CHAPTER 13

Planning for Capital Investments

ASSIGNMENT CLASSIFICATION TABLE

Self-Study Brief Do It! A&B

Study Objectives Questions Exercises Review Exercises Problems

1. Discuss capital budgeting 1, 2, 3 1 10 14, 15, 20, 22A, 23A, 24A,

inputs and apply the cash 21 25A, 27A, 28A,
payback technique. 29A, 30A, 34B,
35B, 36B, 37B,
43B

2. Explain the net present 4, 5, 6 2, 3, 4, 5, 6 11 15, 16, 21 22A, 23A, 24A,

value method. 25A, 26A, 27A,
28A, 29A, 30A,
31A, 32A, 33A,
34B, 35B, 36B,
37B, 38B, 39B,
40B, 41B, 42B,
43B, 44B

3. Identify capital budgeting 7, 8 4, 5, 6 12 16 31A, 32A, 40B,

challenges and 42B, 44B
refinements.

4. Explain the internal rate 9 7, 8 11 17, 18 32A, 33A, 42B,

of return method. 44B

5. Describe the annual 10 9 13 19, 20, 21 27A, 28A, 29A,

rate of return method. 30A, 35B, 37B,
43B

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ASSIGNMENT CHARACTERISTICS TABLE

Problem Difficulty Time

Number Description Level Allotted (min.)

22A Calculate initial investment, cash payback, and net Simple 20–30
present value.

23A Calculate the net present value and payback period. Moderate 30–40

24A Calculate incremental cash flow and net present value. Simple 20–30

25A Calculate the initial investment, cash payback, and net Moderate 30–40
present value.

26A Calculate the net present value and apply the decision Simple 20–30
rule.

27A Calculate the annual rate of return and net present value, Moderate 30–40
and apply decision rules.

28A Calculate the payback period, annual rate of return, and Moderate 20–30
net present value, and apply decision rules.

29A Calculate the payback period, annual rate of return, and Challenging 25–35
net present value, and discuss findings.

30A Calculate payback, annual rate of return, and net present Moderate 25–35
value.

31A Calculate the net present value, considering intangible Moderate 25–35
benefits.

32A Calculate the net present value, profitability index, and Moderate 30–40
internal rate of return.

33A Calculate the net present value and internal rate of return Moderate 35–45
with sensitivity analysis.

34B Calculate the net present value and payback period. Moderate 20–30

35B Calculate the annual rate of return, payback period, and Moderate 30–40
net present value, and apply decision rules.

36B Calculate the initial investment, cash payback, and net Simple 20–30
present value.

37B Calculate the annual rate of return, cash payback, and net Simple 20–30
present value.

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ASSIGNMENT CHARACTERISTICS TABLE (Continued)

38B Calculate the net present value and apply the decision Moderate 20–30
rule.

39B Calculate the net present value and apply the decision Moderate 30–35
rule.

40B Calculate the net present value considering intangible Moderate 25–35
benefits.

41B Calculate the net present value with sensitivity analysis, Moderate 30–40
and discuss findings.

42B Calculate the net present value, profitability index, and Moderate 25–35
internal rate of return.

43B Calculate the payback, annual rate of return, and net Simple 20–30
present value.

44B Calculate the net present value, profitability index, and Moderate 25–35
internal rate of return.

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 Correlation Chart between Bloom’s Taxonomy, Study Objectives and End-of-Chapter Exercises and Problems

Study Objective Knowledge Comprehension Application Analysis Synthesis Evaluation

1. Discuss capital budgeting inputs BE1, D10, E20, P37B, E14, E15, P22A,
and apply the cash payback E21, P30A, P23A, P24A, P25A,
technique. P43B P27A, P28A, P29A,
P34B, P35B, P36B BLO
© 2. Explain the net present value BE3, E21, BE4, P33A, BE2, BE5, BE6, D11, OM’
2018 method. P30A, P43B P37B, P41B E14, E15, E16, P22A,
S
For P23A, P24A, P25A,
Instru P26A, P27A, P28A, TAX
ctor P29A, P31A, P32A, ONO
P34B, P35B, P36B,
Use P38B, P39B, P40B, MY
Only P42B, P44B TAB
3. Identify capital budgeting P43B BE4, BE5 P31A P42B LE
challenges and refinements. BE6 P32A P43B
D12 P40B
E16
4. Explain the internal rate of return BE7, BE8 P33A, D11 P32A
method. E17 P42B
E18 P43B

5. Describe the annual rate of return BE9, D13, E19, P37B, P27A P35B
method. E20, E21, P28A
P30A, P43B P29A

A note about the correlation between CPA competencies and the end-of-chapter exercises and problems.

The CPA competencies are divided into enabling competencies and terminal competencies. Unless otherwise specified, the
terminal competency being tested by the end-of-chapter material in this course is cpa-t003 (Management Accounting). The
enabling competency being tested will differ between questions. The following questions test enabling competency cpa-e002
Problem Solving and Decision-Making:

BE13.1, BE13.2, BE13.3, BE13.4, BE13.5, BE13.6, BE13.7, BE13.8, BE13.9, BE13.10, D13.11, D13.12, D13.13, E13.14, E13.15, E13.16,
E13.17, E13.18, E13.19, E13.20, E13.21, P13.22A, P13.23A, P13.24A, P13.25A, P13.26A, P13.27A, P13.28A, P13.29A, P13.30A,
P13.31A, P13.32A, P13.33A, P13.34B, P13.35B, P13.36B, P13.37B, P13.38B, P13.39B, P13.40B, P13.41B, P13.42B, P13.43B, P13.44B

________________________________________________________________________________
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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

SOLUTIONS TO BRIEF EXERCISES

BRIEF EXERCISE 13.1

($75,000 + $4,000 + $6,000) ÷ $20,000 = 4.25 years

BRIEF EXERCISE 13.2

Present
Value
Net annual cash flows: $40,000 × 5.65 $226,000
Capital investment 215,000
Net present value $ 11,000

The investment should be made because the net present value is positive.

BRIEF EXERCISE 13.3

Time Cash Discount Present

Period Flows Factor at Value
10%
Net annual cash inflows 1-5 $25,000 3.79079 $ 94,770
Salvage value 5 65,000 0.62092 40,360
135,130
Less: Capital investment 136,000
Net present value $ (870)

Since the net present value is negative, the project should be rejected.
However, the value is so small it could easily become positive with just a
slight change in the expected inflows of cash. Other non-financial factors
should be considered before making the final decision.

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BRIEF EXERCISE 13.4

Time Cash Discount Present
Period Flows Factor at Value
9%
Net annual cash flows 1-8 $35,000 5.53482 $193,719
Less: Capital investment 200,000
$ (6,281)

The reduction in downtime would have to have a present value of at least

$6,281 in order for the project to be acceptable.

BRIEF EXERCISE 13.5

Discoun
Time Cash t Present
Factor
Project A Period Flows at Value
9%
Net annual cash flows 1 - 10 $70,000 6.41766 $449,236
Less: Capital investment 395,000
Net present value $ 54,236

Profitability index: $449,236 ÷ $395,000 = 1.14

Discoun
Time Cash t Present
Factor
Project B Period Flows at Value
9%
Net annual cash flows 1 - 10 $50,000 6.41766 $320,883
Less: Capital investment 270,000
Net present value $ 50,883

Profitability index: $320,883 ÷ $270,000 = 1.19

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Project B has a lower net present value than Project A, but because of its
lower capital investment, it has a higher profitability index. Based on its
profitability index, Project B should be accepted.

BRIEF EXERCISE 13.6

Discoun
Time Cash t Present
Original Estimate Period Flows Factor at Value
10%
Net annual cash flows 1-9 $45,000 5.75902 $259,156
Less: Capital investment 250,000
Net present value $ 9,156

Discoun
Time Cash t Present
Actual Results Period Flows Factor at Value
10%
Net annual cash flows 1 - 11 $38,000 6.49506 $246,812
Less: Capital investment 260,000
Net present value $(13,188)

The original net present value was projected to be a positive $9,156;

however, the revised estimate is a negative $13,188. The project did not
turn out as successfully as predicted.

BRIEF EXERCISE 13.7

When net annual cash flows are expected to be the same, dividing the
capital investment by the net annual cash flows will determine the discount
factor. Then it is just a matter of locating this discount factor on the present
value of an annuity table to determine the approximate internal rate of
return.

$176,000 ÷ $33,740 = 5.21636

By tracing across on the 7-year row we see that the discount factor for 8% is
5.20637. Thus, the internal rate of return on this project is approximately 8%.
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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

BRIEF EXERCISE 13.8

When net annual cash flows are expected to be equal, dividing the capital
investment by the net annual cash flows to determine the discount factor,
and then locating this discount factor on the present value of an annuity
table can approximate the internal rate of return.

Since this exercise has a salvage value, not all cash flows are equal. In this
case, identifying the discount rate that will result in a net present value of
zero can approximate the internal rate of return. By experimenting with
various rates, we determined that the net present value is approximately
zero when a discount rate of approximately 9% is used. The project should
be accepted because the rate exceeds 7%.

BRIEF EXERCISE 13.9

The annual rate of return is calculated by dividing expected annual income

by the average investment.

The company’s expected annual income is: $130,000 – $70,000 =

$60,000. Average investment is: ($470,000 + $10,000) ÷ 2 = $240,000

Therefore, its annual rate of return is: $60,000 ÷ $240,000 = 25%

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SOLUTIONS TO DO IT! REVIEW EXERCISES

DO IT! REVIEW 13.10

Estimated annual cash inflows.................................. $80,000

Estimated annual cash outflows............................... 41,000
Net annual cash flow.................................................. $39,000

Cash payback period = $120,000 ÷ $39,000 = 3.08 years.

DO IT! REVIEW 13.11

Discoun
(a) Time Cash t Present
Factor
Period Flows at Value
12%
Net annual cash flows 1-4 $39,000 3.03735 $118,457
Less: Capital investment 120,000
Net present value $ (1,543)

Based on the negative net present value, the company would be wise
to reject this project. However, it is possible there are intangible
benefits that accompany the project, and if their estimated value is
greater than $1,543 then it would be worthwhile accepting the project.

(b) With a negative net present value at 12%, the internal rate of return will
be less than 12%, but only slightly, as the amount is not significant.

The discount factor is $120,000 ÷ $39,000 = 3.07692.

The discount factor for 11% in the four-period row is 3.10245.
The discount factor for 12% in the four-period row is 3.03735.
So the internal rate of return is approximately 11.5% (approximately
half way between 11% and 12%).

Since the project has an internal rate that is less than 12%, the
company’s required rate of return, the project should not be accepted.

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DO IT! REVIEW 13.12

Solar Wind
Present value of annual cash flows $52,580 $128,450
Less: Initial investment 39,500 105,300
Net present value $13,080 $ 23,150

Profitability index Solar Wind

Present value of annual cash flows $52,580 $128,450
Divided by initial investment ÷ 39,500 105,300
1.33 1.22

Ranger Corporation should choose the solar energy source as it has a

higher profitability index.

DO IT! REVIEW 13.13

Revenues...................................................................... $80,000
Less:
Expenses (excluding depreciation)..................... $41,000
Depreciation ($120,000 ÷ 4 years)........................   30,000   71,000
Annual net income...................................................... $ 9,000

Average investment = ($120,000 + $0) ÷ 2 = $60,000.

Annual rate of return = $9,000 ÷ $60,000 = 15%.

Since the annual rate of return of 15% is greater than Sierra’s required rate
of return of 12%, the proposed project is acceptable.

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SOLUTIONS TO EXERCISES
EXERCISE 13.14

(a) The cash payback period is: $56,000 ÷ $7,500 = 7.47 years

Time Cash Discount Present

Period Flows Factor at Value
8%
Net annual cash flows 1-8 $ 7,500 5.74664 $43,100
Salvage value 8 27,000 0.54027 14,587
57,687
Less: Capital investment 56,000
Net present value $ 1,687

(b) In order to meet the cash payback criteria, the project would have to
have a cash payback period of less than 4 years (8 ÷ 2). It does not
meet the criteria. The net present value is positive, however, suggesting
the project should be accepted. The reason for the difference is that
the project’s high estimated salvage value increases the present value
of the project. The net present value is a better indicator of the
project’s worth.

EXERCISE 13.15

(a) Based on average annual cash flows, the project payback periods are:

AA— $25,000 ÷ ($28,000 ÷ 3) = 2.68 years

BB— $25,000 ÷ 9,600 = 2.60 years
CC— $25,000 ÷ ($33,000 ÷ 3) = 2.27 years

The most desirable project is CC because it has the shortest payback

period. The least desirable project is AA because it has the longest
payback period. As indicated, only CC is acceptable because its cash
payback is less than 2.5 years.

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EXERCISE 13.15 (Continued)

(b) Net present value of AA:

Discount
Factor Present
Year 12% Amount Value
1 0.89286 $ 7,000 $6,250
2 0.79719 9,000 7,175
3 0.71178 12,000 8,541
Present value of cash inflows 21,966
Capital investment 25,000
Net present value $(3,034 )

Net present value of BB:

Discount
Factor Present
Year 12% Amount Value
1-3 2.40183 $ 9,600 $23,058
Present value of cash inflows 23,058
Capital investment 25,000
Net present value $(1,942 )

Net present value of CC:

Discount
Factor Present
Year 12% Amount Value
1 0.89286 $13,000 $11,607
2 0.79719 9,000 7,175
3 0.71178 11,000 7,830
Present value of cash inflows 26,612
Capital investment 25,000
Net present value $ 1,612

EXERCISE 13.15 (Continued)

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Project CC is still the most desirable project. However, on the basis of

net present values, the other projects should be rejected because of
the negative net present values.

EXERCISE 13.16

Time Cash Discount Present

Machine A Period Flows Factor at Value
10%
Net annual cash flows 1-8 $20,000 5.33493 $106,699
Less: Capital investment 98,000
Net present value $ 8,699

Profitability index: $106,699 ÷ $98,000 = 1.089

Time Cash Discount Present

Machine B Period Flows Factor at Value
10%
Net annual cash flows 1-8 $28,000 5.33493 $149,378
Less: Capital investment 170,000
Net present value $(20,622)

Profitability index: $149,378 ÷ $170,000 = 0.879

Machine B has a negative net present value, which means its profitability
index is less than one. Machine B should be rejected. Machine A should be
purchased, as it has a positive net present value.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

EXERCISE 13.17

When net annual cash flows are expected to be equal, the capital
investment can be divided by the net annual cash flows to determine the
discount factor. By locating this discount factor on the present value of an
annuity table, the discount rate can be determined.

$430,000 ÷ $101,000 = 4.25743

By tracing across on the 5-year row, we see that the discount factor for 6%
is 4.21236. Thus, the internal rate of return on this project is less than 6%.
Since this is well below the company’s required rate of return, the project
should not be accepted.

EXERCISE 13.18

(a)
Net Annual Closest
Capital Cash IRR Discount Approx.
Project Investment ÷ Flows* = Factor Factor IRR
22A $240,000 ÷ $56,7001 = 4.233 4.23054 11%
23A $270,000 ÷ $50,6002 = 5.336 5.32825 12%
24A $280,000 ÷ $57,5003 = 4.870 4.86842 10%

*(Annual income + Depreciation expense)

1
$16,700 + ($240,000 ÷ 6)
2
$20,600 + ($270,000 ÷ 9)
3
$17,500 + ($280,000 ÷ 7)
(b) The acceptable projects are 22A and 23A because their rates of return
are equal to or greater than the 11% required rate of return.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

EXERCISE 13.19

The annual rate of return is calculated by dividing expected annual income

by the average investment. The company’s expected annual income is:

$70,000 – $41,500 = $28,500

Its average investment is:

$300,000 + $80,000
= $190,000
2
Therefore, its annual rate of return is: $28,500 ÷ $190,000 = 15%

EXERCISE 13.20

(a) Cost of hoist: $18,600 + $3,900 + $900 = $23,400.

Net annual cash flows: (5 x 52 weeks) x ($75 – $35 – $15) = $6,500
Cash payback period ($23,400 ÷ $6,500) = 3.6
years

(b) Average investment: ($23,400 + $1,400) ÷ 2 = $12,400.

Annual depreciation: ($23,400 – $1,400) ÷ 5 = $4,400.
Annual net income: $6,500 – $4,400 = $2,100.
Annual rate of return = $2,100 ÷ $12,400 = 16.9% (rounded).

EXERCISE 13.21

(a) (1) Cash payback period: $210,000 ÷ $60,000 = 3.5 years.

(2) Annual rate of return: $20,000 ÷ [($210,000 + $0) ÷ 2] = 19.05%.

(b)

Time Cash Discount Present

Period Flows Factor at Value
12%
Net annual cash flows 1-5 $60,000 3.60478 $216,287
Less: Capital investment 210,000
Net present value $ 6,287

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

SOLUTIONS TO PROBLEMS—SET A

PROBLEM 13.22A

(a) The initial investment amount would be the cash price of the new
equipment less the salvage value of old equipment, plus any increase
in working capital:
$175,000 – $45,000 + $20,000 = $150,000

(b) Cash payback period for investment of $150,000:

Year Net Annual Cash Flow Cumulative Cash Flow

1 $40,000 $40,000
2 40,000 80,000
3 40,000 120,000
4 40,000 160,000
5 40,000

The payback period will be 3.75 years [= 3 + ($30,000 ÷ $40,000)].

(c) Time Cash Discount Present

Period Flows Factor at Value
10%
Net annual cash flows 1-6 $40,000 4.35526 $174,210
Net annual cash flows* 7 - 10 10,000 1.78931 17,893
Recover working capital 10 20,000 0.38554 7,711
Salvage (new equipment) 10 25,000 0.38554 9,639
209,453
Less: Capital investment (from (a)) 150,000
Net present value $ 59,453
*Discount factor at 10 yrs (6.14457) minus discount factor at 6 yrs (4.35526)

(d) The cash payback period of 3.75 years, which is below their maximum
payback period of five years, and the positive net present value
indicate that BioFarm should go ahead with the purchase.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.23A

(a) Cost of goods sold per unit = $640,000 ÷ 20,000 = $32

Direct labour is 42% of COGS = 42% × $32 = $13.44
Savings in labour is 30% of DL cost = 30% × $13.44 = $4.03

Time Cash Discount Present

Period Flows Factor at Value
12%
Net annual cash flows** 1-2 $80,600 1.69005 $136,218
Net annual cash flows* 3-5 88,660 1.91473 169,760
Salvage (new equipment) 5 25,000 0.56743 14,186
Present value of cash inflows 320,164
Less: Extra supervision 1-5 45,000 3.60478 162,215
Net cash flows 157,949
Less: Capital investment 165,000
Net present value $ (7,051)

*22,000 units x $4.03 labour savings

**20,000 units x $4.03 labour savings

Based on the negative net present value, the company

should not
purchase the equipment.

(b) Year Outflow Inflow Balance

Initial investment $ (165,000) $ (165,000)
Less: Cash flow 1 (45,000) $ 80,600 (129,400)
2 (45,000) 80,600 (93,800)
3 (45,000) 88,660 (50,140)
4 (45,000) 88,660 (6,480)
5 (45,000) 88,660 37,180

Payback period = 4 + ($6,480 ÷ $43,660) = 4.15 years

PROBLEM 13.23A (Continued)

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

Note that the salvage value of the equipment was not included in the
cash flow for the final year. It would be considered a cash inflow at
the end of the year, whereas the other cash flow items were
considered to be received uniformly throughout the year.

(c) The salvage value will be received in 2020, so it will be discounted by

a factor of 0.56743 to determine present value. The incremental
salvage value, when discounted by a factor of 0.56743, must equal the
negative net present value calculated in part (a). The additional inflow
will bring the NPV to zero, at which time the investment will be
earning exactly 12%.

Incremental value = $7,051 ÷ 0.56743 = $12,426.

Therefore, the total salvage value must be $37,426 ($12,426 + $25,000)
for the whole project to earn a 12% return on the investment.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.24A

Net present value of expansion of current facility (based on incremental

analysis), in 000s:

Discount Present
Year Factor, 14% Amount Value
Net cash flows 1–10 5.216 $4,000¹ $20,864
Initial investment (19,000)
Net Present Value $1,864

¹ Revenues of $13 million less costs

of $9 million.

Net present value of conversion of current warehouse (based on

incremental analysis), in 000s:

Discount Present
Year Factor, 14% Amount Value
Net cash flows 1–10 5.216 $ 3,000² $15,648
Initial investment (22,000)
Net Present Value $ (6,352)

² Revenues of $13 million less costs of $10 million.

Note that both alternatives require the use of $3 million working capital at
the beginning of the project and that the working capital will be released at
the end of the project (in 10 years). This has been omitted from the NPV
calculation since it is based on incremental analysis (rather than total
costs).

Based on the net present value calculations, Saskatoon First should

choose the expansion option, as it has a positive net present value.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.25A

(a) The initial investment = $2,850,000 – $150,000 = $2,700,000

(b) Savings on $1.5 million Years Amount Total

Operating costs (30%) 1–3 $450,000 $1,350,000
Operating costs (40%) 4–10 600,000 4,200,000
5,550,000
Less: additional costs
Operator 1–10 30,000 300,000
Net savings $5,250,000

(c) Net present value of the investment:

Discount Present
Year Factor at 12% Amount Value
Savings: 1–3 2.40183 $450,000 $1,080,824
4–10 3.24839¹ 600,000 1,949,034
Costs: 1–10 5.65022 (30,000) (169,507)
Salvage: 10 0.32197 525,000 169,034
Present value of cash inflows 3,029,385
Initial investment (2,700,000)
$ 329,385

¹ Factor at 10 years less factor at 3 years: 5.65022 – 2.40183, or

Factor at 7 years, discounted by 3 years: 4.56376 × 0.71178

(d) Initial investment $2,700,000

Less: Savings from years 1-3 [($450,000 – $30,000) × 3] 1,260,000
Less: Savings from years 4-5 [($600,000 – $30,000) × 2] 1,140,000
Balance remaining at the end of year 5 $300,000
Payback period = 5 + ($300,000 ÷ $570,000) = 5.5 years (rounded)

The company should accept the project, as the payback period is

less than their maximum acceptable payback period of 8 years.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.26A

Net present value of the investment:

Savings per unit: 5% of variable costs = 0.05 × $2.40 = $0.12/unit

Savings per year: 1,000,000 units × $0.12 = $120,000

Discount Present
Year Factor at 12% Amount Value
Savings 1–5 3.60478 $120,000 $432,574
Salvage (new) 5 0.56743 350,000 198,601
Salvage (old) 0 — 230,000 230,000
Present value of cash inflows 861,175
Initial investment (800,000)
$61,175

The president should go ahead and replace the equipment, based on a

positive net present value of $61,175.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.27A

(a) Project Main:

Average annual cash inflow =
Average annual net income + depreciation
Average annual net income = $65,000 ÷ 5 years = $13,000
Annual depreciation = $150,000 ÷ 5 years = $30,000

Payback in years: $150,000 ÷ ($13,000 + $30,000) = 3.49 years

Project Odyssey:
Average annual net income = $72,000 ÷ 5 years = $14,400
Annual depreciation = $160,000 ÷ 5 years = $32,000

Payback in years: $160,000 ÷ ($14,400 + $32,000) = 3.45 years

Project Duo:
Average annual net income = $95,000 ÷ 5 years = $19,000
Annual depreciation = $200,000 ÷ 5 years = $40,000

Payback in years: $200,000 ÷ ($19,000 + $40,000) = 3.39 years

(b) Project Main: Discount Present

Year Factor, 15% Amount Value
Net cash flows 1–5 3.35216 $43,0001 $144,143
Initial investment (150,000)
Net Present Value $ (5,857)
1
$13,000 + $30,000

Project Odyssey: Discount Present

Year Factor, 15% Amount Value
Net cash flows 1–5 3.35216 $46,4002 $155,540
Initial investment (160,000)
Net Present Value $(4,460)
2
$14,400 + $32,000

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.27A (Continued)

Project Duo: Discount Present

Year Factor, 15% Amount Value
Net cash flows 1–5 3.35216 $59,0003 $197,777
Initial investment (200,000)
Net Present Value $ (2,223)

2
$19,000 + $40,000

(c) Annual rate of return = average net income ÷ average investment

Project Main = $13,000 ÷ [($150,000 + $0) ÷ 2] = 17.33%

Project Odyssey = $14,400 ÷ [($160,000 + $0) ÷ 2] = 18%

Project Duo = $19,000 ÷ [($200,000 + $0) ÷ 2] = 19%

(d) Net Annual

Project Cash Payback Present Value Rate of Return

Main 3.49 (3) $(5,857) (3) 17.33% (3)

Odyssey 3.45 (2) $(4,460) (2) 18% (2)
Duo 3.39 (1) $(2,223) (1) 19% (1)

Project Duo is the best project, although if the decision is based on

net present value alone, none of the projects are acceptable as they all
have a negative NPV.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.28A

(a) Total net investment = $30,000 – $2,000 + $1,500 = $29,500

Annual net cash flow = $8,000

Payback period = $29,500 ÷ $8,000 = 3.6875 years

(b) Annual rate of return = annual net income ÷ average investment

Depreciation $29,500 ÷ 5 years = $5,900

Annual net income = $8,000 – $5,900 = $2,100
Average investment = [$29,500 + $0] ÷ 2 = $14,750

Annual rate of return = $2,100 ÷ $14,750 = 14.237%

(c)
Discount Present
Year Factor, 10% Amount Value
Net cash flows 1–5 3.79079 $8,000 $30,326
Initial investment (29,500)
Net Present Value $ 826

(d) The new machine should be purchased because the net present value
is positive.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.29A

(a) Cash payback period = ($38,000 – $10,000) ÷ $6,000 = 4.667 years.

(b) Annual rate of return = $1,8751 ÷ [($38,000 + $5,000) ÷ 2] = 8.72%

1
Incremental annual net income = $6,000 – [($38,000 – $5,000) ÷ 8 yrs]

(c) Present value of annual cash inflows ($6,000 × 4.34359*) = $26,062

Salvage value ($5,000 x 0.30503) 1,525
Capital investment   (28,000)
Net present value $ (413)

*8 years at 16%, PV of ordinary annuity

(d) The calculations show that purchasing the new equipment is not a
wise investment for these reasons: (1) incremental annual net income
will only be $1,875, (2) the annual rate of return (8.72%) is less than the
cost of capital (16%), and (3) the net present value is negative.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.30A

Cumulative
Net Cash
(a) Year Amount Flow
Initial investment 0 $(105,000) $(105,000)
Less: Cash Flow 1 45,000 (60,000)
2 40,000 (20,000)
3 35,000 15,000

Payback period = 2 + ($20,000 ÷ $35,000) = 2.57

(b) Average annual net income = ($16,000 + $18,000 + $20,000 + $22,000 +

$24,000) ÷ 5 = $20,000
Average investment = ($105,000 + $0) ÷ 2 = $52,500
Annual rate of return = $20,000 ÷ $52,500 = 38.10%

(c) Discount Present

Year Factor, 15% Amount Value
Net cash flows 1 0.86957 $45,000 $39,131
2 0.75614 40,000 30,246
3 0.65752 35,000 23,013
4 0.57175 30,000 17,153
5 0.49719 25,000 12,430
Present value of cash inflows 121,973
Initial investment (105,000)
Net Present Value $16,973

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.31A

(a) The net present value based on the original estimates is as follows:

Discount Present
Year Factor, 9% Amount Value
Annual cash inflow 1–8 5.53482 $8,000 $44,279
Overhaul 4 0.70843 (5,000) (3,542)
Salvage value 8 0.50187 15,000 7,528
Present value of cash flows 48,265
Initial investment (60,000)
Net Present Value $(11,735)

Based on these estimates, the tow truck should not be purchased.

(b) The net present value based on the revised estimates is as follows:

Discount Present
Year Factor, 9% Amount Value
Annual cash inflow 1–8 5.53482 $8,000 $44,279
Overhaul 4 0.70843 (5,000) (3,542)
Additional benefits 1–8 5.53482 5,000 27,674
Salvage value 8 0.50187 15,000 7,528
Present value of cash flows 75,939
Initial investment (60,000)
Net Present Value $15,939

Based on the revised figures, the tow truck has a positive net present
value and therefore should be purchased.
(c) In order for the project to be acceptable, the present value of the
intangible benefits would only have to be $11,735. That is the amount
by which the original estimate fell short of having a positive net
present value.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.32A

(a) OPTION A

(1) Discount Present

Year Factor 8% Amount Value
Annual cash inflow 1–7 5.20637 $40,000 $208,255
Cost to rebuild 4 0.73503 (50,000) (36,752)
Salvage value 7 0.58349 — —
Present value of cash flows 171,503
Initial investment (160,000)
Net Present Value $ 11,503

Net annual cash flows = $70,000 – $30,000 = $40,000

(2) Profitability index = $171,503 ÷ $160,000 = 1.07

(3) Because the net present value of the investment at a discount

rate of 8% is positive, we know the internal rate of return will be greater
than 8%, say 10%. Recall that the internal rate of return is the interest
rate that will cause the net present value to equal zero.

Discount Present
Year Factor 10% Amount Value
Annual cash inflow 1–7 4.86842 $40,000 $194,737
Cost to rebuild 4 0.68301 (50,000) (34,151)
Salvage value 7 0.51316 — —
Present value of cash flows 160,586
Initial investment (160,000)
Net Present Value $ 586

Net annual cash flows = $70,000 – $30,000 = $40,000

The internal rate of return will be a little higher than 10%.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.32A (Continued)

OPTION B

(1) Discount Present

Year Factor 8% Amount Value
Annual cash inflow 1–7 5.20637 $54,000 $281,144
Cost to rebuild 4 0.73503 — —
Salvage value 7 0.58349 8,000 4,668
Present value of cash flows 285,812
Initial investment (227,000)
Net Present Value $ 58,812

Net annual cash flows = $80,000 – $26,000 = $54,000

(2) Profitability index = $285,812 ÷ $227,000 = 1.26

(3) Recall that the internal rate of return is the interest rate that will
cause the net present value to equal zero. Internal rate of return on
Option B is 15%, as calculated below:

Discount Present
Year Factor 15% Amount Value
Annual cash inflow 1–7 4.16042 $54,000 $ 224,663
Cost to rebuild 4 0.57175 — —
Salvage value 7 0.37594 8,000 3,008
Present value of cash flows 227,671
Initial investment (227,000)
Net Present Value $ 671

Net annual cash flows = $80,000 – $26,000 = $54,000

(b) Option A has a lower net present value than Option B, and also a lower
profitability index and internal rate of return. Therefore, Option B is the
preferred project.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.33A

(a) Using the original estimates, the net present value is calculated as
follows:

Discount Present
Year Factor 8% Amount Value
Annual cash inflow 1–20 9.81815 $100,000 $ 981,815
Salvage value 20 0.21455 1,500,000 321,825
Present value of cash flows 1,303,640
Initial investment ($300,000 + $600,000) (900,000)
Net Present Value $ 403,640

Net annual cash flows = $940,000 – $840,000

(b) Using the revised estimates, the net present value is calculated as
follows:

Discount Present
Year Factor 8% Amount Value
Annual cash inflow 1–20 9.81815 $50,000 $490,908
Salvage value 20 0.21455 1,500,000 321,825
Present value of cash flows 812,733
Initial investment ($300,000 + $600,000) (900,000)
Net Present Value $ (87,267)

Net annual cash flows = $800,000 – $750,000

Under these revised estimates, the project should be rejected. It

appears that many of the camp’s costs are fixed; thus, when the
number of players declines, cash inflows decline, but cash outflows
don’t decline proportionately.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.33A (Continued)

(c) Using the original estimates, but an 11% discount rate, the net present
value is calculated as follows:

Discount Present
Year Factor 11% Amount Value
Annual cash inflow 1–20 7.96333 $100,000 $ 796,333
Salvage value 20 0.12403 1,500,000 186,045
Present value of cash flows 982,378
Initial investment ($300,000 + $600,000) (900,000)
Net Present Value $ 82,378

Net annual cash flows = $940,000 – $840,000

The positive net present value of the project suggests that it should be
accepted; obviously, it is not nearly as profitable using an 11% discount
rate.

(d) The internal rate of return can be determined by calculating the

discount rate that results in a net present value of approximately zero.
In this case the internal rate of return was approximately 12%.

Discount Present
Year Factor 12% Amount Value
Annual cash inflow 1–5 3.60478 $40,000 $144,191
Salvage value 5 0.56743 1,332,000 755,817
Present value of cash flows 900,008
Initial investment ($300,000 + $600,000) (900,000)
Net Present Value $ 8

The project had a high internal rate of return, even though the
business itself did not appear to be successful, because the property
increased significantly in value during the 5-year period.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

SOLUTIONS TO PROBLEMS—SET B
PROBLEM 13.34B

(a) Cost of goods sold per unit = $900,000 ÷ 25,000 = $36.00

Direct labour is 65% of COGS = 65% × $36.00 = $23.40
Savings in labour is 30% of DL cost = 30% × $23.40 = $7.02

Discount Present
Year Units Amount*   Factor, 12% Value
1 25,000 $175,500 0.89286 $156,697
2 25,000 175,500 0.79719 139,907
3 30,000 210,600 0.71178 149,901
4 30,000 210,600 0.63552 133,841
5 30,000 210,600 0.56743 119,501
Present value of annual cash inflows 699,847
1–5 Supervision (50,000) 3.60478 (180,239)
5 Salvage 25,000 0.56743 14,186
Net cash flows 533,794
Initial Investment (400,000)
Net present value $133,794

*Amount = units × per unit savings in labour

Based on the positive net present value, the company should

purchase the equipment.

(b) Year Outflow Inflow Balance

Initial investment $(400,000) $(400,000)
Less: Cash Flow 1 (50,000) $175,500 (274,500)
2 (50,000) 175,500 (149,000)
3 (50,000) 210,600 11,600

Payback period = 2 + ($149,000 ÷ $160,600) = 2.93 years

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.35B

(a) Average annual cash inflow =

Average annual net income + depreciation

Project Brown:
Average annual net income = $45,000 ÷ 5 years = $9,000
Annual depreciation = $140,000 ÷ 5 years = $28,000

Payback in years: $140,000 ÷ ($9,000 + $28,000) = 3.78 years

Project Red:
Average annual net income = $49,500 ÷ 5 years = $9,900
Annual depreciation = $170,000 ÷ 5 years = $34,000

Payback in years: $170,000 ÷ ($9,900 + $34,000) = 3.87 years

Project Yellow:
Average annual net income = $65,000 ÷ 5 years = $13,000
Annual depreciation = $190,000 ÷ 5 years = $38,000

Payback in years: $190,000 ÷ ($13,000 + $38,000) = 3.73 years

(b) Project Brown: Discount Present

Year Factor, 12% Amount Value
Net cash flows 1–5 3.60478 $37,000 $133,377
Initial investment (140,000)
Net Present Value $ (6,623)

Project Red: Discount Present

Year Factor, 12% Amount Value
Net cash flows 1–5 3.60478 $43,900 $158,250
Initial investment (170,000)
Net Present Value $ (11,750)

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.35B (Continued)

Project Yellow: Discount Present

Year Factor, 12% Amount Value
Net cash flows 1–5 3.60478 $51,000 $183,844
Initial investment (190,000)
Net Present Value $ (6,156)

(c) Annual rate of return = average net income ÷ average investment

Project Brown = $9,000 ÷ [($140,000 + $0) ÷ 2] = 12.86%

Project Red = $9,900 ÷ [($170,000 + $0) ÷ 2] = 11.65%

Project Yellow = $13,000 ÷ [($190,000 + $0) ÷ 2] = 13.68%

(d) Net Annual

Project Cash Payback Present Value Rate of Return

Brown 3.78 (2) $(6,623) (2) 12.68% (2)

Red 3.87 (3) (11,750) (3) 11.65% (3)
Yellow 3.73 (1) (6,156) (1) 13.68% (1)

Project Red is the worst project, as it ranks third using all three
methods. Project Yellow appears to be the best as it takes number one
ranking in all three of the methods. However, if using net present value
alone, the results indicate that none of the projects should be
undertaken as they all show a negative net present value.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.36B

(a) Initial investment amount would be the cash price of the new
equipment less salvage value of old equipment plus increase in
working capital: $200,000 – $75,000 + $25,000 = $150,000

(b) Cash payback period for investment of $150,000:

Year Net Annual Cash Flow Cumulative Net

Cash Flow
0 ($150,000) $(150,000)
1–6 $126,000 ($21,000 × 6) (24,000)
7 $38,800 14,800

In year 7, $24,000 or 62% of the net annual cash flow ($38,800) would
be needed to payback the full initial investment, so we determine that
the cash payback period is 6.62 years.

(c) 10%
Cash Present
× Discount =
Flows Value
Year Factor
Salvage of old equipment 0 75,000 — $75,000
Cash inflows years 1 to 6 1–6 $21,000 4.35526 91,460
(1)
Cash inflows years 7 to 10 7–10 38,800 1.78931 69,425
Recover working capital 10 25,000 0.38554 9,639
Salvage value of new equipment 10 50,000 0.38554 19,277
Total cash inflows 264,801
Less: Capital investment 0 200,000 — (200,000)
Increased working capital 0 25,000 — (25,000)
Net present value $39,801
(1)
Factor at 10 years, 6.14457 less factor at 6 years, 4.35526

(d) Even though the cash payback period of 6.62 years is more than their
maximum payback period of five years, the net present value
calculation is more accurate as it takes into account the time value of
money. Therefore, Biotec should make the purchase.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.37B

(a) Cash payback period = ($80,000 – $30,000) ÷ ($40,000

– $25,000)
= 3.33 years.

(b) Incremental annual net income (loss) = ($40,000 – $25,000) –

[($80,000 – $10,000) ÷ 4 yrs] = ($2,500) (i.e., net loss)
Annual rate of return = ($2,500) ÷ [($80,000 + $10,000) ÷ 2] = (5.56)%

16%
(c) Discount Present
Year Factor Amount Value
Incremental annual net
cash flows 1–4 2.79818 $15,000 $41,973
Salvage of new equipment 4 0.55229 10,000 5,523
Current salvage value 0 30,000
Total cash inflows 77,496
Less: Initial investment 80,000
Net Present Value $(2,504)

(d) The calculations show that the new equipment is not a good
investment. The annual rate of return is negative and the net present
value is negative. A minor negative factor is that the cash payback
period is 83% or (3.33 ÷ 4) of the useful life of the equipment.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.38B

Net present value of the investment:

Savings per unit: 10% of variable costs = 0.10 × $0.40 = $0.04/unit

Savings per year: 850,000 units × $0.04 = $34,000

Discount Present
Year Factor at 12% Amount Value
Savings 1–5 3.60478 $34,000 $122,563
Salvage (new) 5 0.56743 50,000 28,372
Salvage (old) 0 — 30,000 30,000
Present value of cash inflows 180,935
Initial investment (400,000)
$(219,065)

The present value of the cash inflows is significantly smaller than the
investment; clearly they should not replace the old machine with the
new one. It might also be a good idea to check the company’s
estimates, as some of their numbers may be incorrect, leading to this
result.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.39B

Investment in new equipment $2,500,000

Disposal of old equipment (260,000)
Additional training required 85,000
Net initial investment required $2,325,000

Calculation of net present value:

Discount Present
Year Factor, 9% Amount Value
Cash flows 1 0.91743 $390,000 $357,798
2 0.84168 400,000 336,672
3 0.77218 411,000 317,366
4 0.70843 426,000 301,791
5 0.64993 434,000 282,070
6 0.59627 435,000 259,377
7 0.54703 436,000 238,505
Maintenance 5 0.64993 (95,000) (61,743 )
Net cash flows from operations: 2,031,836
Terminal salvage 7 0.54703 380,000 207,871
Present value of cash inflows 2,239,707
Initial investment (2,325,000)
Net Present Value $ (85,293 )

Based on the net present value calculation alone, the sewing machine
should not be purchased. However, the internal rate of return would be
only slightly lower than the 9% minimum required, so the company may
want to look at some of the non-quantitative factors involved.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.40B

(a) The net present value based on the original estimates is as follows:

Discount Present
Year Factor, 10% Amount Value
Annual cash inflow 1–10 6.14457 $12,000 $73,735
Overhaul 5 0.62092 (7,000) (4,346)
Salvage value 10 0.38554 15,000 5,783
Present value of cash flows 75,172
Initial investment (77,000)
Net Present Value $ (1,828)

Based on these estimates, the garbage truck should not be purchased.

(b) The net present value based on the revised estimates is as follows:

Discount Present
Year Factor,10% Amount Value
Annual cash inflow 1–10 6.14457 $12,000 $73,735
Overhaul 5 0.62092 (7,000) (4,346)
Additional benefits 1–10 6.14457 2,000 12,289
Salvage value 10 0.38554 15,000 5,783
Present value of cash flows 87,461
Initial investment (77,000)
Net Present Value $10,461

Based on the revised figures, the garbage truck has a positive net
present value and therefore should be purchased.
(c) In order for the project to be acceptable, the present value of the
intangible benefits would only have to be $1,828. That is the amount by
which the original estimate fell short of having a positive net present
value.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.41B

(a) Using the original estimates, the net present value is calculated as
follows:

Discount Present
Year Factor 12% Amount Value
Annual cash inflow 1–20 7.46944 $130,000 1 $971,027
Salvage value 20 0.10367 700,000 72,569
Present value of cash flows 1,043,596
Initial investment ($200,000 + $350,000) (550,000 )
Net Present Value $493,596

1
Net annual cash flows = $700,000 – $570,000

The positive net present value of the project suggests that it should be
accepted.

(b) Using the revised estimates, the net present value is calculated as
follows:

Discount Present
Year Factor 12% Amount Value
Annual cash inflow 1–20 7.46944 $62,000 1 $463,105
Salvage value 20 0.10367 700,000 72,569
Present value of cash flows 535,674
Initial investment ($200,000 + $350,000) (550,000)
Net Present Value $(14,326)

1
Net annual cash flows = $570,000 – $508,000

Under these revised estimates, the project should be rejected. It

appears that many of the camp’s costs are fixed; thus, when the
number of players declines, cash inflows decline, but cash outflows
don’t decline proportionately.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.41B (Continued)

(c) Using the original estimates, but increasing the discount rate, the net
present value is calculated as follows:

Discount Present
Year Factor 15% Amount Value
Annual cash inflow 1–20 6.25933 $130,000 1 $813,713
Salvage value 20 0.06110 700,000 42,770
Present value of cash flows 856,483
Initial investment ($200,000 + $350,000) (550,000)
Net Present Value $306,483

1
Net annual cash flows = $700,000 – $570,000

The positive net present value of the project suggests that it should be
accepted; however, it is not nearly as profitable using a 15% discount
rate.

(d) The internal rate of return can be determined by calculating the

discount rate that will bring the net present value to zero. By looking at
the values determined in (a) and (c) above, we estimate the rate might
be 15%. Calculate the net present value with a discount rate of 15%.

Discount Present
Year Factor 15% Amount Value
Annual cash inflow 1–5 3.35216 $65,000 $217,890
Salvage value 5 0.49719 668,000 332,123
Present value of cash flows 550,013
Initial investment ($200,000 + $350,000) (550,000)
Net Present Value $ 13

The project had a high internal rate of return, even though the
business itself was not generating much in cash inflows, because the
property significantly increased in value during the five years.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.42B

(a) OPTION A

(1) Discount Present

Year Factor 9% Amount Value
Annual cash inflow 1–8 5.53482 $20,000 $110,696
Cost to rebuild 5 0.64993 (26,500) (17,223)
Salvage value 8 0.50187 — —
Present value of cash flows 93,473
Initial investment (90,000)
Net Present Value $ 3,473

Net annual cash flows = $180,000 – $160,000 = $20,000

(2) Profitability index = $93,743 ÷ $90,000 = 1.04

(3) Because the net present value of the investment at a discount

rate of 9% is positive, we know the internal rate of return will be greater
than 9%, let’s say 10%.

Discount Present
Year Factor 10% Amount Value
Annual cash inflow 1–8 5.33493 $20,000 $106,699
Cost to rebuild 5 0.62092 (26,500) (16,454)
Salvage value 8 0.46651 — —
Present value of cash flows 90,245
Initial investment (90,000)
Net Present Value $ 245

Net annual cash flows = $180,000 – $160,000 = $20,000

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PROBLEM 13.42B (Continued)

OPTION B

(1) Discount Present

Year Factor 9% Amount Value
Annual cash inflow 1–8 5.53482 $32,000 $177,114
Cost to rebuild 5 0.64993 — —
Salvage value 8 0.50187 27,500 13,801
Present value of cash flows 190,915
Initial investment (170,000)
Net Present Value $120,915

Net annual cash flows = $140,000 – $108,000 = $32,000

(2) Profitability index = $190,915 ÷ $170,000 = 1.12

(3) Internal rate of return on Option B is 12%, as calculated below:

Discount Present
Year Factor 12% Amount Value
Annual cash inflow 1–8 4.96764 $32,000 $158,964
Cost to rebuild 5 0.56743 — —
Salvage value 8 0.40388 27,500 11,107
Present value of cash flows 170,071
Initial investment (170,000)
Net Present Value $ 71

(b) Option B has the higher net present value, the higher profitability
index, and it has a higher internal rate of return. Therefore, Option B is
the preferred project.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

PROBLEM 13.43B

(a) Year Amount Balance

Initial investment 0 $(250,000) $(250,000)
Less: Cash Flow 1 90,000 (160,000)
2 75,000 (85,000)
3 60,000 (25,000)
4 40,000 15,000
Payback period = 3 + ($25,000 ÷ $40,000) = 3.625 years

(b) Average annual net income = ($25,000 + $27,000 + $29,000 + $31,000 +

$33,000) ÷ 5 = $29,000
Average investment = ($250,000 + $0) ÷ 2 = $125,000
Annual rate of return = $29,000 ÷ $125,000 = 23.2%

(c) Discount Present

Year Factor, 15% Amount Value
Net cash flows 1 0.86957 $90,000 $78,261
2 0.75614 75,000 56,711
3 0.65752 60,000 39,451
4 0.57175 40,000 22,870
5 0.49719 30,000 14,916
Present value of cash inflows 212,209
Initial investment (250,000)
Net Present Value $(37,791)

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PROBLEM 13.44B

(a) OPTION A

(1) Discount Present

Year Factor 11% Amount Value
Annual cash inflow 1–6 4.23054 $32,000 $135,377
Cost to rebuild 3 0.73119 (53,000) (38,753)
Salvage value 6 0.53464 — —
Present value of cash flows 96,624
Initial investment (100,000)
Net Present Value $ (3,376)

Net annual cash flows = $56,000 – $24,000 = $32,000

(2) Profitability index = $96,624 ÷ $100,000 = 0.97

(3) Because the net present value of the investment at a discount

rate of 11% is negative, we know the internal rate of return will be less
than 11%, let’s say 10%.

Discount Present
Year Factor 10% Amount Value
Annual cash inflow 1–6 4.35526 $32,000 $139,368
Cost to rebuild 3 0.75132 (53,000) (39,820)
Salvage value 6 0.56447 — —
Present value of cash flows 99,548
Initial investment (100,000)
Net Present Value $ (452)

Net annual cash flows = $56,000 – $24,000 = $32,000

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PROBLEM 13.44B (Continued)

OPTION B

(1) Discount Present

Year Factor 11% Amount Value
Annual cash inflow 1–6 4.23054 $36,000 $152,299
Cost to rebuild 3 0.73119 — —
Salvage value 6 0.53464 24,000 12,831
Present value of cash flows 165,130
Initial investment (160,000)
Net Present Value $115,130

Net annual cash flows = $60,000 – $24,000 = $36,000

(2) Profitability index = $165,130 ÷ $160,000 = 1.03

(3) Because the net present value of the investment at a discount

rate of 11% is positive, we know the internal rate of return will be more
than 11%, let’s say 12%.

Discount Present
Year Factor 12% Amount Value
Annual cash inflow 1–6 4.11141 $36,000 $148,011
Cost to rebuild 3 0.73119 — —
Salvage value 6 0.50663 24,000 12,159
Present value of cash flows 160,170
Initial investment (160,000)
Net Present Value $ 170

Net annual cash flows = $60,000 – $24,000 = $36,000

(b) Option A has a lower net present value than Option B, and also a lower
profitability index and internal rate of return. Therefore, Option B is the
preferred project. Option A is unacceptable due to its negative NPV.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

SOLUTIONS TO CASES

CASE 13.45

(a)Annual net cash inflow: Old New

Sales (10,000; 12,000) × $100 $1,000,000 $1,200,000

Cost of goods sold (71.5%; 70%) 715,000 840,000
Gross profit 285,000 360,000
Less:
Selling expenses 160,000 176,000
Administrative expenses 100,000 112,000
260,000 288,000

Net annual cash flow $25,000 72,000

Depreciation 32,500
Annual net operating income $ 39,500

Annual rate of return: $39,500 ÷ [($130,000 + $0) ÷ 2] = 60.8%

(b) Cash payback period = $130,000 ÷ $72,000 = 1.806 years

(c) Incremental cash flow = $72,000 – $25,000 = $47,000

Discount Present
Year Factor, 15% Amount Value
Net cash flows 1–4 2.85498 $47,000 $134,184
Initial investment (130,000)
Net Present Value $114,184

(d) The new machine should be purchased. Every measurement shows an

excellent return.

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CASE 13.46

TAXI Alternative

The City would receive 3% from these incremental revenues:

From current drivers—1,750 taxis × 19,200 trips × 20% from the suburbs ×
10 km average trip × $0.10 per km = $6,720,000

From new drivers in the suburbs—85 taxis × 19,200 trips × 20% × $7.10 1 per
trip = $2,317,440

From new drivers at airport/city centre—85 taxis × 19,200 trips × 80% ×

$6.102 per trip = $7,964,160
1
Regular trip, $6.10 + incentive, ($0.10 × 10 km) = $7.10
2
Flat rate, $1.10 + ($0.50 × 10 km) = $6.10

Total incremental revenue:

Current $ 6,720,000
New—Suburbs 2,317,440
New—Airport/Centre 7,964,160
$17,001,600
City receives 3% $510,048

Total annual saving = $510,048 – $350,000 loss in public transit = $160,048

One-time revenue from sale of licences = 85 × $1,750 = $148,750

Net Present value of the Taxi Option:

Discount Present
Year Factor, 13% Amount Value
Annual revenue 1–5 3.51723 $ 160,048 $ 562,926
Sale of licences 1 1.000 148,750 148,750
Net Present Value $ 711,676

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

CASE 13.46 (Continued)

PUBLIC TRANSIT Option

Total incremental revenue:

Ticket sales ($1.00 × 1,500,000 rides) $1,500,000
Additional salaries ($30,000 × 5) (150,000)
Maintenance (36,000)
$1,314,000

Calculation of net present value:

Discount Present
Year Factor, 13% Amount Value
Annual cash flow 1–5 3.51723 $1,314,000 $4,621,640
Salvage value 5 0.54276 100,000 54,276
NPV of cash inflows 4,675,916
Less: Initial investment (1,400,000)
Net present value $3,275,916

It is clear from this net present value analysis that the City should go with
the public transit option. But with such a large discrepancy, further
investigation should be conducted to make sure the estimates are
reasonable.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

CASE 13.47

Additional annual cash flow:

Years 1 2 3 4 5
Gate receipts $330,000 $300,000 $200,000 $100,000 $40,000
Handling expenses (33,000) (30,000) (20,000) (10,000) (4,000)
McCain’s salary 15,000 15,000 15,000 15,000 15,000
Luc's salary (60,000) (70,000) (80,000) (80,000) (72,000)
Incremental cash $252,000 $215,000 $115,000 $25,000 $(21,000)

Calculation of net present value:

Discount Present
Year Amount Factor, 10% Value
Net annual cash flow 1 $ 252,000 0.90909 $ 229,091
2 215,000 0.82645 177,687
3 115,000 0.75132 86,402
4 25,000 0.68301 17,075
5 (21,000) 0.62092 (13,039)
Residual value of Luc 5 20,000 0.62092 12,418
Payment for Luc 0 (500,000) 1.00000 (500,000)
Net present value of Luc's services $9,634

The hockey club should acquire the services of Luc because the net
present value is positive.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

CASE 13.48

(a) Payback period:

Project A: $200,000 ÷ $50,000 = 4 years

Project B: Cumulative Net

Year Amount Cash Flow
Initial investment 0 $(190,000) $ (190,000)
Cash inflows 1 40,000 (150,000)
2 50,000 (100,000)
3 70,000 (30,000)
4 75,000 45,000

3 + ($30,000 ÷ $75,000) = 3.4 years

Project C: Cumulative Net

Year Amount Cash Flow
Initial investment 0 $(250,000) $ (250,000)
Cash inflows 1 75,000 (175,000)
2 75,000 (100,000)
3 60,000 (40,000)
4 80,000 40,000

3 + ($40,000 ÷ $80,000) = 3.5 years

Project D: 3.0 years

Cumulative Net
Year Amount Cash Flow
Initial investment 0 $(210,000) $ (210,000)
Cash inflows 1 75,000 (135,000)
2 75,000 (60,000)
3 60,000 —

CASE 13.48 (Continued)

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(b) Net Present Value

Project A:
Discount Present
Year Amount Factor, 12% Value
Net Cash Flow 1–5 $ 50,000 3.60478 $180,239
Initial investment 0 (200,000) 1.00000 (200,000)
Net present value of the project $(19,761)

Project B:

Discount Present
Year Amount Factor, 12% Value
Net cash flow 1 $ 40,000 0.89286 $ 35,714
2 50,000 0.79719 39,860
3 70,000 0.71178 49,825
4 75,000 0.63552 47,664
5 75,000 0.56743 42,557
Initial investment 0 (190,000) 1.00000 (190,000)
Net present value of the project $ 25,620

Project C:

Discount Present
Year Amount Factor, 12% Value
Net cash flow 1 $75,000 0.89286 $66,965
2 75,000 0.79719 59,789
3 60,000 0.71178 42,707
4 80,000 0.63552 50,842
5 100,000 0.56743 56,743
Initial investment 0 (250,000) 1.00000 (250,000)
Net present value of the project $27,046

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

CASE 14.48 (Continued)

Project D:

Discount Present
Year Amount Factor, 12% Value
Net cash flow 1 $ 75,000 0.89286 $66,965
2 75,000 0.79719 59,789
3 60,000 0.71178 42,707
4 40,000 0.63552 25,421
5 20,000 0.56743 11,349
Initial investment 0 (210,000) 1.00000 (210,000)
Net present value of the project $(3,769)

(c) Using net present value analysis, Project C should be funded.

Although it has one of the longest payback periods, there are
substantial cash inflows after the payback period. This is one of the
weaknesses of using payback period alone in making capital
investment decisions. As well, before making any type of funding
decision, qualitative factors should be considered.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

CASE 13.49

Net present value for keeping the old machine:

Discount Present
Year Amount Factor, 10% Value
Variable cost 1–6 $(800,000) 4.35526 $(3,484,208)
Fixed cost 1–6 (60,000) 4.35526 (261,316)
Salvage value 6 20,000 0.56447 11,289
Initial investment —
Net present value of the project $(3,734,235)

Net present value for buying the new machine:

Discount Present
Year Amount Factor, 10% Value
Variable cost 1–6 $(450,000) 4.35526 $(1,959,867)
Fixed cost 1–6 (50,000) 4.35526 (217,763)
Initial investment 0 (520,000) 1.00000 (520,000)
Current disposal 0 80,000 1.00000 80,000
Salvage value 6 20,000 0.56447 11,289
Net present value of the project $(2,606,341)

The decision should be to purchase the new machine because the net
present value of the relevant costs is lower than with the old machine.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

CASE 13.50

(a) Using the original estimates, the present value is calculated as follows:

Discount Present
Year Amount Factor, 8% Value
Net cash flow 1–15 $450,000 8.55948 $3,851,766
Salvage 15 1,000,000 0.31524 315,240
PV of cash inflows 4,167,006
Initial investment (6,000,000)
Net present value of the project $(1,832,994)

The negative net present value of the project suggests that it should
be rejected.

(b) Using the revised estimates, the net present value is calculated as
follows:

Discount Present
Year Amount Factor, 8% Value
Net cash flow 1–15 $450,000 8.55948 $3,851,766
Salvage 15 1,000,000 0.31524 315,240
Additional inflows 1–15 350,000 8.55948 2,995,818
PV of cash
inflows 7,162,824
Initial investment (6,000,000)
Net present value of the project $1,162,824

Taking into consideration the additional benefits suggested, the decision

would be reversed and the project should be accepted because it shows a
significantly positive net present value.

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CASE 13.50 (Continued)

(c) Discount Present

Year Amount Factor, 6% Value
Net cash flow 1–15 $450,000 9.71225 $4,370,513
Salvage 15 1,000,000 0.41727 417,270
PV of cash inflows 4,787,783
Initial investment (6,000,000)
Net present value of the project $(1,212,217)

Lowering the discount rate is not sufficient to bring the project to a

positive net present value. The company’s CFO should check to make
certain the estimates are reasonable and should take a serious look at
the suggestions Mahmoud has made in terms of intangible benefits.

(d) As noted above, the only situation in which the project should be
accepted would be with confirmation that some of the intangible
benefits are reasonable and attainable. At a minimum, this analysis
suggests that further investigation is warranted.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

CASE 13.51

(a) The stakeholders are:

 Yourself.
 Your spouse and children.
 Employees of Impro Company.
 Citizens of the town where the company is presently located.
 The shareholders of Impro Company.

(b) The ethical issue is:

 An employee’s personal interests and those of his co-workers and

the town versus the best interests of the company and its
shareholders.

(c) The student should recognize a conflict of interest. The company

should hire an outside consultant to study and evaluate such a move
rather than place one of its employees in this dilemma.

You should rise above the conflict of interest and perform an objective
economic evaluation, but also be prepared to remind management,
should they be so oblivious, of the consequences to the employees and
the town. Knowingly preparing a biased or false report is unethical.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

SOLUTION TO “ALL ABOUT YOU” ACTIVITY

CASE 13.52

The costs per month of each property:

These numbers are based on MLS listings for Vancouver Yaletown and Burnaby Metrotown in
June 2011.

Downtown condo Suburban condo

Mortgage payments $2,566 $1,555
(note 1)
Condo fees 237 360
Property taxes 186 147
Transit pass (note 2) 110
TOTAL $2,989 $2,172

Notes:
1. Mortgage payment calculations assume that the $100,000 has been used as a
down payment. Payments are for a 20-year mortgage at 3.89% (the ING five-year fixed
rate on 17 June 2011) with bi-weekly payments (restated on a monthly basis).
Mortgage rates are calculated using the Mortgage Calculator on the ING Canada
website.

2. You can walk to work from the downtown condo, so you won’t need a transit
pass to get to work. For the suburban condo, only one transit pass is included. Your
partner’s travel costs are excluded from this solution.

Financially, you would save $817 per month by choosing the suburban
condo. But you would spend at least an hour a day in travel. Living in the
downtown core you could manage without owning a car; in the suburbs a
car would likely be necessary.

However, you will have to consider what your partner wants—for example,
your partner may not want to move – even though there is work available
locally.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

SOLUTION TO DECISION-MAKING AT CURRENT DESIGNS

DM13.1

(a) Average investment = ($256,000 + 0) ÷ 2 = $128,000

Annual rate of return = $15,200 ÷ $128,000 = 11.88%

(b) Net annual cash flow = $15,200 + $32,000 = $47,200

Payback period = $256,000 ÷ $47,200 = 5.42 years

(c) Time Cash 9% Discount Present

Event Period Flows Factor Value
Net annual cash flow 1-8 $ 47,200 5.53482 $ 261,244
Oven purchase 0 (256,000) 1.00000 (256,000)
Net present value $ 5,244

Accept the proposal

(d) Time Cash 15% Discount Present

Event Period Flows Factor Value
Net annual cash flow 1-8 $ 47,200 4.48732 $ 211,802
Oven purchase 0 (256,000) 1.00000 (256,000)
Net present value $ (44,198)

Do not accept the proposal

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

SOLUTION TO WATERWAYS CONTINUING PROBLEM

WCP.13

(a) (1)
NET PRESENT VALUE
Buy New Backhoes
8%
Time Cash Discount Present
Period Flow Rate Value
Equipment purchase 0 $( 200,000) 1.00000 $ (200,000)
Salvage value of old equip 0 42,000 1.00000 42,000
Net cash flow 1–8 41,000 5.74664 235,612
Salvage value 8 50,000 0.54027 27,014
Net present value     $ 104,626
       

NET PRESENT VALUE

Keep Old Backhoes
Time 8%
Perio Cash Discount Present
d Flow Rate Value
$
Overhaul cost 1 (55,000) 0.92593 $ (50,926)
Net cash flow 1–8 25,250 5.74664 145,103
Salvage value 8 — 0.54027 —
Net present value     $ 94,177
       
(2)
PAYBACK METHOD
Cost of Capital Investment / Net Annual Cash Flow =
Cash Payback Period
New Old
Cost of capital investment $200,000 $ 55,000
Net annual cash flow $ 41,000 $ 25,250
Payback time 4.88 years 2.18 years

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly
WCP.13 (Continued)
(3)
PROFITABILITY INDEX
Present Value of Net Cash Flows / Initial Investment =
Profitability Index
New Old
Present value of net cash flows $262,626 $145,103
Initial investment $158,000 $ 55,000
Profitability index 1.66 2.64
(4)
INTERNAL RATE OF RETURN
Investment Required / Net Annual Cash Flows =
Internal Rate of Return Factor
   
$158,000 = 3.8537 New machines
$41,000
 
$55,000
= 2.1782 Old machines
$25,250

Based on the discount factors determined above, the IRR

for the new machines would be about 20%, and for the old
machines would be greater than 40%.

(b) Intangible benefits include faster completion of jobs due to the

increased speed of the backhoes. The depth and width of the
trenches will be more accurate. Also, the new backhoes have
considerably more comforts for the operator than the old backhoes.

However, there would be time involved in training the operators to

use the new backhoes. There may also be some resistance from the
operators to change from the machines in which they now feel
competent in handling. Because of the increased speed, these
operators who are paid on an hourly basis may find their incomes
decreased if the increased speed does not also result in increased
jobs requiring the use of the backhoes.

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WCP.13 (Continued)

(d) The decision would be a difficult one to make. All the indicators,
except the NPV, suggest that keeping the old backhoes for another 8
years may be the best decision at this time. However, the NPVs of
both investments are very close in amount and should have the
greater influence because they consider the time value of money.

Buying new backhoes would decrease maintenance costs and the

time spent on maintenance. This may allow for additional jobs to be
added to the schedule. Depreciation would also increase, which
would lower income—and therefore income taxes—without affecting
actual cash flow. Both decisions would yield a much higher than 8%
return on the money invested. Either decision could actually be
defended.

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Managerial Accounting: Tools for Business Decision-Making, Fifth Canadian Edition Weygandt, Kimmel, Kieso, Aly

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