 20a. The internal rates of return have been correctly computed since they all produce
an NPV of $0 when inserted into the NPV formulae as the discount rate: Project Year Cash Flows Present Values (using IRR = —42.265%)
Peanut 0 ($3,000) ($3,000)
Butter: 1 $0 $0
2 $1,000 $3,000
3 $0 $0
NPV (sum): $0 Note that negative interest rates are handled exactly as positive interest rates: they
are simply inserted into the formula (using a two year example): PV = FV/( (1+r) * (1+r)) PV = $1,000/ ( (1—.42265) * (1—.42265)) PV = $1,000/ (.57735 * .57735) PV = $3,000 46 Project Year Cash Flows Present Values (using IRR=0%) Chocolate: 0 $0 $0
1 $9,053 $9,053
2 $0 $0
3 ($9,053) ($9,053)
NPV (sum): $0
Combining the cash flows into a single combined project:
Project Year Cash Flows Present Values (using IRR=20%)
Combined: 0 ($3,000) ($3,000)
1 $9,053 $7,544
2 $1,000 $694
3 ($9,053) ($5,239)
NPV (sum): ($0) . The NPV’s using a discount rate of 15% can be found using the NPV formula as
shown below: Project Year Cash Flows Present Values
Peanut 0 ($3,000) ($3,000)
Butter: 1 $0 $0
2 $1,000 $756
3 $0 $0
NPV (sum): ($2,244)
Project Year Cash Flows Present Values
Chocolate: 0 $0 $0
1 $9,053 $7,872
2 $0 $0
3 ($9,053) ($5,952)
NPV (sum): $1,920
Combining the cash ﬂows into a single combined project:
Project Year Cash Flows Present Values
Combined: 0 ($3,000) ($3,000)
1 $9,053 $7,872
2 $1,000 $756
3 ($9,053) ($5,952)
NPV (sum): ($324) . The firm should accept Project Chocolate since it has a positive N PV and should
reject Project Peanut Butter since it has a negative NPV. Notice that the NPV of
the combination is negative, it indicates that the combination should be rejected,
and it is equal to the combination of the individual NPV’s. The reason that IRR
failed to generate correct decisions is that some of the projects are nonstandard. Project Chocolate is a borrowing project in which low IRR’s should be accepted and the Project Combined has multiple sign changes and thus may have more than
one IRR. 47 CHAPTER 7 DISCUSSION QUESTIONS 1. The common link between almost all successful firms is that they possess
some advantage that can not be quickly and easily duplicated. For some firms it
is a patent or a special technology. For others, the advantage is a reputation or
superior management. We can usually expect that the firms will remain in
business for ten years, but will they still have the advantage that makes them
special today? The important point is that success is linked to superior
performance in the market for real assets where the market for real assets is
broadly defined to include people, ideas, patents and so forth. Thus, the tools of
this chapter, especially NPV, assist the financial manager in valuing real assets
and making decisions regarding real assets. Conversely, few firms build
successful records based upon their performance in trading financial assets. In
other words, this chapter has demonstrated the tools involved in the primary
method of maximizing shareholder wealth—making superior investment decisions. 2. Some people argue that the NPV requires a discount rate to be input whereas
IRR analysis produces a discount rate (the IRR) and therefore is easier. However,
it is important to realize that once the IRR is computed it must be compared to a
benchmark in order to make a decision. Thus, using the IRR method requires a
benchmark rate just as the NPV requires a discount rate. 3. Payback period is especially dangerous in circumstances including:
a. comparing projects of different risk,
b. comparing projects of uneven cash ﬂows,
c. analyzing projects with cash outﬂows after cash inflows, and
d. making decisions requiring precision. Thus, a firm that has performed well in the past using payback period may not
necessarily be able to continue to succeed using such a primitive method ——
especially as its competitors improve their decision making. 4. It is extremely easy to fall into the trap of believing that nobody should make a
decision that could cause death, injury or pollution. However, in a modern society
everybody makes such decisions on a basis almost too numerous to mention. Note,
virtually everytime a person gets behind the wheel of a vehicle, they are
increasing the probabilities that someone will die or get injured and that increased
pollution will result. People make these decisions in order to: a. travel further to work at a higher paying job, b. shop at a place with lower prices, c. avoid a toll road, d. work an extra day for overtime pay, and e. save time or money relative to using public transportation. 48 Note that when a consumer selects a product that is cheaper to the consumer, it is
very often true that the cost savings to the consumer were created using procedures
that placed somebody at a greater risk of death or injury. For example, pesticides
allow cheaper food production but likely at great costs to the exposed farm
workers. Heavily loeaded trucks produce transportation savings but are often more
risky. The examples go on and on leading us to no conclusion other than that life
is very often a tradeoff between money and safety which consumers accept. Similarly, when corporations make decisions they also must recognize that some
projects will cause more injury, death and pollution than other projects. If
potential injury or death were priceless disadvantages that should nix any project
then no biulding, bridge, highway, machine, or vehicle would ever be built. No
land would be cleared for farms, no houses built, etc. Obviously, the rational solution is to price potential death, injury and pollution as
accurately as possible and to include these costs in a NPV analysis just as all
other costs are included. When someone criticizes NPV analysis for not including
such concepts, they should more accurately be viewed as criticizing the person
using the NPV for omitting the costs, since NPV is designed to include all
advantages (benefits) and disadvantages (costs). . One of the most popular criticisms of NPV is that it ignores the long run
implications of a decision and will result in the long run destruction of the firm. As
in question 4, when someone criticizes NPV for omitting the value of long run
benefits and costs they should really be criticizing the person applying the
NPV analysis since the NPV method requires that all benefits and costs be
included —— including long run benefits and costs. Some people will argue that
when long term advantages are discounted over long periods of time at high
discount rates they are diminished in present values to the point of being
undervalued. In this case, the person is really criticizing market interest rates
since it is the market, not the NPV user, that determines interest rate levels. Note
using discounting that an interest rate such as 18% will cause the present value of
$1,000,000 due in 70 years to be less than $10. Thus a project with enormous
benefits far into the future will be rejected since people trading in the marketplace
have agreed that benefits far into the future are worth far less than benefits in the
near term. Corporate financial managers have been hired by shareholders to
serve them, not to squander their money by over—valuing long term benefits. . Without further information, the answer should be nothing. There are two
potential tricks to high IRR’s. First, the IRR may be available for only a very brief
period of time —— for example one second. Over a very brief period of time a
high IRR is virtualy worthless. For example, $1,000,000 invested at 100% interest
for just one minute will produce only about $1 in interest. Second, the opportunity
may be limited in terms of how much money may be invested. For example,
earning a 100% IRR for a period of two years is worth very little if only $1 can be 49 invested. Both tricks reﬂect the scale problem discussed in the chapter. That is,
IRR ignores the scale of a project — — both the size of the project and the length of time involved. This is an important problem and it is trickier than this
exaggeragted example implies. 50 ...
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This note was uploaded on 11/30/2011 for the course FINOPMGT 301 taught by Professor Lacey during the Spring '10 term at UMass (Amherst).
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