Solution manual accounting 25th edition warren chapter 26

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.


CHAPTER 26

Capital Investment Analysis

PRACTICE EXERCISES
PE 26–1A
Estimate average annual income
Average investment
Average rate of return

$29,700 ($148,500 ÷ 5 years)
$165,000 [($300,000 + $30,000) ÷ 2]
18% ($29,700 ÷ $165,000)

PE 26–1B
Estimate average annual income
Average investment
Average rate of return

$12,000 ($36,000 ÷ 3 years)
$40,000 [($70,000 + $10,000) ÷ 2]
30% ($12,000 ÷ $40,000)

PE 26–2A
5.8 years ($787,640 ÷ $135,800)

PE 26–2B
4.5 years ($41,850 ÷ $9,300)

PE 26–3A
a.
b.

$4,181
1.11

[($12,200 × 3.605) – $39,800]
($43,981 ÷ $39,800)

PE 26–3B

a.
b.

($10,546)
0.97

[($96,200 × 3.170) – $315,500]
($304,954 ÷ $315,500)

PE 26–4A
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
[($362,672 ÷ $76,000) = 4.772, the present value of an annuity factor for nine
15%
periods at 15%, from Exhibit 2]


PE 26–5A
a.

Present value of $5,000 per year at 12% for 6 years*……………………………
Present value of $12,000 at 12% at the end of 6 years**………………………
Total present value of Project A……………………………………………………
Less total cost of Project A…………………………………………………………
Net present value of Project A………………………………………………………

$20,555
6,084
$26,639
22,500
$ 4,139

* [$5,000 × 4.111 (Exhibit 2, 12%, 6 years)]
** [$12,000 × 0.507 (Exhibit 1, 12%, 6 years)]
b.

Project A. Project A’s net present value of $4,139 is more than the net present
value of Project B, $3,500.

PE 26–5B
a.

$38,835
Present value of $15,000 per year at 20% for 4 years*…………………………
18,316
Present value of $38,000 at 20% at the end of 4 years**………………………
Total present value of Project 1……………………………………………………
$57,151
55,000
Less total cost of Project 1……………………………………………………………
Net present value of Project 1……………………………………………………… $ 2,151
* [$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.


EXERCISES
Ex. 26–1

Testing
Equipment

Vehicle

Estimated average annual income:
$18,720 ÷ 6………………………………………………………………
$15,360 ÷ 8………………………………………………………………

$3,120
$1,920

Average investment:
($104,000 + $0) ÷ 2……………………………………………………… $52,000
($32,000 + $0) ÷ 2………………………………………………………

$16,000

Average rate of return:
$3,120 ÷ $52,000…………………………………………………………
$1,920 ÷ $16,000………………………………………………………

Ex. 26–2

Average Rate
=
of Return

6%
12%

Average Annual Income
Average Investment
Average Savings* – Annual Depreciation – Additional Operating Costs

(Beginning Cost + Residual Value) ÷ 2

=

=

=

$34,000 – [($132,000 – $16,000) ÷ 10 years] – $5,380
($132,000 + $16,000) ÷ 2
$17,020
$74,000

= 23%
* The effect of the savings in wages expense is an increase in income.


Ex. 26–3
Average Rate

=
of Return

Average Annual Income
Average Investment
Average Revenues – Annual Product Costs*
(Beginning Cost + Residual Value) ÷ 2

=

($410 × 4,000 units) – ($350 × 4,000 units)

=

=

($525,000 + $75,000) ÷ 2
$240,000
$300,000

= 80%
* The depreciation of the equipment is included in the factory overhead cost per unit.

Ex. 26–4

Year 1

Years 2–9

Last Year

$ 272,000
(13,600)

$ 272,000
(13,600)

(198,600)
$ 59,800

(198,600)

Initial investment………………………………………… $(107,000)
Operating cash flows:
Annual revenues (4,000 units × 68)……………… $ 272,000
(13,600)
Selling expenses (5% × $272,000)………………
Cost to manufacture
(4,000 units × $49.65)*…………………………… (198,600)
Net operating cash flows…………………………… $ 59,800
$ (47,200)
Total for Year 1…………………………………………
Total for Years 2–9 (operating cash flow)…………
Residual value………………………………………
Total for last year…………………………………………

$ 59,800

$ 59,800
13,000

$ 72,800

* 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


CHAPTER 26

Capital Investment Analysis

Ex. 26–5
Location 1: $380,000 ÷ $76,000 = 5-year cash payback period.
Location 2: 4-year cash payback period, as indicated below.

Year
Year
Year
Year

Cumulative
Net Cash

Net Cash

Flow

Flows

1………………………………………………………………………… $120,000
90,000

2………………………………………………………………………
90,000
3…………………………………………………………………………
80,000
4………………………………………………………………………

$120,000
210,000
300,000
380,000

Ex. 26–6
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
Liquid Soap

Body Lotion

Cumulative

Year
Year
Year
Year
Year
Year

1………………………………
2………………………………
3………………………………
4………………………………
5………………………………
6………………………………

Cumulative

Net Cash

Net Cash

Net Cash

Net Cash

Flow

Flows

Flow

Flows

$170,000
150,000
120,000
100,000

$170,000
320,000
440,000
540,000

$90,000
90,000
90,000
90,000
90,000
90,000

$ 90,000
180,000
270,000
360,000
450,000
540,000

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

Ex. 26–7

Capital Investment Analysis

Present Value
of $1 at 15%

a.

Present Value of

Flow

Net Cash Flow

Year

1

0.870

$19,000

$16,530

2
3

0.756
0.658

23,000
20,000
15,000

17,388
13,160
8,580

$77,000

$55,658
48,500

4
0.572
Total…………………………………………
Less amount to be invested……………
Net present value…………………………
b.

Net Cash

$ 7,158

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
a.
Revenues…………………
Driver salary………………
Operating costs…………
Residual value……………
Annual net cash flow……

b.

Year

2014
2015
2016
2017

2014

2015

2016

2017

2018

$ 58,000
(42,000)
(3,000)

$ 58,000
(43,000)
(3,000)

$ 58,000
(44,000)
(3,000)

$ 58,000
(45,000)
(3,000)

$ 13,000

$ 12,000

$ 11,000

$ 10,000

$ 58,000
(46,000)
(3,000)
15,000
$ 24,000

Net Cash Flow

Present Value

Present Value of

[from part (a)]

of $1 at 12%

Net Cash Flow

$13,000
12,000
11,000
10,000

0.893
0.797
0.712
0.636

$11,609
9,564
7,832
6,360

2018

24,000

0.567
Total present value of cash flows…………………………………………
Less investment in delivery truck…………………………………………
Net present value of delivery truck………………………………………
c.

13,608
$48,973
55,000
$ (6,027)

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.


Ex. 26–9
a.

in millions

Annual revenues…………………………………………………………………
Total expenses…………………………………………………………………… $32
4
Less noncash depreciation expense*…………………………………………
Annual cash expenses…………………………………………………………
Annual net cash flow……………………………………………………………

$47

28
$19

* Annual depreciation expense, $120 million ÷ 30 years = $4 million per year
(in millions

except present
value factor)

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……………………………………………

$

19
7.00266 *

$

133
120

$

13

* From Appendix A in the text
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.


Ex. 26–10
a.

Cash inflows :
1,500
$ 110

Hours of operation……………………………………
× Revenue per hour……………………………………
Revenue per year………………………………………

$165,000

Cash outflows:
Hours of operation………………………………………
Fuel cost per hour…………………………………
Labor cost per hour…………………………………
× Total fuel and labor costs per hour……………
Fuel and labor costs per year…………………………
Maintenance costs per year…………………………
Annual net cash flow…………………………………
b.

1,500
$46
28
$

74

Annual net cash flow (at the end of each of five years)…………
× Present value of annuity of $1 at 10% for five periods…………
Present value of annual net cash flows……………………………
Less amount to be invested…………………………………………
Net present value………………………………………………………

(111,000)
(8,000)
$ 46,000
$ 46,000
3.791
$174,386
132,000
$ 42,386

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.


Ex. 26–11
a.

b.

Revenues (3,600 × 330 days × $340)……………………………………………
Less: Variable expenses (3,600 × 330 days × $140)…………………………
Fixed expenses (other than depreciation)………………………………………
Annual net cash flow…………………………………………………………………

$403,920,000
(166,320,000)
(80,000,000)

Present value of annual net cash flows ($157,600,000 × 5.650)……………
Present value of residual value ($140,000,000 × 0.322)………………………
Total present value…………………………………………………………………
Less amount to be invested………………………………………………………
Net present value……………………………………………………………………

$890,440,000

45,080,000

Ex. 26–12
a.

b.

Present Value Index =

Total Present Value of Net Cash Flow
Amount to Be Invested

Present value index =
of Blue Springs:

$540,750
$525,000

= 1.03

Present value index =
of Lee’s Summit:

$484,800
$505,000

= 0.96

The analysis supports investing in Blue Springs because the present value
index is greater than one. The Lee’s Summit investment is not supported.

$157,600,000

$935,520,000
750,000,000
$185,520,000


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 Machine:
Annual net cash flow (at the end of each of 8 years)…………………………
× Present value of an annuity of $1 at 15% for 8 years (Exhibit 2)…………
Present value of annual net cash flows…………………………………………
Less amount to be invested………………………………………………………
Net present value……………………………………………………………………

$ 80,640
4.487

$361,832
260,000
$101,832

Packing Machine:
Annual net cash flow (at the end of each of 8 years)…………………………
× Present value of an annuity of $1 at 15% for 8 years (Exhibit 2)…………
Present value of annual net cash flows…………………………………………
Less amount to be invested………………………………………………………
Net present value……………………………………………………………………
b.

c.

Present Value Index

=

$ 29,400
4.487
$131,918
85,000
$ 46,918

Total Present Value of Net Cash Flow
Amount to Be Invested

Present value index
=
of the sewing machine:

$361,832
$260,000

= 1.39

Present value index
=
of the packing machine:

$131,918
$85,000

= 1.55

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.


Ex. 26–14
a.

$30,000 *
($450,000 + $0) ÷ 2

Average rate of return on investment:

= 13.3%

* The annual earnings are equal to the cash flow less the annual depreciation expense,
shown as follows:
$75,000 – ($450,000 ÷ 10 years) = $30,000

$450,000
$75,000

= 6 years

b.

Cash payback period:

c.

Present value of annual net cash flows ($75,000 × 6.145*)………………………… $460,875
450,000
Less amount to be invested……………………………………………………………
Net present value………………………………………………………………………… $ 10,875
* Present value of an annuity of $1 at 10% for 10 periods from Exhibit 2.

Ex. 26–15
a.

Payback period:

b.

Net present value:

$1,400,000
$350,000

= 4 years

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.


Ex. 26–16
a.

Present Value Factor for an
=
Annuity of $1 for 6 Periods
=
=

b.

12%

$82,220
$20,000
4.111

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

Ex. 26–17
a.

Amount to Be Invested
Annual Net Cash Flow

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.


Ex. 26–18
a.

Delivery Truck
Cash received from additional delivery (95,000 bags × $0.45)………………
Cash used for operating expenses (24,000 miles × $1.35)……………………
Net cash flow for delivery truck……………………………………………………
Present Value Factor for an Annuity
=
of $1 for 7 Periods
=
=

$42,750
32,400

$10,350

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.)………………
Present Value Factor for an Annuity
=
of $1 for 7 Periods
=
=

$13,500

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:
Re:

Management
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.


Ex. 26–19
a.

Present value of annual net cash flows ($35,000 × 4.968*)……………………
Less amount to be invested………………………………………………………
Net present value……………………………………………………………………

$173,880
186,725
$ (12,845)

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

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

Amount to Be Invested
Present Value Factor
=
Annual Net Cash Flow
for an Annuity of $1
=
=

$186,725
$35,000
5.335

Internal Rate of Return = 10% (from text Exhibit 2, 8 periods)

Ex. 26–20
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.


Ex. 26–21
Processing Mill
Present Value
Year

of $1 at 15%

Net Cash

Present Value of

Flow

Net Cash Flow

$ 310,000

$269,700

1

0.870

2
3

0.756
0.658

260,000
260,000

196,560
171,080

4

0.572

260,000

148,720

280,000

160,160

$1,370,000

$946,220
750,000

4 (residual value)

0.572
Total………………………………………
Less amount to be invested……………
Net present value………………………
Electric Shovel
Year

1
2

$196,220

Present Value
of $1 at 15%

Net Cash
Flow

0.870

$ 330,000

$287,100

0.756

325,000
325,000
320,000

245,700
213,850
183,040

$1,300,000

$929,690
750,000

0.658
3

0.572
4
Total………………………………………
Less amount to be invested……………
Net present value………………………

Present Value of
Net Cash Flow

$179,690

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.


Ex. 26–22
a.

Blending Equipment
Equal annual cash flows for Years 1–5………………………………… $19,000
3.791
× Present value of a $1 annuity at 10% for five periods………………
Present value of operating cash flows……………………………………
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…………………………………………
Total present value of cash flows…………………………………………
Less amount to be invested………………………………………………
Net present value……………………………………………………………

$ 72,029

9,315
$ 81,344
75,000
$ 6,344

Computer System
Equal annual cash flows for Years 1–5…………………………………… $27,000
3.791
× Present value of a $1 annuity at 10% for five periods………………
Present value of operating cash flows…………………………………
Less amount to be invested…………………………………………………
Net present value………………………………………………………………
b.

Present value index of blending equipment:

$81,344
$75,000

= 1.08

Present value index of computer system:

$102,357
$90,000

= 1.14

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.

$102,357
90,000
$ 12,357


PROBLEMS
Prob. 26–1A
1.

a.

Average annual rate of return for both projects:
$7,000
= 17.5%
$35,000 ÷ 5
=
$40,000
($80,000 + $0) ÷ 2

b.

Net present value analysis:
Present
Value of

Year

$1 at 12%

Net Cash Flow
Greenhouse

Front End Loader

Present Value of
Net Cash Flow
Greenhouse

Front End Loader

1
0.893
$ 38,000
$ 23,000
$33,934
0.797
23,000
2
28,000
22,316

0.712
23,000
3
25,000
17,800
0.636
23,000
4
12,000
7,632
23,000
12,000
6,804
0.567
5
$115,000
Total…… ……………………… $115,000
$88,486
Less amount to be invested………………………………………… 80,000
Net present value……………………………………………………… $ 8,486
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.

$20,539
18,331
16,376
14,628
13,041
$82,915
80,000
$ 2,915


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:
Retail Store Expansion

Plant Expansion

b.

Year

Net Cash
Flow

Cumulative
Net Cash Flow

Year

Net Cash
Flow

Cumulative
Net Cash Flow

1

$390,000

$390,000

1

$375,000

$375,000

2

360,000

750,000

2

375,000

750,000

Net present value analysis:
Present

Net Cash Flow

Year

Value of
$1 at 15%

1
2

0.870
0.756

$ 390,000
360,000

$ 375,000
375,000

$339,300
272,160

$326,250
283,500

3

0.658

140,000

150,000

92,120

98,700

4

0.572

5

0.497

120,000
70,000

100,000
80,000

68,640
34,790

57,200
39,760

$1,080,000

$1,080,000

$807,010
750,000

$805,410
750,000

Total………………………………

Plant
Expansion

Retail Store
Expansion

Less amount to be invested………………………………………
Net present value………………………………………………………

2.

Present Value of
Net Cash Flow
Plant
Expansion

Retail Store
Expansion

$ 57,010 $ 55,410

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.


Prob. 26–3A
1.
Year

New Maintenance Yard
Present Value

Net Cash

Present Value of

of $1 at 20%

Flow

Net Cash Flow

1
0.833
$ 5,000,000
2
0.694
4,000,000
4,000,000
3
0.579

Total……………………………………………… $13,000,000
Less amount to be invested……………………………………………
Net present value…………………………………………………………

$4,165,000
2,776,000
2,316,000
$9,257,000
7,000,000
$2,257,000

Route Expansion

Year

Present Value
of $1 at 20%

Net Cash
Flow

$10,000,000
1
0.833
2
0.694
9,000,000
7,000,000
3
0.579

$26,000,000
Total……………………………………………
Less amount to be invested……………………………………………
Net present value…………………………………………………………

Present Value of
Net Cash Flow

$ 8,330,000
6,246,000
4,053,000
$18,629,000
16,000,000
$ 2,629,000

Acquire Railcars

Year

Present Value
of $1 at 20%

Net Cash
Flow

$ 5,000,000
1
0.833
2
0.694

4,000,000
4,000,000
3
0.579
$13,000,000
Total……………………………………………
Less amount to be invested……………………………………………
Net present value…………………………………………………………

Present Value of
Net Cash Flow

$ 4,165,000
2,776,000
2,316,000
$ 9,257,000
10,000,000
$ (743,000)


Prob. 26–3A (Concluded)
2.
Present Value Index =
Amount to Be Invested

Total Present Value of Net Cash Flow

Present value index of
new maintenance yard:

$9,257,000

Present value index of
route expansion:

$18,629,000

Present value index of
acquiring railcars:

$9,257,000

$7,000,000

$16,000,000

$10,000,000

=

1.32*

=

1.16*

=

0.93*

* Rounded
3.

The new maintenance yard has the largest present value index. Although route
expansion has the largest net present value, it returns less present value per dollar
invested than does the new maintenance yard, as revealed by the present value
indexes (1.32 compared to 1.16). (The present value index for the railcars is less than
1, indicating that it does not meet the minimum rate of return standard.)


Prob. 26–4A
1. a.

Wind Turbines:
Annual net cash flow (at the end of each of 4 years)……………………
× Present value of an annuity of $1 at 6% for 4 years (Exhibit 2)………
Present value of annual net cash flows……………………………………
Less amount to be invested…………………………………………………
Net present value………………………………………………………………

$ 320,000
3.465
$1,108,800
971,840
$ 136,960

Bio Fuel Equipment:
Annual net cash flow (at the end of each of 4 years)……………………
× Present value of an annuity of $1 at 6% for 4 years (Exhibit 2)………
Present value of annual net cash flows……………………………………

Less amount to be invested……………………………………………………
Net present value…………………………………………………………………
b. Present Value Index

=

$ 350,000
3.465
$1,212,750
1,109,500
$ 103,250

Total Present Value of Net Cash Flow
Amount to Be Invested

Present value index of
wind turbines:

$1,108,800
= 1.14*
$971,840

Present value index of the
bio fuel equipment:
* Rounded
2. a.

$1,212,750
$1,109,500

Present Value Factor for an Annuity of $1

Wind turbines:

Bio fuel equipment:

=

= 1.09*
Amount to Be Invested
Annual Net Cash Flow

$971,840
$320,000

= 3.037

$1,109,500
$350,000

= 3.170

b. Internal rate of return (determined from Exhibit 2 for 4 years in text)
Wind turbines: 12%
Bio fuel equipment: 10%


Prob. 26–4A (Concluded)
3.

The net present value, present value index, and internal rate of return all indicate that
the wind turbines are a better financial opportunity compared to the bio fuel
equipment, although both investments meet the minimum return criterion of 6%. The
present value index indicates that the wind turbines had a greater present value
per dollar of investment. The internal rate of return method places all proposals on
a common basis. As a result, it is possible to compare proposals with different
investment amounts, cash flows, and time periods, using the internal rate of return
method. The internal rate of return method indicates that the wind turbine internal
rate of return of 12% is greater than the bio fuel equipment internal rate of return
of 10%.


Prob. 26–5A
1.

Net present value analysis:
Office Expansion:
Annual net cash flow (at the end of each of 6 years)……………………………
× Present value of an annuity of $1 at 12% for 6 years (Exhibit 2)……………
Present value of annual net cash flows……………………………………………
Less amount to be invested…………………………………………………………
Net present value………………………………………………………………………

$125,000
4.111
$513,875
490,000
$ 23,875

Server Upgrade:

Annual net cash flow (at the end of each of 4 years)……………………………
× Present value of an annuity of $1 at 12% for 4 years (Exhibit 2)……………
Present value of annual net cash flows……………………………………………
Less amount to be invested…………………………………………………………
Net present value………………………………………………………………………
2.

Net present value analysis:

$ 11,105

Net Cash Flow

Net Cash Flow

Value of
$1 at 12%

$501,105
490,000

Present Value of

Present

Year

$165,000
3.037

Expansion

Servers

Expansion

Servers

1
0.893
$125,000
$165,000
$111,625
0.797
2
125,000
165,000
99,625
0.712
3
125,000
165,000
89,000
0.636
4
125,000
165,000
79,500
180,000
0

114,480
(residual
value)
0.636
4
$680,000
$660,000
Total…………………………………
$494,230
Less amount to be invested………………………………………… 490,000
Net present value……………………………………………………… $ 4,230

$147,345
131,505
117,480
104,940
0
$501,270
490,000
$ 11,270 *

* This amount differs from the net present value calculation in part (1) due to
rounding errors in the present value factors.

3.

To: Investment Committee
Both projects have a positive net present value. This means that both
projects meet our minimum expected return of 12% and would be acceptable
investments. However, if funds are limited and only one of the two projects

can be funded, then the two projects must be compared over equal lives.
Thus, the residual value of the office expansion at the end of period 4 is
used to equalize the two lives. The net present value of the two projects over
equal lives indicates that the server upgrade has a higher net present value
and would be a superior investment.


Prob. 26–6A
1.

Proposal A: 3-year, 6-month cash payback period, as follows:
Year
1
2
3
6 months*

Net Cash

Cumulative

Flow

Net Cash Flows

$200,000
200,000
200,000
80,000

$200,000
400,000
600,000
680,000

* The cash flow required is $80,000 out of $160,000 in Year 4. Thus, 1/2 of 12 months
is 6 months.

Proposal B: 4-year cash payback period, as follows:
Year
1
2
3
4

Net Cash

Cumulative

Flow

Net Cash Flows

$90,000
90,000
70,000
70,000

$ 90,000
180,000

250,000
320,000

Proposal C: 2-year cash payback period, as follows:
Year

Net Cash
Flow

Cumulative
Net Cash Flows

1
2

$55,000
53,000

$ 55,000
108,000

Proposal D: 2-year, 3-month cash payback period, as follows:
Year
1
2
3 months*

Net Cash

Cumulative

Flow

Net Cash Flows

$180,000
180,000
40,000

$180,000
360,000
400,000

* The cash flow required is $40,000 out of $160,000 in Year 3. Thus, 1/4 of 12 months
is 3 months.