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Solution manual accounting 25th edition warren chapter 26

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The principal limitations of the cash payback method are its failure to consider cash flows occurring after the payback period and its failure to use present value concepts.. A one-year

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CHAPTER 26 CAPITAL INVESTMENT ANALYSIS

DISCUSSION QUESTIONS

1 The principal objections to the use of the average rate of return method are its failure to

consider the expected cash flows from the proposals and the timing of these flows

2 The principal limitations of the cash payback method are its failure to consider cash flows

occurring after the payback period and its failure to use present value concepts

3 The average rate of return is not based on cash flows, but on operating income Thus, for

example, the average rate of return will include the impact of depreciation, but the internal

rate of return will not In addition, the internal rate of return approach will use time value of money concepts, while the average rate of return does not

4 A one-year payback will not equal a 100% average rate of return because the payback period

is based on cash flows, while the average rate of return is based on income The depreciation

on the project will prevent the two methods from reconciling

5 The cash payback period ignores cash flows occurring after the payback period, which will

often include large residual values

6 The majority of the cash flows of a new motion picture are earned within two years of

release Thus, the time value of money aspect of the cash flows is less significant for motion pictures than for projects with time-extended cash flows This would favor the use of a cash payback period for evaluating the cash flows of the project

7 The $7,900 net present value indicates that the proposal is desirable because the proposal is

expected to recover the investment and provide more than the minimum rate of return

8 The net present values indicate that both projects are desirable, but not necessarily equal in

desirability The present value index can be used to compare the two projects For example,assume one project required an investment of $10,000 and the other an investment of

$100,000 The present value indexes would be calculated as 0.9 and 0.09, respectively, for

the two projects That is, a $9,000 net present value on a $10,000 investment would be more desirable than the same net present value on a $100,000 investment

9 The computations for the net present value method are more complex than those for the

methods that ignore present value Also, the method assumes that the cash received from the proposal during its useful life will be reinvested at the rate of return used to compute the

present value of the proposal This assumption may not always be reasonable

10 The computations for the internal rate of return method are more complex than those for the

methods that ignore present value Also, the method assumes that the cash received from the proposal during its useful life will be reinvested at the internal rate of return This assumption may not always be reasonable

11 The major advantages of leasing are that it avoids the need to use funds to purchase assets

and reduces some of the risk of loss if the asset becomes obsolete There may also be some income tax advantages to leasing

12 Quicker delivery of products, higher production quality, and greater manufacturing flexibility

are examples of qualitative factors that should be considered

26-1

© 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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10% [($74,035 ÷ $17,000) = 4.355, the present value of an annuity factor for six

periods at 10%, from Exhibit 2]

PE 26–4B

15% [($362,672 ÷ $76,000) = 4.772, the present value of an annuity factor for nine

periods at 15%, from Exhibit 2]

CHAPTER 26 Capital Investment Analysis

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PE 26–5A

a Present value of $5,000 per year at 12% for 6 years*……… $20,555 Present value of $12,000 at 12% at the end of 6 years**……… 6,084 Total present value of Project A……… $26,639 Less total cost of Project A……… 22,500 Net present value of Project A……… $ 4,139

* [$15,000 × 2.589 (Exhibit 2, 20%, 4 years)]

** [$38,000 × 0.482 (Exhibit 1, 20%, 4 years)]

b Project 2 Project 1’s net present value of $2,151 is less than the net present

value of Project 2, $5,000.

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Ex 26–1

Estimated average annual income:

Testing Equipment Vehicle

(Beginning Cost + Residual Value) ÷ 2

Trang 5

Average Revenues – Annual Product Costs*

(Beginning Cost + Residual Value) ÷ 2

Operating cash flows:

Annual revenues (4,000 units × 68)……… $ 272,000 $ 272,000 $ 272,000 Selling expenses (5% × $272,000)………

Cost to manufacture

(13,600) (13,600) (13,600)

(4,000 units × $49.65)*……… (198,600 ) (198,600 ) (198,600 ) Net operating cash flows……… $ 59,800 59,800 $ $ 59,800 Total for Year 1……… $ (47,200 )

Total for Years 2–9 (operating cash flow)………… $ 59,800

* The fixed overhead relates to the depreciation on the equipment Depreciation is not a cash

flow and should not be considered in the analysis Thus, $9.00 + $36.00 + $4.65 = $49.65

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Location 1: $380,000 ÷ $76,000 = 5-year cash payback period

Location 2: 4-year cash payback period, as indicated below.

Cumulative Net Cash Net Cash

a The Liquid Soap product line is recommended, based on its shorter cash

payback period The cash payback period for both products can be determined using the following schedule:

Initial investment: $540,000

Net Cash Flow

Cumulative Net Cash Flows

Net Cash Flow

Cumulative Net Cash Flows

Liquid Soap has a four-year cash payback period, and Body Lotion has a six-

year cash payback.

b The cash payback periods are different between the two product lines because

Liquid Soap earns cash faster than does Body Lotion Even though both

products earn the same total net cash flow over the eight-year planning horizon, Liquid Soap returns cash faster in the earlier years The cash payback method

emphasizes the initial years’ net cash flows in determining the cash payback

period Thus, the project with the greatest net cash flows in the early years of

the project life will be favored over the one with less net cash flows in the initial years.

CHAPTER 26 Capital Investment Analysis

Ex 26–5

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b Yes The $7,158 net present value indicates that the return on the proposal is

greater than the minimum desired rate of return of 15%.

Ex 26–8

Revenues……… $ 58,000 $ 58,000 $ 58,000 $ 58,000 $ 58,000 Driver salary……… (42,000) (43,000) (44,000) (45,000) (46,000)

Total present value of cash flows……… $48,973

Less investment in delivery truck……… 55,000

Net present value of delivery truck……… $ (6,027 )

c The total present value of cash flows from the delivery truck investment is

less than the total purchase price of the truck That is, the net present value

is negative Thus, this analysis does not support investment in the truck.

CHAPTER 26 Capital Investment Analysis

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Ex 26–9

Annual revenues……… $47

Total expenses……… $32

Less noncash depreciation expense*……… 4

Annual cash expenses……… 28

Annual net cash flow……… $19

* Annual depreciation expense, $120 million ÷ 30 years = $4 million per year b Annual cash flows………

× Present value of an annuity of $1 at 14% for 30 periods………

Present value of hotel project cash flows, rounded………

Less hotel construction costs………

Net present value of hotel project………

* From Appendix A in the text (in millions except present value factor) $ 19 7.00266 * $ 133 120

$ 13

c The present value of the hotel’s operating cash flows exceeds the construction costs by $13 million That is, the net present value is positive Therefore,

construction of the new hotel can be supported by this analysis.

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Ex 26–10

a Cash inflow s :

Hours of operation……… 1,500 × Revenue per hour……… $ 110

Revenue per year……… $165,000 Cash outflow s :

Hours of operation……… 1,500 Fuel cost per hour……… $46

Labor cost per hour………

× Total fuel and labor costs per hour………

28

$ 74

b Annual net cash flow (at the end of each of five years)………… $ 46,000

× Present value of annuity of $1 at 10% for five periods………… 3.791 Present value of annual net cash flows……… $174,386

c Yes Briggs should accept the investment because the bulldozer cost is less

than the present value of the cash flows at the minimum desired rate of return

of 10%.

d 3.791 [(Hrs × $110) – (Hrs × $74) – $8,000] = $132,000

(Hrs × $417) – (Hrs × $281) – $30,328 = $132,000

Hrs × $136 = $162,328

Hrs = 1,194 (rounded)

Thus, the bulldozer operating hours must exceed 1,194 annually in order for

the investment to be justified.

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Ex 26–11

a Revenues (3,600 × 330 days × $340)……… $403,920,000 Less: Variable expenses (3,600 × 330 days × $140)……… (166,320,000) Fixed expenses (other than depreciation)……… (80,000,000 ) Annual net cash flow……… $157,600,000

b Present value of annual net cash flows ($157,600,000 × 5.650)……… $890,440,000 Present value of residual value ($140,000,000 × 0.322)……… 45,080,000

Less amount to be invested……… 750,000,000

Ex 26–12

a Present Value Index =

Total Present Value of Net Cash Flow

b The analysis supports investing in Blue Springs because the present value

index is greater than one The Lee’s Summit investment is not supported.

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Ex 26–13

a Annual net cash flow—Sewing Machine:

$80,640 = 1,800 hours × (290 baseballs – 150 baseballs) × $0.32 per baseball Annual net cash flow—Packing Machine:

$29,400 = 1,400 hours × $21 labor cost saved per hour

Sewing Machin e :

Annual net cash flow (at the end of each of 8 years)……… $ 80,640

× Present value of an annuity of $1 at 15% for 8 years (Exhibit 2)………… 4.487 Present value of annual net cash flows……… $361,832 Less amount to be invested……… 260,000

Packing Machin e :

Annual net cash flow (at the end of each of 8 years)……… $ 29,400

× Present value of an annuity of $1 at 15% for 8 years (Exhibit 2)………… 4.487 Present value of annual net cash flows……… $131,918 Less amount to be invested……… 85,000 Net present value……… 46,918 $

b Present Value Index =

Total Present Value of Net Cash Flow

Amount to Be Invested

Present value index

of the sewing machine: =

Present value index

of the packing machine: =

c The present value index indicates that the packing machine would be the

preferred investment, assuming that all other qualitative considerations are

equal Note that the net present value of the sewing machine is greater than

the packing machine’s However, the sewing machine requires over triple the

investment than the packing machine ($260,000 vs $85,000), for barely

double the extra net present value ($101,832 vs $46,918) Thus, the present

value index indicates the packing machine is favored If there were sufficient

capital for both investments, then they would both be attractive opportunities

This solution does not consider the alternative use of remaining cash, which is

an additional complexity beyond the scope of this text.

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* Present value of an annuity of $1 at 10% for 10 periods from Exhibit 2.

Ex 26–15

a Payback period: $1,400,000 $350,000 = 4 years

b Net present value:

Present value factor for an annuity of $1, 10 periods at 10%: 6.145

Net present value = (6.145 × $350,000) – $1,400,000 = $750,750

c Some critical elements that are missing from this analysis are:

● The manager is viewing the acquisition of automated assembly equipment as

a labor-saving device This is probably a limited way to view the investment

Instead, the equipment should allow the company to assemble the product

with higher quality and higher flexibility This should translate into greater

sales volume, better pricing, and lower inventories All of these could be

brought into the analysis.

● The cost of the automated assembly equipment does not stop with the initial purchase price and installation costs The equipment will require the company

to hire engineers and support personnel to keep the machines running, to

program the software, and to debug new programs The operators will require new training Thus, extensive training costs will likely be incurred It would not

be surprising to see a large portion of the direct labor savings lost by hiring

expensive indirect labor support for the technology.

● There will likely be a start-up or learning curve with this new technology that

will cause the benefits to be delayed.

● The analysis fails to account for taxes.

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Ex 26–16

a Present Value Factor for an

Annuity of $1 for 6 Periods =

=

Amount to Be Invested Annual Net Cash Flow

$82,220

$20,000

b 12%

= 4.111 Row 6 in Exhibit 2 The column associated with the factor 4.111 is 12%.

Ex 26–17

a Present Value Factor for an

Annuity of $1 for 10 Periods =

=

Amount to Be Invested Annual Net Cash Flow

$415 million

$99 million

= 4.192 4.192 is the present value of an annuity factor for 10 years at 20% from Exhibit 2; thus, the internal rate of return on the cash flows for 10 years is 20%.

b There are many uncertainties that could adversely impact a project of this scale and scope There are uncertainties affecting the initial investment and the annual cash flow assumptions Regarding the initial investment, the

construction cost could be higher than $415 million, due to delays, labor

issues, and other construction site problems The annual cash flow

assumptions could be adversely impacted by uncertainties such as:

1 warm weather conditions, or no snow.

2 recessionary economic conditions that reduce the demand for ski holidays.

3 competitor property improvements that siphon demand from the project.

4 increased fuel costs that increase the cost of travel to ski resorts, thus reducing demand from non-local patrons.

5 industry overbuilding that causes a price war to maintain volume.

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Ex 26–18

a Delivery Truck

Cash received from additional delivery (95,000 bags × $0.45)……… $42,750 Cash used for operating expenses (24,000 miles × $1.35)……… 32,400 Net cash flow for delivery truck……… $10,350

Present Value Factor for an Annuity

of $1 for 7 Periods =

=

Amount to Be Invested Annual Net Cash Flow

$43,056

$10,350

= 4.160 Internal Rate of Return = 15% (from text Exhibit 2 for 7 periods)

Bagging Machine

Direct labor savings (3 hrs./day × $18/hr × 250 days/yr.)……… $13,500

Present Value Factor for an Annuity

of $1 for 7 Periods =

=

Amount to Be Invested Annual Net Cash Flow

$61,614

$13,500

= 4.564 Internal Rate of Return = 12% (from text Exhibit 2 for 7 periods)

b To: Management

Re: Investment Recommendation

An internal rate of return analysis was performed for the delivery truck and

bagging machine investments The internal rate of return for the bagging

machine is 12%, while the delivery truck is 15% (detailed analysis available).

The bagging machine fails to exceed our minimum rate of return requirement of 13% In addition, there do not appear to be any qualitative considerations that

would favor the bagging machine Therefore, the recommendation is to invest in the delivery truck.

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Ex 26–19

a Present value of annual net cash flows ($35,000 × 4.968*)……… $173,880 Less amount to be invested……… 186,725 Net present value……… (12,845 $ )

* Present value of an annuity of $1 at 12% for 8 periods from text Exhibit 2.

b The rate of return is less than 12% because there is a negative net present

With an expected useful life of five years, the cash payback period cannot be

greater than five years This would indicate that the cost of the initial investment

would not be recovered during the useful life of the asset In addition, there would

be no positive average rate of return because a net loss would result If the 20%

average rate of return and useful life are correct, the cash payback period must

be less than five years Alternatively, if both the 20% average rate of return and 5.5

years for the cash payback period are correct, the machinery must have a useful life much more than five years.

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Ex 26–21

Processing Mill

Present Value Net Cash Present Value of

260,000 260,000

196,560 171,080

4 (residual value) 0.572 280,000 160,160 Total………

Less amount to be invested………

Net present value………

The net present value of both proposals is positive; thus, both pieces of equipment are acceptable However, the net present value of the processing mill exceeds that

of the electric shovel Thus, the processing mill should be preferred if there is

enough investment money for only one of the projects.

Note to Instructors: Since the investment amount is the same, the net present value

can be compared to determine preference That is, the present value index will show the same preference ordering.

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Ex 26–22

a Blending Equipment

Equal annual cash flows for Years 1–5……… $19,000

× Present value of a $1 annuity at 10% for five periods……… 3.791

Present value of operating cash flows……… $ 72,029 Residual value at end of fifth year……… $15,000

× Present value of $1 at 10% for five periods……… 0.621

Present value of of residual value……… 9,315

Less amount to be invested……… 75,000 Net present value……… $ 6,344 Computer System

Equal annual cash flows for Years 1–5……… $27,000

× Present value of a $1 annuity at 10% for five periods……… 3.791

b Present value index of blending equipment:

Present value index of computer system:

Both the net present value calculations in part (a) and the present value index

calculations in part (b) suggest that the computer system should be selected

between the two options if there is sufficient capital for only one project

investment.

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Prob 26–1A

1 a Average annual rate of return for both projects:

$35,000 ÷ 5 ($80,000 + $0) ÷ 2

… Less amount to be invested……… 80,000 80,000

2 The report to the capital investment committee can take many forms The

report should, as a minimum, present the following points:

a Both projects offer the same average annual rate of return.

b Although both projects exceed the selected rate established for discounted

cash flows, the greenhouse offers a larger net present value The greenhouse

has a larger net present value because larger cash flows occur earlier in time

compared to the front end loader Thus, if only one of the two projects can be

accepted, the greenhouse would be the more attractive.

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Prob 26–2A

1 a Cash payback period for both projects: 2 years (the year in which

accumulated net cash flows equal $750,000), shown as follows:

b Net present value analysis:

Present Value of Net Cash Flow

2 The report can take many forms and should include, as a minimum, the

following points:

a Both projects offer the same total net cash flow.

b Both projects offer the same cash payback period.

c Because of the timing of the receipt of the net cash flows, the plant

expansion offers a higher net present value.

d Both projects provide a positive net present value This means both

projects would be acceptable, since they exceed the minimum rate of

return.

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Prob 26–3A

Present Value Net Cash Present Value of

3 0.579 4,000,000 2,316,000

Less amount to be invested……… 7,000,000

Route Expansion Present Value Net Cash Present Value of

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Prob 26–3A (Concluded)

2 Present Value Index = Total Present Value of Net Cash Flow Amount to Be Invested

1, indicating that it does not meet the minimum rate of return standard.)

Present value index of $9,257,000 new maintenance yard: $7,000,000 Present value index of $18,629,000 route expansion: $16,000,000 Present value index of $9,257,000

acquiring railcars: $10,000,000

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Prob 26–4A

1 a Wind Turbines:

Annual net cash flow (at the end of each of 4 years)……… $ 320,000

× Present value of an annuity of $1 at 6% for 4 years (Exhibit 2)……… 3.465 Present value of annual net cash flows……… $1,108,800 Less amount to be invested……… 971,840

Bio

Fuel Equipment :

Annual net cash flow (at the end of each of 4 years)……… $ 350,000

× Present value of an annuity of $1 at 6% for 4 years (Exhibit 2)……… 3.465 Present value of annual net cash flows……… $1,212,750 Less amount to be invested……… 1,109,500 Net present value……… $ 103,250

b Present Value Index = Total Present Value of Net Cash Flow

Amount to Be Invested

Present value index of

wind turbines:

Present value index of the

bio fuel equipment:

2 a Present Value Factor for an Annuity of $1 = Amount to Be Invested

Annual Net Cash Flow

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