Schneider, Arnold, (2012) Managerial Accounting, United States, Bridgepoint Education Inc The Evaluation Methods The evaluation methods discussed here are: 1. Present value methods (also called discounted cash-flow methods). (a) Net present value method (NPV). (b) Internal rate of return method (IRR). 2. Payback period method. 3. Accounting rate of return method. Nearly all managerial accountants agree that methods using present value (Methods 1a and 1b) give the best assessment of long-terminvestments. Methods that do not involve the time value of money (Methods 2 and 3) have serious flaws; however, since they are commonlyused for investment evaluation, their strengths and weaknesses are discussed. Net Present Value Method The net present value (NPV) method includes the time value of money by using an interest rate that represents the desired rate of return or, atleast, sets a minimum acceptable rate of return. The decision rule is: If the present value of incremental net cash inflows is greater than the incremental investment net cash outflow, approve the project. Using Tables 1 and 2 found at the end of this chapter, the net cash flows for each year are brought back (i.e., discounted) to Year 0 andsummed for all years. An interest rate must be specified. This rate is often viewed as the cost of funds needed to finance the project and is theminimum acceptable rate of return. To discount the cash flows, we use the interest rate and the years that the cash flows occur to obtain theappropriate present value factors from the present value tables. A portion of Table 1 appears below showing the present value factors (theshaded numbers), corresponding to an interest rate of 12 percent, for each year during the Clairmont Timepieces project's life. Periods (n) 1% 2% 4% 5% 6% 8% 10% 12% 14% 15% 16% 0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1 0.990 0.980 0.962 0.952 0.943 0.926 0.909 0.893 0.877 0.870 0.862 2 0.980 0.961 0.925 0.907 0.890 0.857 0.826 0.797 0.769 0.756 0.743 3 0.971 0.942 0.889 0.864 0.840 0.794 0.751 0.712 0.675 0.658 0.641 4 0.961 0.924 0.855 0.823 0.792 0.735 0.683 0.636 0.592 0.572 0.552 5 0.951 0.906 0.822 0.784 0.747 0.681 0.621 0.567 0.519 0.497 0.476 6 0.942 0.888 0.790 0.746 0.705 0.630 0.564 0.507 0.456 0.432 0.410 7 0.933 0.871 0.760 0.711 0.665 0.583 0.513 0.452 0.400 0.376 0.354 8 0.923 0.853 0.731 0.677 0.627 0.540 0.467 0.404 0.351 0.327 0.305 9 0.914 0.837 0.703 0.645 0.592 0.500 0.424 0.361 0.308 0.284 0.263 10 0.905 0.820 0.676 0.614 0.558 0.463 0.386 0.322 0.270 0.247 0.227 These present value factors are used in Figure 10.2 to discount the yearly cash flows to their present values. In Figure 10.2, the net cashinvestment ($95,000) is subtracted from the sum of cash-inflow present values ($137,331). When the residual is positive, the project's rate ofreturn (ROR) is greater than the minimum acceptable ROR. If: Present value of incremental net cash inflows ≥ Incremental investment cash outf.

1. Schneider, Arnold, (2012) Managerial Accounting, United
States, Bridgepoint Education Inc
The Evaluation Methods
The evaluation methods discussed here are:
1.
Present value methods (also called discounted cash-
flow methods).
(a)
Net present value method (NPV).
(b)
Internal rate of return method (IRR).
2.
Payback period method.
3.
Accounting rate of return method.
Nearly all managerial accountants agree that methods using pres
ent value (Methods 1a and 1b) give the best assessment of long-
terminvestments. Methods that do not involve the time value of
money (Methods 2 and 3) have serious flaws; however, since th
ey are commonlyused for investment evaluation, their strengths
and weaknesses are discussed.
Net Present Value Method
The net present value (NPV) method includes the time value of
money by using an interest rate that represents the desired rate o
f return or, atleast, sets a minimum acceptable rate of return. Th
e decision rule is:
If the present value of incremental net cash inflows is greater th
an the incremental
investment net cash outflow, approve the project.
Using Tables 1 and 2 found at the end of this chapter, the net ca

2. sh flows for each year are brought back (i.e., discounted) to Yea
r 0 andsummed for all years. An interest rate must be specified.
This rate is often viewed as the cost of funds needed to finance t
he project and is theminimum acceptable rate of return. To disc
ount the cash flows, we use the interest rate and the years that t
he cash flows occur to obtain theappropriate present value facto
rs from the present value tables. A portion of Table 1 appears be
low showing the present value factors (theshaded numbers), corr
esponding to an interest rate of 12 percent, for each year during
the Clairmont Timepieces project's life.
Periods
(n)
1%
2%
4%
5%
6%
8%
10%
12%
14%
15%
16%
0
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1

3. 0.990
0.980
0.962
0.952
0.943
0.926
0.909
0.893
0.877
0.870
0.862
2
0.980
0.961
0.925
0.907
0.890
0.857
0.826
0.797
0.769
0.756
0.743
3
0.971
0.942
0.889
0.864
0.840
0.794
0.751
0.712
0.675
0.658
0.641
4

4. 0.961
0.924
0.855
0.823
0.792
0.735
0.683
0.636
0.592
0.572
0.552
5
0.951
0.906
0.822
0.784
0.747
0.681
0.621
0.567
0.519
0.497
0.476
6
0.942
0.888
0.790
0.746
0.705
0.630
0.564
0.507
0.456
0.432
0.410
7

5. 0.933
0.871
0.760
0.711
0.665
0.583
0.513
0.452
0.400
0.376
0.354
8
0.923
0.853
0.731
0.677
0.627
0.540
0.467
0.404
0.351
0.327
0.305
9
0.914
0.837
0.703
0.645
0.592
0.500
0.424
0.361
0.308
0.284
0.263
10

6. 0.905
0.820
0.676
0.614
0.558
0.463
0.386
0.322
0.270
0.247
0.227
These present value factors are used in Figure 10.2 to discount t
he yearly cash flows to their present values. In Figure 10.2, the
net cashinvestment ($95,000) is subtracted from the sum of cash
-
inflow present values ($137,331). When the residual is positive,
the project's rate ofreturn (ROR) is greater than the minimum a
cceptable ROR. If:
Present value of incremental net cash inflows ≥ Incremental inv
estment cash outflows
then:
Project's ROR ≥ Minimum acceptable ROR
Net present value is the difference between the present value of
the incremental net cash inflows and the incremental investment
cashoutflows. If net present value is zero or positive, the projec
t is acceptable. When the sum is negative, the project's ROR is l
ess than the discountrate. If:
Present value of incremental net cash inflows < Incremental inv
estment cash outflows
then:
Project's ROR < Minimum acceptable ROR
If net present value is negative, the project should be rejected.
Figure 10.2: Net present value of capital investment cash flows
Life of the Project

7. Today
Year 1
Year 2
Year 3
Year 4
Year 5
Net cash flow (Figure 11.1)
$(95,000)
$40,000
$40,000
$40,000
$40,000
$53,000
Present value factors at 12%
× 1.000
× .893
× .797
× .712
× .636
× .567
Present values at 12%
$(95,000)
$35,720
$31,720
$14,240
$25,440
$30,051
Sum of PVs for Years 1 to 5
137,331
Net present value

8. $42,331
The Interest Rate. What interest rate should be used for discount
ing the cash flows? This rate has many names that help explain i
ts source anduse. Among them are:
1. Cost of capital – a weighted-average cost of long-
term funds. Only projects that can earn at least what the firm pa
ys for funds should beaccepted. Later, we illustrate a calculatio
n of cost of capital.
2. Minimum acceptable rate of return –
a particular rate that is considered to be the lowest ROR that m
anagement will accept.
3.
Desired rate of return, target rate of return, or required rate of r
eturn – a rate that reflects management ROR expectations.
4. Hurdle rate –
a threshold that a project's ROR must "jump over" or exceed.
5. Cutoff rate –
the rate at which projects with a higher ROR are accepted and t
hose with a lower ROR are rejected; often the rate where allavai
lable capital investment funds are committed.
A firm will use one or more of these terms as its discount rate.
While these terms sometimes produce different rates in the busi
ness world, wewill use these terms interchangeably here. Genera
lly, if a project's ROR is below the chosen discount rate, it is rej
ected; above this rate, theproject is acceptable. Still, whether it
is funded depends on the availability of capital funds.
In the Clairmont Timepieces example, we assume that managem
ent has decided that 12 percent is the minimum acceptable rate
of return.Calculations needed to obtain a net present value are s
hown in Figure 10.2. The net present value is a positive $42,331
; therefore, the projectearns more than a 12 percent ROR. The n
et present value method does not provide information about the
project's exact ROR; it merelyinforms whether the project is ear
ning more than, less than, or equal to the minimum acceptable R

9. OR.
If other discount rates had been selected, we would find the foll
owing net present values:
Percentage
Present value of net cashinflows
−
Investment
=
Net presentvalue
16%
$124,328
$95,000
$29,328
20
113,246
95,000
18,246
24
103,713
95,000
8,713
28
95,523
95,000
523
30
91,797

10. 95,000
(3,203)
Notice that, as the interest rate increases, the present values of t
he future cash flows decrease. At 30 percent per year, the projec
t's net presentvalue is negative, and the project is unacceptable.
The project's rate of return must be between 28 and 30 percent.
Project Ranking. Even though a project has a positive net presen
t value, too many attractive projects may exist, given the invest
ment dollarsavailable. A ranking system is needed. We can rank
projects by the amount of net present value each generates, but
this ignores the relativesize of the initial investments. An extens
ion of the net present value method is the profitability index. It
is found by dividing the present valueof a project's net cash infl
ows by its net initial investment. The resulting ratio is cash in t
o cash out. The higher the ratio is, the more attractivethe invest
ment becomes. Notice that an acceptable project should have a p
rofitability index of at least 1. The following projects are ranke
d bythe profitability index.
Project
Present value of
net cash inflows
Initial
investment
Net present
value
Profitability
index
Ranking
A
$235,000
$200,000
$35,000
1.18
5
B

11. 170,000
140,000
30,000
1.21
4
C
80,000
60,000
20,000
1.33
1
D
98,000
80,000
18,000
1.23
3
E
52,000
40,000
12,000
1.30
2
We would typically accept projects with the highest profitabilit
y index until we exhaust the capital budget or the list of accepta
ble projects.
Internal Rate of Return (IRR) Method
The internal rate of return is the project's ROR and is the rate w
here the:
Net initial investment cash outflow = Present value of the incre
mental net cash inflows
Without calculator or computer assistance, the specific ROR is f
ound by trial and error. We search for the rate that yields a zero
net presentvalue.
In the Clairmont Timepieces example, the internal rate of return
was found to be between 28 and 30 percent. The net present val

12. ue at 28percent is positive and at 30 percent is negative. By inte
rpolation, we can approximate a "more accurate" rate as follows
:
Rate of return
Net present value
Calculations
28%
$523
Base rate
= 28.00%
30
(3,202)
($523 ÷$3,725) X 2%
= 0.28%
2% difference
$3,725 absolute difference
Internal rate ofreturn
28.28%
In most cases, however, knowing that the rate is between 28 and
30 percent is adequate.
Estimating the Internal Rate of Return. By using Table 2 and kn
owing certain project variables, we can estimate other unknown
variables,including a project's internal rate of return. This estim
ate requires that the annual net cash inflows be an annuity. The
variables and a sampleset of data are:
Variable
Example data
A = Initial investment cash outflow
$37,910
B = Life of project
5 years
C = Annual net cash inflow
$10,000 per year

13. D = Internal rate of return
10 percent
E = Present value factory at 10 percent (Table 2)
3.791
If we know any three of A, B, C, or D, we can find E and the mi
ssing variable. A variety of questions can be answered:
1.
What is the internal rate of return of the project? If A, B, and C
are known, we can calculate E and find D as follows:
E = A ÷ C
$37,910 ÷ $10,000 = 3.791
On Table 2, we go to the 5-
period (year) row and move across until we find 3.791 (E) in the
10 percent column (D). At 10 percent, the cashoutflow ($37,91
0) equals the present value of the net cash inflows (3.791 X $10
,000). The internal rate of return is 10 percent.
2.
What annual cash inflow will yield a 10 percent IRR from the pr
oject? If A, B, and D are known, we can find E and calculate C.
E is found inTable 2 by using five years and 10 percent ROR. T
he annual cash inflow is found as follows:
C = A ÷ E
$37,910 ÷ 3.791 = $10,000 per year
We need $10,000 per year in cash inflow to earn a 10 percent IR
R.
3.
What can we afford to invest if the project earns $10,000 each y
ear for five years and we want a 10 percent IRR? If we know B,
C, and D, wecan find E and then calculate A. The investment is
found by using the annual net cash inflow and 3.791 as follows:
A = C X E
$10,000 X 3.791 = $37,910
We can pay no more than $37,910 and still earn at least a 10 per
cent return.
4.
How long must the project last to earn at least a 10 percent IRR

14. ? If we know A, C, and D, we calculate E and find B as follows:
E = A ÷ C
$37,910 ÷ $10,000 = 3.791
For a 10 percent IRR, 3.791 is on the 5-
period row. The project's life must be at least five years.
Most spreadsheet software and business calculators have built-
in functions to find the internal rate of return. This simplifies th
e calculationburden that has limited its use in the past.
Project Ranking. Since each project has a specific rate of return,
ranking projects under the IRR method is relatively simple. All
projects arelisted according to their rates of return from high to
low. The cost of capital or a cutoff rate can establish a minimu
m acceptable rate of return.Then, projects are selected by movin
g down the list until the budget is exhausted or the cutoff rate is
reached.
Reinvestment Assumption. The internal rate of return method as
sumes that cash flows are reinvested at the project's internal rat
e of return.While this assumption may be realistic for cost of ca
pital rates, it may be wishful thinking for projects with high inte
rnal rates of return. Thisissue, however, is best left to finance te
xts and courses.
High Discount Rates. A concern exists about the use of high dis
count rates in present value methods. A project with significant
long-termpayoffs may not appear favorable because the long-
term payoffs will be discounted so severely. Even huge cash infl
ows due ten years or moreinto the future appear to be less valua
ble than minor cost savings earned in the first year of another pr
oject. High discount rates may encouragemanagers to think only
short term, to ignore research, market innovations, and creative
product development projects, and to ignore long-
termenvironmental effects. Thus, positive or negative impacts c
an result from the wise or unwise use of accounting tools and po
licies.
The Payback Period Method
The payback period method is a "quick and dirty" evaluation of
capital investment projects. It is likely that no major firm makes

15. investmentdecisions based solely on the payback period, but ma
ny ask for the payback period as part of their analyses. The pay
back period method asks:
How fast do we get our initial cash investment back?
No ROR is given, only a time period. If annual cash flows are e
qual, the payback period is found as follows:
Net initial investment ÷ Annual net cash inflow = Payback perio
d
If the investment is $120,000 and annual net cash inflow is $48,
000, the payback period is 2.5 years. We do not know how long
the project willlast nor what cash flows exist after the 2.5 years.
It might last 20 years or 20 days beyond the payback point.
If annual cash flows are uneven, the payback period is found by
recovering the investment cost year by year. In the Clairmont Ti
mepiecesexample:
Year
Cash flows
Unrecovered investment
0
$(95,000)
$95,000
1
40,000
55,000
2
40,000
15,000
3
20,000
0
In Year 3, the cost is totally recovered, using only $15,000 of Y
ear 3's $20,000 (75 percent). The payback period is 2.75 years.
The payback method is viewed as a "bail-
out" risk measure. How long do we need to stick with the projec
t just to get our initial investmentmoney back? It is used freque
ntly in short-

16. term projects where the impact of present values is not great. Su
ch projects as efficiencyimprovements, cost reductions, and pers
onnel savings are examples. Several major companies set an arb
itrary payback period, such as sixmonths, for certain types of co
st-saving projects.
Using the Payback Reciprocal to Estimate the IRR. The payback
period can be used to estimate a project's IRR, assuming a fairl
y high ROR (over20 percent) and project life that is more than t
wice the payback period. For example, if a $40,000 investment
earns $10,000 per year for anexpected 12 years, the payback per
iod is four years. The reciprocal of the payback period is 1 divid
ed by 4 and gives an IRR estimate of 25percent. From Table 2 f
or 12 years, the present value factor (payback period) of 4 indic
ates a rate of return of between 22 and 24 percent. Thepayback r
eciprocal will always overstate the IRR somewhat. If the project
's life is very long, say 50 years, the payback reciprocal is an al
mostperfect estimator. (See the present value factor of 4.000 for
25 percent and 50 periods on Table 2.)
Ranking Projects. When the payback period is used to rank proj
ects, the shortest payback period is best. Thus, all projects are li
sted from lowto high. A firm's policy may say that no project wi
th a payback period of over four years will be considered. This
acts like a cutoff point. Afterthat, projects would be selected un
til capital funds are exhausted. The major complaints about the
payback period method are that it ignores:
1. The time value of money.
2. The cash flows beyond the payback point.
These are serious deficiencies, but the method is easily applied
and can be a rough gauge of potential success.
Accounting Rate of Return Method
This method:
1. Ignores the time value of money.
2. Presumes uniform flows of income over the project's life.
3.
Includes depreciation expense and other accounting accruals in t
he calculation of project income, losing the purity of cash flows

17. .
In fact, we only discuss this approach because many internal cor
porate performance reporting systems use accrual accounting da
ta. Manycompanies use discounted cash flows for investment de
cisions but report actual results using accrual income and expen
se measures.
The accounting rate of return (ARR) method attempts to measur
e the return from accrual net income from the project. The ARR
subtractsdepreciation expense on the incremental investment fro
m the annual net cash inflows. Other accrual adjustments may al
so be made. Thegeneral formula is:
Annual net operating
cash inflow
−
Annual depreciation
expense in incremental
investment
=
Accounting rate of return
Average investment
The average investment, the denominator, is the average of the
net initial investment and the ending investment base ($0 if no s
alvage valueexists). This is the average book value of the invest
ment over its life. Some analysts prefer to use the original cost
of the investment orreplacement cost as the denominator. The n
umerator is the annual incremental accrual net income from the
project. To illustrate, assume thefollowing:
Initial investment
$110,000
Salvage value
$10,000
Annual cash inflow
35,000

18. Project life
5 years
Depreciation expense
20,000
ARR calculations are:
$35,000 - $20,000
=
$15,000
=
25 percent
($110,000 + $10,000) ÷ 2
$60,000
The 25 percent must be viewed relative to other projects' ARR a
nd cannot be compared to present value rates of return. For rank
ing purposes,projects are ranked from high to low. An arbitrary
percentage may be set as a minimum rate, similar to an accrual r
eturn on equity.
Another problem with the ARR is the impression it gives of an i
ncreasing ROR on an annual basis as an asset grows older. A ma
nager would seethis project's performance on annual investment
center responsibility report as follows:
Average
investment
(book value)
Project
net income
Annual
ARR
Year 1
$100,000
$15,000
15.0%

19. Year 2
80,000
15,000
18.8
Year 3
60,000
15,000
25.0
Year 4
40,000
15,000
37.5
Year 5
20,000
15,000
75.0
The average annual book value declines each year, and net inco
me is assumed to remain constant. As the asset gets older, the A
RR increases. Itis tempting for managers to reject any proposal t
hat will make their performance reports look less favorable. Thi
s is particularly true when theirbonuses are tied to accrual accou
nting performance numbers. Managers will be biased toward sti
cking with older assets with higher accountingrates of return. T
hey forego new investments that offer new technology, lower op
erating costs, and greater productivity.